description stringlengths 171 4k | code stringlengths 94 3.98k | normalized_code stringlengths 57 4.99k |
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Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | n = int(input())
arr = list(map(int, input().split()))
def to_bin(n):
return bin(n).replace("0b", "")
for i in range(n):
arr[i] = to_bin(arr[i])
max_len = len(arr[0])
for i in arr:
temp_len = len(i)
if temp_len > max_len:
max_len = temp_len
for i in range(n):
arr[i] = "0" * (max_len - len(arr[i])) + arr[i]
arr.sort(reverse=True)
def max_x(i, l, r):
if i == max_len:
return ""
for j in range(l, r + 1):
if arr[j][i] == "0":
if j != l:
return min("1" + max_x(i + 1, j, r), "1" + max_x(i + 1, l, j - 1))
else:
return "0" + max_x(i + 1, j, r)
return "0" + max_x(i + 1, l, r)
ans = max_x(0, 0, n - 1)
print(int(ans, 2)) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL FUNC_CALL VAR VAR STRING STRING FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF VAR VAR ASSIGN VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR BIN_OP BIN_OP STRING BIN_OP VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR NUMBER FUNC_DEF IF VAR VAR RETURN STRING FOR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR VAR VAR STRING IF VAR VAR RETURN FUNC_CALL VAR BIN_OP STRING FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR BIN_OP STRING FUNC_CALL VAR BIN_OP VAR NUMBER VAR BIN_OP VAR NUMBER RETURN BIN_OP STRING FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR RETURN BIN_OP STRING FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR ASSIGN VAR FUNC_CALL VAR NUMBER NUMBER BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def solve(group, bit):
if bit == t - 1:
for i in range(1, len(group)):
if group[i][bit] != group[0][bit]:
return 1
return 0
g0, g1 = [], []
for i in range(len(group)):
if int(group[i][bit]):
g1.append(group[i])
else:
g0.append(group[i])
if len(g0) == 0:
x.append("1")
return solve(g1, bit + 1)
elif len(g1) == 0:
x.append("0")
return solve(g0, bit + 1)
else:
s1 = solve(g0, bit + 1)
s2 = solve(g1, bit + 1)
if s1 < s2:
x.append("1")
return 2 ** (t - bit - 1) + s1
else:
x.append("0")
return 2 ** (t - bit - 1) + s2
n = int(input())
l = list(map(int, input().split()))
l.sort()
t = len(bin(l[-1])[2:])
for i in range(n):
b = bin(l[i])[2:]
l[i] = "0" * (t - len(b)) + b
ans = []
x = []
print(solve(l, 0)) | FUNC_DEF IF VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FUNC_CALL VAR VAR IF VAR VAR VAR VAR NUMBER VAR RETURN NUMBER RETURN NUMBER ASSIGN VAR VAR LIST LIST FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR STRING RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR STRING RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR VAR EXPR FUNC_CALL VAR STRING RETURN BIN_OP BIN_OP NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR EXPR FUNC_CALL VAR STRING RETURN BIN_OP BIN_OP NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR VAR BIN_OP BIN_OP STRING BIN_OP VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST ASSIGN VAR LIST EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def get_bit(val, id):
return val >> id & 1
trie = []
def new_node():
trie.append([-1] * 2)
def add(val):
indx = 0
for i in range(30, -1, -1):
x = get_bit(val, i)
if trie[indx][x] == -1:
new_node()
trie[indx][x] = len(trie) - 1
indx = trie[indx][x]
def DFS(bit, u):
if bit < 0:
return 0
ans0 = int(2**30)
ans1 = int(2**30)
if trie[u][0] != -1:
ans0 = DFS(bit - 1, trie[u][0])
if trie[u][1] != -1:
ans1 = DFS(bit - 1, trie[u][1])
if trie[u][0] != -1 and trie[u][1] != -1:
return min(ans0, ans1) + (1 << bit)
return min(ans0, ans1)
n = int(input())
new_node()
a = list(map(int, input().split()))
for i in range(n):
add(a[i])
print(DFS(30, 0)) | FUNC_DEF RETURN BIN_OP BIN_OP VAR VAR NUMBER ASSIGN VAR LIST FUNC_DEF EXPR FUNC_CALL VAR BIN_OP LIST NUMBER NUMBER FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR VAR VAR NUMBER EXPR FUNC_CALL VAR ASSIGN VAR VAR VAR BIN_OP FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR VAR VAR FUNC_DEF IF VAR NUMBER RETURN NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER IF VAR VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR NUMBER IF VAR VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR NUMBER IF VAR VAR NUMBER NUMBER VAR VAR NUMBER NUMBER RETURN BIN_OP FUNC_CALL VAR VAR VAR BIN_OP NUMBER VAR RETURN FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR NUMBER NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | mx = 32
def f(a, pos):
if pos < 0 or len(a) == 0:
return 0
on = []
off = []
for x in a:
if x & 1 << pos:
on.append(x)
else:
off.append(x)
if len(on) == 0:
return f(off, pos - 1)
if len(off) == 0:
return f(on, pos - 1)
a.clear()
return (1 << pos) + min(f(on, pos - 1), f(off, pos - 1))
def solve(n):
li = list(map(int, input().split()))
print(f(li, mx))
while True:
try:
n = int(input())
solve(n)
except EOFError:
break | ASSIGN VAR NUMBER FUNC_DEF IF VAR NUMBER FUNC_CALL VAR VAR NUMBER RETURN NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR RETURN BIN_OP BIN_OP NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_DEF ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR WHILE NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | n = int(input())
seq = sorted(list(map(int, input().split())))
queue = [(0, n, 30, 0)]
best = 2**30
while queue:
l, r, b, v = queue.pop()
if b >= 0:
mask = 1 << b
if not mask & seq[l] and mask & seq[r - 1]:
for i in range(l, r):
if mask & seq[i]:
queue.append((l, i, b - 1, v + mask))
queue.append((i, r, b - 1, v + mask))
break
else:
queue.append((l, r, b - 1, v))
else:
best = min(best, v)
print(best) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST NUMBER VAR NUMBER NUMBER ASSIGN VAR BIN_OP NUMBER NUMBER WHILE VAR ASSIGN VAR VAR VAR VAR FUNC_CALL VAR IF VAR NUMBER ASSIGN VAR BIN_OP NUMBER VAR IF BIN_OP VAR VAR VAR BIN_OP VAR VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR VAR VAR IF BIN_OP VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER BIN_OP VAR VAR EXPR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER BIN_OP VAR VAR EXPR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | import sys
def input():
return sys.stdin.readline().strip()
def list2d(a, b, c):
return [([c] * b) for i in range(a)]
def list3d(a, b, c, d):
return [[([d] * c) for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e):
return [[[([e] * d) for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1):
return int(-(-x // y))
def INT():
return int(input())
def MAP():
return map(int, input().split())
def LIST(N=None):
return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes():
print("Yes")
def No():
print("No")
def YES():
print("YES")
def NO():
print("NO")
sys.setrecursionlimit(10**9)
INF = 10**18
MOD = 10**9 + 7
N = INT()
A = LIST()
def rec(li, k):
if not li or k < 0:
return 0
li1, li2 = [], []
for a in li:
if a & 1 << k:
li1.append(a)
else:
li2.append(a)
if not li1 or not li2:
return rec(li, k - 1)
return min(rec(li1, k - 1), rec(li2, k - 1)) + (1 << k)
print(rec(A, 30)) | IMPORT FUNC_DEF RETURN FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF RETURN BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF RETURN BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF NUMBER RETURN FUNC_CALL VAR BIN_OP VAR VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF NONE RETURN VAR NONE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_DEF EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR STRING EXPR FUNC_CALL VAR BIN_OP NUMBER NUMBER ASSIGN VAR BIN_OP NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP NUMBER NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_DEF IF VAR VAR NUMBER RETURN NUMBER ASSIGN VAR VAR LIST LIST FOR VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF VAR VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP NUMBER VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def argmin(a):
if len(a[0]) == 0:
return "", 0
start_zeros = [item for item in a if item[0] == "0"]
start_ones = [item for item in a if item[0] == "1"]
if len(start_zeros) == 0:
a_ones, ans_ones = argmin([item[1:] for item in start_ones])
return "1" + a_ones, ans_ones
if len(start_ones) == 0:
a_zeros, ans_zeros = argmin([item[1:] for item in start_zeros])
return "0" + a_zeros, ans_zeros
a_zeros, ans_zeros = argmin([item[1:] for item in start_zeros])
a_ones, ans_ones = argmin([item[1:] for item in start_ones])
if ans_zeros < ans_ones:
return "1" + a_zeros, ans_zeros + int(2 ** (len(a[0]) - 1))
else:
return "0" + a_ones, ans_ones + int(2 ** (len(a[0]) - 1))
n = int(input())
a = ["{0:b}".format(item) for item in map(int, input().split())]
max_len = max([len(item) for item in a])
for i in range(n):
a[i] = "0" * (max_len - len(a[i])) + a[i]
print(argmin(a)[1]) | FUNC_DEF IF FUNC_CALL VAR VAR NUMBER NUMBER RETURN STRING NUMBER ASSIGN VAR VAR VAR VAR VAR NUMBER STRING ASSIGN VAR VAR VAR VAR VAR NUMBER STRING IF FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR NUMBER VAR VAR RETURN BIN_OP STRING VAR VAR IF FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR NUMBER VAR VAR RETURN BIN_OP STRING VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR NUMBER VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR NUMBER VAR VAR IF VAR VAR RETURN BIN_OP STRING VAR BIN_OP VAR FUNC_CALL VAR BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER RETURN BIN_OP STRING VAR BIN_OP VAR FUNC_CALL VAR BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL STRING VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR BIN_OP BIN_OP STRING BIN_OP VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def dp(bit, arr, left, right):
if bit == -1:
return 0, 0
mask = 1 << bit
piv = None
for i in range(left, right):
if arr[i] & mask:
piv = i
break
if piv is None:
ans, msk = dp(bit - 1, arr, left, right)
return ans, msk + mask
if piv == left:
ans, msk = dp(bit - 1, arr, left, right)
return ans, msk
ans_0, msk_0 = dp(bit - 1, arr, left, piv)
ans_1, msk_1 = dp(bit - 1, arr, piv, right)
if ans_0 < ans_1:
return ans_0 + mask, msk_0 + mask
else:
return ans_1 + mask, msk_1
n = int(input())
arr = list(map(int, input().split()))
arr.sort()
ans, mask = dp(30, arr, 0, n)
print(ans) | FUNC_DEF IF VAR NUMBER RETURN NUMBER NUMBER ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR NONE FOR VAR FUNC_CALL VAR VAR VAR IF BIN_OP VAR VAR VAR ASSIGN VAR VAR IF VAR NONE ASSIGN VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR VAR RETURN VAR BIN_OP VAR VAR IF VAR VAR ASSIGN VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR VAR RETURN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR VAR IF VAR VAR RETURN BIN_OP VAR VAR BIN_OP VAR VAR RETURN BIN_OP VAR VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR NUMBER VAR NUMBER VAR EXPR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | n = int(input())
a = list(map(int, input().split()))
def check(l, b):
if b == 0:
ans = int(not all(map(lambda x: x == l[0], l)))
return ans
l.sort()
u = 0
while u < len(l):
if l[u] & 1 << b:
break
u += 1
for i in range(len(l)):
l[i] &= (1 << b) - 1
if u == 0 or u == len(l):
return check(l, b - 1)
return 1 << b | min(check(l[:u], b - 1), check(l[u:], b - 1))
print(check(a, 31)) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR NUMBER VAR RETURN VAR EXPR FUNC_CALL VAR ASSIGN VAR NUMBER WHILE VAR FUNC_CALL VAR VAR IF BIN_OP VAR VAR BIN_OP NUMBER VAR VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR BIN_OP BIN_OP NUMBER VAR NUMBER IF VAR NUMBER VAR FUNC_CALL VAR VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP BIN_OP NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | DIG = 29
def build_xor_tree(a, n):
tree = [[-1, -1]]
for i in range(n):
cur = 0
for pos in range(DIG, -1, -1):
if a[i] & 1 << pos:
if tree[cur][1] == -1:
tree.append([-1, -1])
tree[cur][1] = len(tree) - 1
cur = tree[cur][1]
else:
if tree[cur][0] == -1:
tree.append([-1, -1])
tree[cur][0] = len(tree) - 1
cur = tree[cur][0]
return tree
def possible(tree, cur, x, pos):
if pos < 0:
return True
if cur == -1:
return False
if x & 1 << pos:
return possible(tree, tree[cur][0], x, pos - 1) or possible(
tree, tree[cur][1], x, pos - 1
)
if tree[cur][0] != -1 and tree[cur][1] != -1:
return False
if tree[cur][0] != -1:
return possible(tree, tree[cur][0], x, pos - 1)
return possible(tree, tree[cur][1], x, pos - 1)
n = int(input())
a = list(map(int, input().split()))
tree = build_xor_tree(a, n)
lo = 0
hi = (1 << DIG + 1) - 1
while lo < hi - 1:
mid = (lo + hi) // 2
if possible(tree, 0, mid, DIG):
hi = mid
else:
lo = mid + 1
if possible(tree, 0, lo, DIG):
print(lo)
else:
print(hi) | ASSIGN VAR NUMBER FUNC_DEF ASSIGN VAR LIST LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR NUMBER NUMBER IF BIN_OP VAR VAR BIN_OP NUMBER VAR IF VAR VAR NUMBER NUMBER EXPR FUNC_CALL VAR LIST NUMBER NUMBER ASSIGN VAR VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR VAR NUMBER IF VAR VAR NUMBER NUMBER EXPR FUNC_CALL VAR LIST NUMBER NUMBER ASSIGN VAR VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR VAR NUMBER RETURN VAR FUNC_DEF IF VAR NUMBER RETURN NUMBER IF VAR NUMBER RETURN NUMBER IF BIN_OP VAR BIN_OP NUMBER VAR RETURN FUNC_CALL VAR VAR VAR VAR NUMBER VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR VAR NUMBER VAR BIN_OP VAR NUMBER IF VAR VAR NUMBER NUMBER VAR VAR NUMBER NUMBER RETURN NUMBER IF VAR VAR NUMBER NUMBER RETURN FUNC_CALL VAR VAR VAR VAR NUMBER VAR BIN_OP VAR NUMBER RETURN FUNC_CALL VAR VAR VAR VAR NUMBER VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR BIN_OP BIN_OP NUMBER BIN_OP VAR NUMBER NUMBER WHILE VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER IF FUNC_CALL VAR VAR NUMBER VAR VAR ASSIGN VAR VAR ASSIGN VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def abc(x, i, l):
a = []
b = []
for j in l:
if x[j][i] == "1":
a.append(j)
else:
b.append(j)
if i == 30:
if a and b:
return "1"
return "0"
if a and b:
return "1" + min(abc(x, i + 1, a), abc(x, i + 1, b))
if a:
return "0" + abc(x, i + 1, a)
return "0" + abc(x, i + 1, b)
n = int(input())
l = list(map(int, input().split()))
x = []
for i in l:
d = "{0:031b}".format(i)
x.append(d)
d = abc(x, 0, [i for i in range(n)])
print(int(d, 2)) | FUNC_DEF ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR VAR IF VAR VAR VAR STRING EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER IF VAR VAR RETURN STRING RETURN STRING IF VAR VAR RETURN BIN_OP STRING FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR IF VAR RETURN BIN_OP STRING FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR RETURN BIN_OP STRING FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR VAR ASSIGN VAR FUNC_CALL STRING VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER VAR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def dfs(s, k):
if k < 0:
return 0
s1 = [i for i in s if i & ex2[k]]
s0 = [i for i in s if i & ex2[k] == 0]
if len(s1) == 0:
return dfs(s0, k - 1)
if len(s0) == 0:
return dfs(s1, k - 1)
return ex2[k] + min(dfs(s1, k - 1), dfs(s0, k - 1))
n = int(input())
s = list(map(int, input().split()))
ex2 = [(2**i) for i in range(31)]
print(dfs(s, 30)) | FUNC_DEF IF VAR NUMBER RETURN NUMBER ASSIGN VAR VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR VAR VAR BIN_OP VAR VAR VAR NUMBER IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR BIN_OP NUMBER VAR VAR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | from sys import stdin
input = stdin.readline
n = int(input())
l = list(map(int, input().split()))
cyk = [1] * 50
for i in range(1, 50):
cyk[i] = cyk[i - 1] * 2
def wyn(lista):
m = max(lista)
if m == min(lista):
return 0
le = len(bin(m))
duze = []
male = []
pyk = cyk[le - 3]
for i in lista:
if i >= cyk[le - 3]:
duze.append(i - pyk)
else:
male.append(i)
if len(male) == 0:
k = [(lista[i] - pyk) for i in range(len(lista))]
return wyn(k)
else:
return pyk + min(wyn(duze), wyn(male))
print(wyn(l)) | ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR IF VAR FUNC_CALL VAR VAR RETURN NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR LIST ASSIGN VAR LIST ASSIGN VAR VAR BIN_OP VAR NUMBER FOR VAR VAR IF VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR NUMBER ASSIGN VAR BIN_OP VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR RETURN FUNC_CALL VAR VAR RETURN BIN_OP VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | import sys
input = sys.stdin.readline
def calc(arr, b):
if not arr or b < 0:
return 0
bit1, bit0 = [], []
for x in arr:
if x >> b & 1:
bit1.append(x)
else:
bit0.append(x)
if not bit1:
return calc(bit0, b - 1)
elif not bit0:
return calc(bit1, b - 1)
else:
return min(calc(bit1, b - 1), calc(bit0, b - 1)) + 2**b
n = int(input())
a = list(map(int, input().split()))
print(calc(a, 32)) | IMPORT ASSIGN VAR VAR FUNC_DEF IF VAR VAR NUMBER RETURN NUMBER ASSIGN VAR VAR LIST LIST FOR VAR VAR IF BIN_OP BIN_OP VAR VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | n = int(input())
a = [int(x) for x in input().split(" ")]
a.sort()
b = pow(2, 30)
while b > 0 and a[n - 1] % b == a[n - 1]:
b /= 2
b = int(b)
if b == 0:
print(0)
exit(0)
def sol(nums, lo, hi, bit):
bit = int(bit)
if bit < 1:
return nums[lo] % 2, 0
if hi - lo == 0:
return nums[lo] % (bit * 2), 0
ind = lo
while ind <= hi and nums[ind] & bit != bit:
ind += 1
if ind - 1 - lo < 0:
x, maxi = sol(nums, ind, hi, bit / 2)
return x + bit, maxi
elif hi - ind < 0:
x, maxi = sol(nums, lo, ind - 1, bit / 2)
return x, maxi
else:
x_l, maxi_l = sol(nums, lo, ind - 1, bit / 2)
x_r, maxi_r = sol(nums, ind, hi, bit / 2)
if maxi_l <= maxi_r:
return x_l + bit, maxi_l + bit
else:
return x_r, maxi_r + bit
X, ans = sol(a, 0, n - 1, b)
print(ans) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR STRING EXPR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR NUMBER NUMBER WHILE VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR IF VAR NUMBER RETURN BIN_OP VAR VAR NUMBER NUMBER IF BIN_OP VAR VAR NUMBER RETURN BIN_OP VAR VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR WHILE VAR VAR BIN_OP VAR VAR VAR VAR VAR NUMBER IF BIN_OP BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP VAR VAR VAR IF BIN_OP VAR VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER RETURN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR NUMBER IF VAR VAR RETURN BIN_OP VAR VAR BIN_OP VAR VAR RETURN VAR BIN_OP VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR NUMBER BIN_OP VAR NUMBER VAR EXPR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | n = int(input())
a = list(map(int, input().split()))
bit = []
for i in range(n):
s = bin(a[i])[2:]
if len(s) < 30:
s = "0" * (30 - len(s)) + s
bit.append(s)
def ans(p, j, an):
if j == 30:
return an
if len(p) == 1:
return an + "0" * (30 - j)
d1 = []
d0 = []
for i in p:
if bit[i][j] == "1":
d1.append(i)
else:
d0.append(i)
if len(d1) == 0:
return ans(d0, j + 1, an + "0")
elif len(d0) == 0:
return ans(d1, j + 1, an + "0")
return min(ans(d1, j + 1, an + "1"), ans(d0, j + 1, an + "1"))
print(int(ans([i for i in range(n)], 0, ""), 2)) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR NUMBER IF FUNC_CALL VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP STRING BIN_OP NUMBER FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR FUNC_DEF IF VAR NUMBER RETURN VAR IF FUNC_CALL VAR VAR NUMBER RETURN BIN_OP VAR BIN_OP STRING BIN_OP NUMBER VAR ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR VAR IF VAR VAR VAR STRING EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP VAR STRING IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP VAR STRING RETURN FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP VAR STRING FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP VAR STRING EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR NUMBER STRING NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def solve(a, b=32):
if b == -1:
return 0
a1 = []
a2 = []
n = len(a)
for i in range(n):
if a[i] // 2**b % 2 == 1:
a1.append(a[i])
else:
a2.append(a[i])
if len(a1) == 0:
return solve(a2, b - 1)
elif len(a2) == 0:
return solve(a1, b - 1)
else:
return 2**b + min(solve(a1, b - 1), solve(a2, b - 1))
n = int(input())
a = list(map(int, input().split()))
print(solve(a)) | FUNC_DEF NUMBER IF VAR NUMBER RETURN NUMBER ASSIGN VAR LIST ASSIGN VAR LIST ASSIGN VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF BIN_OP BIN_OP VAR VAR BIN_OP NUMBER VAR NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP BIN_OP NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def q(s, b):
if not s or b < 0:
return 0
n, f = [], []
for i in s:
if i & 1 << b:
n += (i,)
else:
f += (i,)
if not n:
return q(f, b - 1)
if not f:
return q(n, b - 1)
return min(q(n, b - 1), q(f, b - 1)) + 2**b
input()
print(q([*map(int, input().split())], 32)) | FUNC_DEF IF VAR VAR NUMBER RETURN NUMBER ASSIGN VAR VAR LIST LIST FOR VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR VAR VAR VAR VAR IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP NUMBER VAR EXPR FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR LIST FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR NUMBER |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def func(arr, bitmask):
if bitmask == 0:
return 0
arr_off = []
arr_on = []
for num in arr:
if num & bitmask == 0:
arr_off.append(num)
else:
arr_on.append(num)
if not arr_off:
return func(arr_on, bitmask >> 1)
if not arr_on:
return func(arr_off, bitmask >> 1)
return bitmask + min(func(arr_on, bitmask >> 1), func(arr_off, bitmask >> 1))
n = int(input())
arr = map(int, input().split())
ans = func(arr, 1 << 29)
print(ans) | FUNC_DEF IF VAR NUMBER RETURN NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR VAR IF BIN_OP VAR VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR BIN_OP NUMBER NUMBER EXPR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | def answer(ans1, ans2):
if max(len(ans1), len(ans2)) == 0:
return 0
if len(ans2) > 0 and len(ans1) == 0:
ans1, ans2 = ans2, ans1
if len(ans1) > 0 and len(ans2) == 0:
g1 = []
g2 = []
flag = 1
for t in range(len(ans1[0])):
k1 = []
for j in range(len(ans1)):
k1.append(ans1[j][t])
if len(k1) != k1.count(k1[0]):
flag = 0
if t == len(ans1[0]) - 1:
flag = 2
break
for i in range(len(ans1)):
if ans1[i][t] == "0":
g1.append(ans1[i][t + 1 :])
else:
g2.append(ans1[i][t + 1 :])
break
if flag == 2:
return 1
if flag == 0:
if min(len(g1), len(g2)) == 0:
return answer(g1, g2)
else:
return pow(2, len(g1[0])) + answer(g1, g2)
else:
return 0
if len(ans1[0]) == 1:
if min(len(ans1), len(ans2)) == 0:
return 0
elif len(ans1) == ans1.count(ans1[0]):
return 0
elif len(ans2) == ans2.count(ans2[0]):
return 0
else:
return 1
g1 = []
g2 = []
for i in range(len(ans1)):
if ans1[i][0] == "1":
g1.append(ans1[i][1:])
else:
g2.append(ans1[i][1:])
x = answer(g1, g2)
if min(len(g1), len(g2)) != 0:
x += pow(2, len(g1[0]))
g1 = []
g2 = []
for i in range(len(ans2)):
if ans2[i][0] == "1":
g1.append(ans2[i][1:])
else:
g2.append(ans2[i][1:])
y = answer(g1, g2)
if min(len(g1), len(g2)) != 0:
y += pow(2, len(g1[0]))
return min(x, y)
def calcu(ans):
total = 0
ans1 = []
ans2 = []
cnt1 = 0
cnt2 = 0
for i in range(len(ans)):
if ans[i][0] == "0":
ans1.append(ans[i][1:])
cnt1 += 1
else:
ans2.append(ans[i][1:])
cnt2 += 1
if min(cnt1, cnt2) == 0:
return answer(ans1, ans2)
else:
return pow(2, len(ans[i]) - 1) + answer(ans1, ans2)
a = int(input())
z = list(map(int, input().split()))
ans = []
for i in range(len(z)):
t = bin(z[i])
t = t[2:]
t = "0" * (32 - len(t)) + t
ans.append(t)
total = 0
print(calcu(ans)) | FUNC_DEF IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER RETURN NUMBER IF FUNC_CALL VAR VAR NUMBER FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR VAR VAR IF FUNC_CALL VAR VAR NUMBER FUNC_CALL VAR VAR NUMBER ASSIGN VAR LIST ASSIGN VAR LIST ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR NUMBER IF VAR BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR VAR STRING EXPR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER IF VAR NUMBER RETURN NUMBER IF VAR NUMBER IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR VAR RETURN BIN_OP FUNC_CALL VAR NUMBER FUNC_CALL VAR VAR NUMBER FUNC_CALL VAR VAR VAR RETURN NUMBER IF FUNC_CALL VAR VAR NUMBER NUMBER IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER RETURN NUMBER IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER RETURN NUMBER IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER RETURN NUMBER RETURN NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER STRING EXPR FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR NUMBER FUNC_CALL VAR VAR NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER STRING EXPR FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR NUMBER FUNC_CALL VAR VAR NUMBER RETURN FUNC_CALL VAR VAR VAR FUNC_DEF ASSIGN VAR NUMBER ASSIGN VAR LIST ASSIGN VAR LIST ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER STRING EXPR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER IF FUNC_CALL VAR VAR VAR NUMBER RETURN FUNC_CALL VAR VAR VAR RETURN BIN_OP FUNC_CALL VAR NUMBER BIN_OP FUNC_CALL VAR VAR VAR NUMBER FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP STRING BIN_OP NUMBER FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | n = int(input())
nums = [int(x) for x in input().split(" ")]
totor = 0
for num in nums:
totor |= num
exp = 1
while totor:
exp <<= 1
totor >>= 1
exp >>= 1
def ans(s, exp):
if not exp:
return 0
ones = []
zeros = []
for e in s:
if e >= exp:
ones.append(e - exp)
else:
zeros.append(e)
if not ones:
return ans(zeros, exp >> 1)
if not zeros:
return ans(ones, exp >> 1)
return exp + min(ans(zeros, exp >> 1), ans(ones, exp >> 1))
print(ans(nums, exp)) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR STRING ASSIGN VAR NUMBER FOR VAR VAR VAR VAR ASSIGN VAR NUMBER WHILE VAR VAR NUMBER VAR NUMBER VAR NUMBER FUNC_DEF IF VAR RETURN NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR VAR IF VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR VAR EXPR FUNC_CALL VAR VAR IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise XOR operation.
As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Input-----
The first line contains integer $n$ ($1\le n \le 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$).
-----Output-----
Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
-----Examples-----
Input
3
1 2 3
Output
2
Input
2
1 5
Output
4
-----Note-----
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$. | t = int(input())
lst = [int(ele) for ele in input().split()]
maxn = max(lst)
n = len(bin(maxn)[2:])
newlst = [("0" * (n - len(bin(ele)[2:])) + bin(ele)[2:]) for ele in lst]
def catchEvil(lstrino, loc):
count0, count1 = [], []
for ele in lstrino:
if ele[n - 1 - loc] == "1":
count1.append(ele)
else:
count0.append(ele)
if len(count0) == 0:
if loc == 0:
return 0
else:
return catchEvil(lstrino, loc - 1)
elif len(count1) == 0:
if loc == 0:
return 0
else:
return catchEvil(lstrino, loc - 1)
elif loc == 0:
return 1
else:
return min(catchEvil(count1, loc - 1), catchEvil(count0, loc - 1)) + (1 << loc)
if n == 0:
print(0)
else:
print(int(catchEvil(newlst, n - 1))) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP STRING BIN_OP VAR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER FUNC_CALL VAR VAR NUMBER VAR VAR FUNC_DEF ASSIGN VAR VAR LIST LIST FOR VAR VAR IF VAR BIN_OP BIN_OP VAR NUMBER VAR STRING EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR NUMBER IF VAR NUMBER RETURN NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER IF VAR NUMBER RETURN NUMBER RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR NUMBER RETURN NUMBER RETURN BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER BIN_OP NUMBER VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | from sys import stdin, stdout
def getans(n, m, arr):
if n == 2 or m == 2:
lim = 0
if m == 2:
lim = n
mark = [((arr[i][0] + arr[i][1]) % 2) for i in range(lim)]
sol = [[(0) for i in range(lim)] for j in range(2)]
else:
lim = m
mark = [((arr[0][i] + arr[1][i]) % 2) for i in range(lim)]
sol = [[(0) for i in range(lim)] for j in range(2)]
for i in range(lim):
if i % 2 == 0:
if mark[i] == 0:
sol[1][i] = sol[1][i - 1] + 1
sol[0][i] = sol[0][i - 1]
else:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1]
elif mark[i] == 0:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1]
else:
sol[1][i] = sol[1][i - 1] + 1
sol[0][i] = sol[0][i - 1]
return min(sol[0][-1], sol[1][-1])
elif n == 3 or m == 3:
lim = 0
if m == 3:
lim = n
mark = [
[((arr[i][0] + arr[i][1]) % 2) for i in range(lim)],
[((arr[i][1] + arr[i][2]) % 2) for i in range(lim)],
]
sol = [[(0) for i in range(lim)] for j in range(4)]
else:
lim = m
mark = [
[((arr[0][i] + arr[1][i]) % 2) for i in range(lim)],
[((arr[1][i] + arr[2][i]) % 2) for i in range(lim)],
]
sol = [[(0) for i in range(lim)] for j in range(4)]
for i in range(lim):
if i % 2 == 0:
if mark[0][i] % 2 == 0:
if mark[1][i] % 2 == 0:
sol[0][i] = sol[0][i - 1]
sol[1][i] = sol[1][i - 1] + 1
sol[2][i] = sol[2][i - 1] + 1
sol[3][i] = sol[3][i - 1] + 1
else:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1] + 1
sol[2][i] = sol[2][i - 1]
sol[3][i] = sol[3][i - 1] + 1
elif mark[1][i] % 2 == 0:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1] + 1
sol[2][i] = sol[2][i - 1] + 1
sol[3][i] = sol[3][i - 1]
else:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1]
sol[2][i] = sol[2][i - 1] + 1
sol[3][i] = sol[3][i - 1] + 1
elif mark[0][i] % 2 == 0:
if mark[1][i] % 2 == 0:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1]
sol[2][i] = sol[2][i - 1] + 1
sol[3][i] = sol[3][i - 1] + 1
else:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1] + 1
sol[2][i] = sol[2][i - 1] + 1
sol[3][i] = sol[3][i - 1]
elif mark[1][i] % 2 == 0:
sol[0][i] = sol[0][i - 1] + 1
sol[1][i] = sol[1][i - 1] + 1
sol[2][i] = sol[2][i - 1]
sol[3][i] = sol[3][i - 1] + 1
else:
sol[0][i] = sol[0][i - 1]
sol[1][i] = sol[1][i - 1] + 1
sol[2][i] = sol[2][i - 1] + 1
sol[3][i] = sol[3][i - 1] + 1
return min(sol[0][-1], sol[1][-1], sol[2][-1], sol[3][-1])
def solve(n, m, arr):
if n >= 4 and m >= 4:
return -1
elif n == 1 or m == 1:
return 0
else:
return getans(n, m, arr)
n, m = map(int, stdin.readline().strip().split(" "))
arr = []
for i in range(n):
arr.append(list(map(int, list(stdin.readline().strip()))))
stdout.write(str(solve(n, m, arr)) + "\n") | FUNC_DEF IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR NUMBER ASSIGN VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF VAR VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER IF VAR VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER RETURN FUNC_CALL VAR VAR NUMBER NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR NUMBER ASSIGN VAR VAR ASSIGN VAR LIST BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR FUNC_CALL VAR VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR ASSIGN VAR LIST BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR NUMBER VAR NUMBER NUMBER IF BIN_OP VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR NUMBER VAR NUMBER NUMBER IF BIN_OP VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER IF BIN_OP VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER RETURN FUNC_CALL VAR VAR NUMBER NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER FUNC_DEF IF VAR NUMBER VAR NUMBER RETURN NUMBER IF VAR NUMBER VAR NUMBER RETURN NUMBER RETURN FUNC_CALL VAR VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL FUNC_CALL VAR STRING ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR STRING |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
def input():
return sys.stdin.readline().rstrip()
def input_split():
return [int(i) for i in input().split()]
n, m = input_split()
grid = []
for _ in range(n):
grid.append([int(i) for i in input()])
if n >= 4 and m >= 4:
ans = -1
elif n < 2 or m < 2:
ans = 0
elif n == 2 or m == 2:
if n == 2:
arr = []
for i in range(m):
arr.append((grid[0][i] + grid[1][i]) % 2)
elif m == 2:
arr = []
for i in range(n):
arr.append((grid[i][0] + grid[i][1]) % 2)
cost1 = 0
cost2 = 0
current = 0
for i in range(len(arr)):
cost1 += abs(current - arr[i])
cost2 += abs(1 - current - arr[i])
current = 1 - current
ans = min(cost1, cost2)
elif n == 3 or m == 3:
if n == 3:
arr1 = []
arr2 = []
for i in range(m):
arr1.append((grid[0][i] + grid[1][i]) % 2)
arr2.append((grid[1][i] + grid[2][i]) % 2)
else:
arr1 = []
arr2 = []
for i in range(n):
arr1.append((grid[i][0] + grid[i][1]) % 2)
arr2.append((grid[i][1] + grid[i][2]) % 2)
cost1 = 0
cost2 = 0
cost3 = 0
cost4 = 0
current = 0
for i in range(len(arr1)):
cost1 += max(abs(current - arr1[i]), abs(current - arr2[i]))
cost3 += max(abs(current - arr1[i]), abs(1 - current - arr2[i]))
cost2 += max(abs(1 - current - arr1[i]), abs(1 - current - arr2[i]))
cost4 += max(abs(1 - current - arr1[i]), abs(current - arr2[i]))
current = 1 - current
ans = min(cost1, cost2, cost3, cost4)
print(ans) | IMPORT FUNC_DEF RETURN FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR BIN_OP VAR VAR VAR VAR FUNC_CALL VAR BIN_OP BIN_OP NUMBER VAR VAR VAR ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR BIN_OP VAR VAR VAR FUNC_CALL VAR BIN_OP VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR BIN_OP VAR VAR VAR FUNC_CALL VAR BIN_OP BIN_OP NUMBER VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR BIN_OP BIN_OP NUMBER VAR VAR VAR FUNC_CALL VAR BIN_OP BIN_OP NUMBER VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR BIN_OP BIN_OP NUMBER VAR VAR VAR FUNC_CALL VAR BIN_OP VAR VAR VAR ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | def p(f):
for i in range(len(f)):
print(i, end=": ")
for j in range(len(f[i])):
print(int(f[i][j]), end=" ")
print()
def build_mask(n, m, f):
global mask
mask1 = [([0] * n) for i in range(2)]
for i in range(1 << n):
for j in range(1 << n):
for k in range(n):
mask1[0][k] = bool(i & 1 << k)
mask1[1][k] = bool(j & 1 << k)
cnt1, cnt2 = 0, 0
cnt = mask1[0][0] + mask1[0][1] + mask1[1][0] + mask1[1][1]
if n == 3:
cnt2 = mask1[0][1] + mask1[0][2] + mask1[1][1] + mask1[1][2]
if n == 3 and cnt % 2 == 1 and cnt2 % 2 == 1:
mask[i].append(j)
elif n == 2 and cnt % 2 == 1:
mask[i].append(j)
def dp(n, m, f):
global mask
dp = [0] * 2**n
dp1 = [0] * 2**n
for i in range(1 << n):
for k in range(n):
if bool(i & 1 << k) != bool(f[k][0]):
dp[i] += 1
for i in range(1, m):
for j in range(1 << n):
cnt = 0
for k in range(n):
if bool(j & 1 << k) != bool(f[k][i]):
cnt += 1
mini = 1 << 30
for k in range(len(mask[j])):
mini = min(mini, dp[int(mask[j][k])])
dp1[j] = cnt + mini
for j in range(1 << n):
dp[j] = dp1[j]
print(min(dp))
exit()
n, m = map(int, input().split())
f = [([0] * max(n, m)) for i in range(min(n, m))]
if n > m:
for i in range(n):
s = str(input())
for j in range(m):
f[j][i] = int(s[j])
n, m = m, n
else:
for i in range(n):
s = str(input())
for j in range(m):
f[i][j] = int(s[j])
if min(n, m) > 3:
print(-1)
exit()
if min(n, m) == 1:
print(0)
exit()
mask = [[] for i in range(2**n)]
build_mask(n, m, f)
dp(n, m, f)
p(mask) | FUNC_DEF FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR STRING FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR STRING EXPR FUNC_CALL VAR FUNC_DEF ASSIGN VAR BIN_OP LIST NUMBER VAR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR BIN_OP NUMBER VAR ASSIGN VAR VAR NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER IF VAR NUMBER BIN_OP VAR NUMBER NUMBER BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR IF VAR NUMBER BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FUNC_DEF ASSIGN VAR BIN_OP LIST NUMBER BIN_OP NUMBER VAR ASSIGN VAR BIN_OP LIST NUMBER BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR BIN_OP VAR BIN_OP NUMBER VAR FUNC_CALL VAR VAR VAR NUMBER VAR VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR BIN_OP VAR BIN_OP NUMBER VAR FUNC_CALL VAR VAR VAR VAR VAR NUMBER ASSIGN VAR BIN_OP NUMBER NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR VAR VAR ASSIGN VAR VAR BIN_OP VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR BIN_OP LIST NUMBER FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR ASSIGN VAR LIST VAR FUNC_CALL VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
a = [[int(j) for j in input()[:-1]] for i in range(n)]
if n >= 4 and m >= 4:
print(-1)
exit()
if n == 1 or m == 1:
print(0)
exit()
inf = 10000000000000
if n == 2 or m == 2:
bitcheck = [([0] * 4) for i in range(4)]
for j in range(4):
for k in range(4):
for i in range(1):
if (
(j >> i & 1) + (k >> i & 1) + (j >> i + 1 & 1) + (k >> i + 1 & 1)
) % 2 == 0:
bitcheck[j][k] = False
break
else:
bitcheck[j][k] = True
bitcalc = [([0] * 4) for i in range(4)]
for j in range(4):
for k in range(4):
for i in range(2):
if j >> i & 1 ^ k >> i & 1:
bitcalc[j][k] += 1
if n == 2:
n, m = m, n
b = [list(x) for x in zip(*a)]
else:
b = [i for i in a]
dp = [([inf] * 4) for i in range(n)]
for i in range(n):
if i != 0:
for j in range(4):
for k in range(4):
if bitcheck[j][k]:
dp[i][k] = min(
dp[i][k], dp[i - 1][j] + bitcalc[b[i][0] + b[i][1] * 2][k]
)
else:
for k in range(4):
dp[i][k] = bitcalc[b[i][0] + b[i][1] * 2][k]
print(min(dp[n - 1]))
exit()
if n == 3 or m == 3:
bitcheck = [([0] * 8) for i in range(8)]
for j in range(8):
for k in range(8):
for i in range(2):
if (
(j >> i & 1) + (k >> i & 1) + (j >> i + 1 & 1) + (k >> i + 1 & 1)
) % 2 == 0:
bitcheck[j][k] = False
break
else:
bitcheck[j][k] = True
bitcalc = [([0] * 8) for i in range(8)]
for j in range(8):
for k in range(8):
for i in range(3):
if j >> i & 1 ^ k >> i & 1:
bitcalc[j][k] += 1
if n == 3:
n, m = m, n
b = [list(x) for x in zip(*a)]
else:
b = [i for i in a]
dp = [([inf] * 8) for i in range(n)]
for i in range(n):
if i != 0:
for j in range(8):
for k in range(8):
if bitcheck[j][k]:
dp[i][k] = min(
dp[i][k],
dp[i - 1][j]
+ bitcalc[b[i][0] + b[i][1] * 2 + b[i][2] * 4][k],
)
else:
for k in range(8):
dp[i][k] = bitcalc[b[i][0] + b[i][1] * 2 + b[i][2] * 4][k]
print(min(dp[n - 1]))
exit() | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP BIN_OP BIN_OP BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR BIN_OP VAR NUMBER NUMBER BIN_OP BIN_OP VAR BIN_OP VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR VAR VAR NUMBER ASSIGN VAR VAR VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR VAR VAR NUMBER IF VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP LIST VAR NUMBER VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR VAR NUMBER BIN_OP VAR VAR NUMBER NUMBER VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR VAR VAR BIN_OP VAR VAR NUMBER BIN_OP VAR VAR NUMBER NUMBER VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP BIN_OP BIN_OP BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR BIN_OP VAR NUMBER NUMBER BIN_OP BIN_OP VAR BIN_OP VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR VAR VAR NUMBER ASSIGN VAR VAR VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR VAR VAR NUMBER IF VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP LIST VAR NUMBER VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR BIN_OP VAR NUMBER VAR VAR BIN_OP BIN_OP VAR VAR NUMBER BIN_OP VAR VAR NUMBER NUMBER BIN_OP VAR VAR NUMBER NUMBER VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR VAR VAR BIN_OP BIN_OP VAR VAR NUMBER BIN_OP VAR VAR NUMBER NUMBER BIN_OP VAR VAR NUMBER NUMBER VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
if n > 3:
print(-1)
elif n == 1:
print(0)
else:
l = []
for i in range(n):
temp = list(map(int, list(input())))
l.append(temp)
if n == 2:
A = l[:]
BU = [((A[0][i] + A[1][i]) % 2) for i in range(m)]
odd = 0
even = 0
for i in range(m):
if BU[i] % 2 == i % 2:
odd += 1
else:
even += 1
print(min(even, odd))
else:
newLU = []
newLD = []
ans = 0
A = l[:]
BU = [((A[0][i] + A[1][i]) % 2) for i in range(m)]
BD = [((A[1][i] + A[2][i]) % 2) for i in range(m)]
oddodd = 0
oddeven = 0
evenodd = 0
eveneven = 0
for i in range(m):
if BU[i] == i % 2 and BD[i] == i % 2:
oddodd -= 1
if BU[i] != i % 2 and BD[i] == i % 2:
evenodd -= 1
if BU[i] != i % 2 and BD[i] != i % 2:
eveneven -= 1
if BU[i] == i % 2 and BD[i] != i % 2:
oddeven -= 1
oddeven += 1
evenodd += 1
eveneven += 1
oddodd += 1
print(min([oddodd, oddeven, evenodd, eveneven])) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST ASSIGN VAR LIST ASSIGN VAR NUMBER ASSIGN VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR LIST VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
if n == 1 or m == 1:
for i in range(n):
input()
print(0)
elif n >= 4 and m >= 4:
for i in range(n):
input()
print(-1)
else:
matrix = []
for i in range(n):
row = input()
matrix.append([])
for j in range(m):
matrix[-1].append(int(row[j]))
if n == 2:
counter = 0
redmat = [([0] * m) for k in range(n - 1)]
for i in range(n - 1):
for j in range(m):
redmat[i][j] = (matrix[i][j] + matrix[i + 1][j]) % 2
if redmat[i][j] == j % 2:
counter += 1
print(min(counter, m - counter))
elif m == 2:
counter = 0
redmat = [([0] * m - 1) for k in range(n)]
for j in range(m - 1):
for i in range(n):
redmat[i][j] = (matrix[i][j] + matrix[i][j + 1]) % 2
if redmat[i][j] == i % 2:
counter += 1
print(min(counter, m - counter))
elif n == 3:
counteree = 0
counteroo = 0
countereo = 0
redmat = [([0] * m) for k in range(n - 1)]
for i in range(n - 1):
for j in range(m):
redmat[i][j] = (matrix[i][j] + matrix[i + 1][j]) % 2
for j in range(m):
if redmat[0][j] == j % 2 and redmat[1][j] == j % 2:
counteree += 1
if redmat[0][j] == (j + 1) % 2 and redmat[1][j] == (j + 1) % 2:
counteroo += 1
if redmat[0][j] == j % 2 and redmat[1][j] == (j + 1) % 2:
countereo += 1
print(
min(
m - counteree,
m - counteroo,
m - countereo,
counteree + counteroo + countereo,
)
)
elif m == 3:
counteree = 0
counteroo = 0
countereo = 0
redmat = [([0] * m - 1) for k in range(n)]
for j in range(m - 1):
for i in range(n):
redmat[i][j] = (matrix[i][j] + matrix[i][j + 1]) % 2
for i in range(n):
if redmat[i][0] == i % 2 and redmat[i][1] == i % 2:
counteree += 1
if redmat[i][0] == (i + 1) % 2 and redmat[i][1] == (i + 1) % 2:
counteroo += 1
if redmat[i][0] == i % 2 and redmat[i][1] == (i + 1) % 2:
countereo += 1
print(
min(
m - counteree,
m - counteroo,
m - countereo,
counteree + counteroo + countereo,
)
) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR EXPR FUNC_CALL VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR EXPR FUNC_CALL VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR NUMBER FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR BIN_OP BIN_OP VAR VAR VAR VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR VAR VAR BIN_OP VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR VAR IF VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR BIN_OP BIN_OP LIST NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR BIN_OP BIN_OP VAR VAR VAR VAR VAR BIN_OP VAR NUMBER NUMBER IF VAR VAR VAR BIN_OP VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR VAR IF VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR BIN_OP BIN_OP VAR VAR VAR VAR BIN_OP VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR NUMBER VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER IF VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR BIN_OP VAR VAR BIN_OP VAR VAR BIN_OP VAR VAR BIN_OP BIN_OP VAR VAR VAR IF VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR BIN_OP BIN_OP LIST NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR BIN_OP BIN_OP VAR VAR VAR VAR VAR BIN_OP VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER BIN_OP VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER IF VAR VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER IF VAR VAR NUMBER BIN_OP VAR NUMBER VAR VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR BIN_OP VAR VAR BIN_OP VAR VAR BIN_OP VAR VAR BIN_OP BIN_OP VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
A = [list(map(int, list(input()))) for i in range(n)]
def diff3(X, i, j):
if i == 1 and j == 1:
k = [0, 1, 0]
elif i == 0 and j == 1:
k = [0, 0, 1]
elif i == 1 and j == 0:
k = [0, 1, 1]
else:
k = [0, 0, 0]
dif = 0
for ii in range(3):
if X[ii] != k[ii]:
dif += 1
return min(dif, 3 - dif)
if n == 1 or m == 1:
print(0)
elif n >= 4 and m >= 4:
print(-1)
elif n == 2 or m == 2:
if m > n:
m, n = n, m
B = [([0] * m) for i in range(n)]
for i in range(n):
for j in range(m):
B[i][j] = A[j][i]
else:
B = A
ans = float("inf")
C = [(sum(B[i]) % 2) for i in range(n)]
ans0 = 0
p = 0
for i in range(n):
if C[i] != p:
ans0 += 1
p = (p + 1) % 2
ans = min(ans, ans0)
ans0 = 0
p = 1
for i in range(n):
if C[i] != p:
ans0 += 1
p = (p + 1) % 2
ans = min(ans, ans0)
print(ans)
else:
if m > n:
m, n = n, m
B = [([0] * m) for i in range(n)]
for i in range(n):
for j in range(m):
B[i][j] = A[j][i]
else:
B = A
ans = float("inf")
for i in range(2):
for j in range(2):
ans0 = 0
ii = i
jj = j
for k in range(n):
ans0 += diff3(B[k][:], ii, jj)
ii = (ii + 1) % 2
jj = (jj + 1) % 2
ans = min(ans, ans0)
print(ans) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_DEF IF VAR NUMBER VAR NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR NUMBER RETURN FUNC_CALL VAR VAR BIN_OP NUMBER VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP LIST NUMBER VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR STRING ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP LIST NUMBER VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR STRING FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR VAR ASSIGN VAR VAR FOR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR VAR VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II():
return int(sys.stdin.readline())
def MI():
return map(int, sys.stdin.readline().split())
def LI():
return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number):
return [LI() for _ in range(rows_number)]
def SI():
return sys.stdin.readline()[:-1]
inf = 10**16
h, w = MI()
aa = [SI() for _ in range(h)]
if h > 3:
print(-1)
exit()
if h == 1:
print(0)
exit()
aa = [int("".join(row), 2) for row in zip(*aa)]
def solve(to):
dp = [([inf] * (1 << h)) for _ in range(w + 1)]
for s in range(1 << h):
dp[0][s] = 0
for i, a in enumerate(aa):
for s in range(1 << h):
pre = dp[i][s]
if pre == inf:
continue
for ns in to[s]:
dp[i + 1][ns] = min(dp[i + 1][ns], pre + popcnt[a ^ ns])
return min(dp[w])
to2 = [[1, 2], [0, 3], [0, 3], [1, 2]]
to3 = [[2, 5], [3, 4], [0, 7], [1, 6], [1, 6], [0, 7], [3, 4], [2, 5]]
popcnt = [bin(i).count("1") for i in range(8)]
if h == 2:
print(solve(to2))
if h == 3:
print(solve(to3)) | IMPORT ASSIGN VAR BIN_OP FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR STRING FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_DEF RETURN FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP NUMBER NUMBER ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL STRING VAR NUMBER VAR FUNC_CALL VAR VAR FUNC_DEF ASSIGN VAR BIN_OP LIST VAR BIN_OP NUMBER VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR VAR VAR VAR IF VAR VAR FOR VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR BIN_OP VAR VAR BIN_OP VAR VAR RETURN FUNC_CALL VAR VAR VAR ASSIGN VAR LIST LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER ASSIGN VAR LIST LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER ASSIGN VAR FUNC_CALL FUNC_CALL VAR VAR STRING VAR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | def is_valid(prev_mask, curr_mask, N):
bits = prev_mask ^ curr_mask
if N == 2:
return bits != 0 and bits != 3
else:
check1 = bits != 0 and bits != 1 and bits != 4
check2 = bits != 7 and bits != 6 and bits != 3
return check1 and check2
def solve():
N, M = map(int, input().split())
A = [list(map(int, input())) for _ in range(N)]
if N >= 4 and M >= 4:
return -1
if N == 1 or M == 1:
return 0
state = [0] * M
for c in range(M):
for r in range(N):
if A[r][c] == 1:
state[c] |= 1 << N - 1 - r
popcounts = [bin(x).count("1") for x in range(1 << N)]
dp = [([N * M] * (1 << N)) for _ in range(M)]
for mask in range(1 << N):
dp[0][mask] = popcounts[state[0] ^ mask]
for i in range(1, M):
for curr_mask in range(1 << N):
dp[i][curr_mask] = (
min(
[
dp[i - 1][prev_mask]
for prev_mask in range(1 << N)
if is_valid(prev_mask, curr_mask, N)
]
)
+ popcounts[state[i] ^ curr_mask]
)
return min(dp[-1])
print(solve()) | FUNC_DEF ASSIGN VAR BIN_OP VAR VAR IF VAR NUMBER RETURN VAR NUMBER VAR NUMBER ASSIGN VAR VAR NUMBER VAR NUMBER VAR NUMBER ASSIGN VAR VAR NUMBER VAR NUMBER VAR NUMBER RETURN VAR VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR NUMBER RETURN NUMBER IF VAR NUMBER VAR NUMBER RETURN NUMBER ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR NUMBER VAR VAR BIN_OP NUMBER BIN_OP BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR VAR STRING VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR BIN_OP LIST BIN_OP VAR VAR BIN_OP NUMBER VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR VAR BIN_OP VAR NUMBER VAR FOR VAR FUNC_CALL VAR NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR VAR FUNC_CALL VAR BIN_OP NUMBER VAR FUNC_CALL VAR VAR VAR VAR VAR BIN_OP VAR VAR VAR RETURN FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
mat = []
for i in range(n):
p = list(map(int, input()))
mat.append(p)
if min(n, m) >= 4:
print(-1)
if min(n, m) == 1:
print(0)
if n == 2 or m == 2:
p1 = 0
p2 = 0
temp1 = min(n, m)
temp2 = max(n, m)
n = temp1
m = temp2
for i in range(m):
s = (mat[0][i] + mat[1][i]) % 2
if s == i % 2:
p1 += 1
elif s == (i + 1) % 2:
p2 += 1
p = max(p1, p2)
print(m - p)
if n == 3 or m == 3:
ans = [[] for i in range(max(n, m))]
temp1 = min(n, m)
temp2 = max(n, m)
n = temp1
m = temp2
for i in range(m):
x1, x2 = 0, 0
x1a = [0, 0, 0]
x2a = [1, 1, 1]
for j in range(3):
if mat[j][i] == x2a[j]:
x1 += 1
elif mat[j][i] == x1a[j]:
x2 += 1
ans[i].append(min(x1, x2))
for i in range(m):
x1, x2 = 0, 0
x1a = [0, 0, 1]
x2a = [1, 1, 0]
for j in range(3):
if mat[j][i] == x2a[j]:
x1 += 1
elif mat[j][i] == x1a[j]:
x2 += 1
ans[i].append(min(x1, x2))
for i in range(m):
x1, x2 = 0, 0
x1a = [0, 1, 1]
x2a = [1, 0, 0]
for j in range(3):
if mat[j][i] == x2a[j]:
x1 += 1
elif mat[j][i] == x1a[j]:
x2 += 1
ans[i].append(min(x1, x2))
for i in range(m):
x1, x2 = 0, 0
x1a = [1, 0, 1]
x2a = [0, 1, 0]
for j in range(3):
if mat[j][i] == x2a[j]:
x1 += 1
elif mat[j][i] == x1a[j]:
x2 += 1
ans[i].append(min(x1, x2))
s1, s2, s3, s4 = 0, 0, 0, 0
for i in range(m):
if i % 2 == 0:
s1 += ans[i][0]
s3 += ans[i][1]
s2 += ans[i][3]
s4 += ans[i][2]
else:
s1 += ans[i][3]
s3 += ans[i][2]
s2 += ans[i][0]
s4 += ans[i][1]
print(min(s1, s2, s3, s4)) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR VAR IF VAR NUMBER VAR NUMBER ASSIGN VAR LIST VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR VAR VAR NUMBER NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
if min(n, m) == 1:
print(0)
elif n >= 4:
print(-1)
elif n == 2:
lis = []
c = d = 0
for i in range(2):
s = list(input())
lis.append(s)
for i in range(m):
if (int(lis[0][i]) + int(lis[1][i]) + i) % 2:
c += 1
else:
d += 1
print(min(c, d))
else:
lis = []
c = d = 0
ans = [0, 0, 0, 0]
for i in range(3):
s = list(input())
lis.append(s)
for i in range(m):
c = (int(lis[0][i]) + int(lis[1][i])) % 2
d = (int(lis[1][i]) + int(lis[2][i])) % 2
if i % 2 == 0:
if d != 0 or c != 0:
ans[0] += 1
if d == 0 or c == 0:
ans[1] += 1
if c != 0 or d != 1:
ans[2] += 1
if c != 1 or d != 0:
ans[3] += 1
else:
if d != 0 or c != 0:
ans[1] += 1
if d == 0 or c == 0:
ans[0] += 1
if c != 1 or d != 0:
ans[2] += 1
if c != 0 or d != 1:
ans[3] += 1
print(min(ans)) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST ASSIGN VAR VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF BIN_OP BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST ASSIGN VAR VAR NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER IF BIN_OP VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | from sys import stdin, stdout
def five_O_five(n, m, a_2d):
if n > 3:
return -1
if n == 1:
return 0
MAX = 10**9
if n == 2:
preMask = [0, 0, 0, 0]
for i in range(m):
curMask = [MAX, MAX, MAX, MAX]
for j in range(4):
val = ord(a_2d[0][i]) - ord("0") + 2 * (ord(a_2d[1][i]) - ord("0"))
cnt = 0
for k in range(2):
if j >> k & 1 != val >> k & 1:
cnt += 1
for k in range(4):
bits = (j & 1) + (j >> 1 & 1) + (k & 1) + (k >> 1 & 1)
if bits % 2 == 1:
curMask[j] = min(curMask[j], preMask[k] + cnt)
preMask = curMask
return min(preMask)
else:
preMask = [0, 0, 0, 0, 0, 0, 0, 0]
for i in range(m):
curMask = [MAX, MAX, MAX, MAX, MAX, MAX, MAX, MAX]
for j in range(8):
val = (
ord(a_2d[0][i])
- ord("0")
+ 2 * (ord(a_2d[1][i]) - ord("0"))
+ 4 * (ord(a_2d[2][i]) - ord("0"))
)
cnt = 0
for k in range(3):
if j >> k & 1 != val >> k & 1:
cnt += 1
for k in range(8):
bits_up = (j & 1) + (j >> 1 & 1) + (k & 1) + (k >> 1 & 1)
bits_down = (
(j >> 1 & 1) + (j >> 2 & 1) + (k >> 1 & 1) + (k >> 2 & 1)
)
if bits_up % 2 == 1 and bits_down % 2 == 1:
curMask[j] = min(curMask[j], preMask[k] + cnt)
preMask = curMask
return min(preMask)
n, m = map(int, stdin.readline().split())
a_2d = []
for _ in range(n):
a_2d.append(stdin.readline().strip())
stdout.write(str(five_O_five(n, m, a_2d)) + "\n") | FUNC_DEF IF VAR NUMBER RETURN NUMBER IF VAR NUMBER RETURN NUMBER ASSIGN VAR BIN_OP NUMBER NUMBER IF VAR NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR LIST VAR VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR STRING BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR STRING ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP BIN_OP VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR RETURN FUNC_CALL VAR VAR ASSIGN VAR LIST NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR LIST VAR VAR VAR VAR VAR VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR STRING BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR STRING BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR STRING ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP BIN_OP VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP BIN_OP BIN_OP VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR NUMBER NUMBER BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR RETURN FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR STRING |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = [int(i) for i in input().split()]
matrix = ["" for i in range(n)]
for i in range(n):
matrix[i] = input()
if n >= 4:
print(-1)
elif n == 1:
print(0)
elif n == 2:
ps = 0
ptl = 0
for i in range(m):
if (int(matrix[0][i]) + int(matrix[1][i])) % 2 == i % 2:
ps += 1
else:
ptl += 1
print(min([ps, ptl]))
else:
ans = [[m, m], [m, m]]
for i in range(m):
up = (int(matrix[0][i]) + int(matrix[1][i])) % 2
down = (int(matrix[1][i]) + int(matrix[2][i])) % 2
if down == i % 2:
if up == i % 2:
ans[0][0] -= 1
else:
ans[0][1] -= 1
elif up == i % 2:
ans[1][0] -= 1
else:
ans[1][1] -= 1
final = min([min(ans[0]), min(ans[1])])
print(final) | ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR STRING VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR LIST VAR VAR ASSIGN VAR LIST LIST VAR VAR LIST VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER IF VAR BIN_OP VAR NUMBER IF VAR BIN_OP VAR NUMBER VAR NUMBER NUMBER NUMBER VAR NUMBER NUMBER NUMBER IF VAR BIN_OP VAR NUMBER VAR NUMBER NUMBER NUMBER VAR NUMBER NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR LIST FUNC_CALL VAR VAR NUMBER FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
A = [list(map(int, list(input().strip()))) for i in range(n)]
if n >= 4 and m >= 4:
print(-1)
sys.exit()
if n == 1 or m == 1:
print(0)
sys.exit()
if m == 2 or m == 3:
B = [([0] * n) for i in range(m)]
for i in range(m):
for j in range(n):
B[i][j] = A[j][i]
n, m = m, n
A = B
if n == 2:
DP0 = [1 << 30] * m
DP1 = [1 << 30] * m
if (A[0][0] + A[1][0]) % 2 == 0:
DP0[0] = 0
DP1[0] = 1
else:
DP0[0] = 1
DP1[0] = 0
for i in range(1, m):
if (A[0][i] + A[1][i]) % 2 == 0:
DP0[i] = DP1[i - 1]
DP1[i] = DP0[i - 1] + 1
else:
DP0[i] = DP1[i - 1] + 1
DP1[i] = DP0[i - 1]
print(min(DP0[-1], DP1[-1]))
if n == 3:
DP0 = [1 << 30] * m
DP1 = [1 << 30] * m
DP2 = [1 << 30] * m
DP3 = [1 << 30] * m
if (A[0][0] + A[1][0]) % 2 == 0 and (A[1][0] + A[2][0]) % 2 == 0:
DP0[0] = 0
DP1[0] = 1
DP2[0] = 1
DP3[0] = 1
elif (A[0][0] + A[1][0]) % 2 == 0 and (A[1][0] + A[2][0]) % 2 == 1:
DP0[0] = 1
DP1[0] = 0
DP2[0] = 1
DP3[0] = 1
elif (A[0][0] + A[1][0]) % 2 == 1 and (A[1][0] + A[2][0]) % 2 == 0:
DP0[0] = 1
DP1[0] = 1
DP2[0] = 0
DP3[0] = 1
elif (A[0][0] + A[1][0]) % 2 == 1 and (A[1][0] + A[2][0]) % 2 == 1:
DP0[0] = 1
DP1[0] = 1
DP2[0] = 1
DP3[0] = 0
for i in range(1, m):
if (A[0][i] + A[1][i]) % 2 == 0 and (A[1][i] + A[2][i]) % 2 == 0:
DP0[i] = DP3[i - 1]
DP1[i] = DP2[i - 1] + 1
DP2[i] = DP1[i - 1] + 1
DP3[i] = DP0[i - 1] + 1
elif (A[0][i] + A[1][i]) % 2 == 0 and (A[1][i] + A[2][i]) % 2 == 1:
DP0[i] = DP3[i - 1] + 1
DP1[i] = DP2[i - 1]
DP2[i] = DP1[i - 1] + 1
DP3[i] = DP0[i - 1] + 1
elif (A[0][i] + A[1][i]) % 2 == 1 and (A[1][i] + A[2][i]) % 2 == 0:
DP0[i] = DP3[i - 1] + 1
DP1[i] = DP2[i - 1] + 1
DP2[i] = DP1[i - 1]
DP3[i] = DP0[i - 1] + 1
elif (A[0][i] + A[1][i]) % 2 == 1 and (A[1][i] + A[2][i]) % 2 == 1:
DP0[i] = DP3[i - 1] + 1
DP1[i] = DP2[i - 1] + 1
DP2[i] = DP1[i - 1] + 1
DP3[i] = DP0[i - 1]
print(min(DP0[-1], DP1[-1], DP2[-1], DP3[-1])) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP LIST BIN_OP NUMBER NUMBER VAR ASSIGN VAR BIN_OP LIST BIN_OP NUMBER NUMBER VAR IF BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER VAR IF BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR VAR VAR BIN_OP VAR NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP LIST BIN_OP NUMBER NUMBER VAR ASSIGN VAR BIN_OP LIST BIN_OP NUMBER NUMBER VAR ASSIGN VAR BIN_OP LIST BIN_OP NUMBER NUMBER VAR ASSIGN VAR BIN_OP LIST BIN_OP NUMBER NUMBER VAR IF BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER IF BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER IF BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER IF BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER VAR NUMBER NUMBER NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER VAR IF BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR VAR VAR BIN_OP VAR NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER IF BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR VAR BIN_OP VAR NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER IF BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR VAR BIN_OP VAR NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER IF BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
b = []
D = dict()
for _ in range(n):
s = input().rstrip()
b.append(s)
if n > m:
c = [(["0"] * n) for i in range(m)]
for i in range(m):
for j in range(n):
c[i][j] = b[j][i]
m, n = n, m
b = c
if n >= 4:
print(-1)
elif n == 1:
print(0)
elif n == 2:
masks = ["00", "01", "10", "11"]
for mask in masks:
D[mask] = 0
c = 0
for bit in mask:
D[mask] += int(bit) ^ int(b[c][0])
c += 1
check = dict()
DIF = dict()
for mask in masks:
check[mask] = []
for prev_mask in masks:
cc, hh = 0, 0
for bit in mask:
hh += int(bit) ^ int(prev_mask[cc])
cc += 1
DIF[mask, prev_mask] = hh
a = mask[:2] + prev_mask[:2]
if a.count("1") % 2 == 1:
check[mask].append(prev_mask)
for i in range(1, m):
G = dict()
temp = b[0][i] + b[1][i]
for mask in masks:
G[mask] = float("inf")
h = DIF[mask, temp]
if h < 2:
for prev_mask in check[mask]:
G[mask] = min(G[mask], D[prev_mask] + h)
D = G
ans = float("inf")
for key in D:
ans = min(D[key], ans)
print(ans)
elif n == 3:
masks = ["000", "001", "010", "011", "100", "101", "110", "111"]
for mask in masks:
D[mask] = 0
c = 0
for bit in mask:
D[mask] += int(bit) ^ int(b[c][0])
c += 1
check = dict()
DIF = dict()
for mask in masks:
check[mask] = []
for prev_mask in masks:
cc, hh = 0, 0
for bit in mask:
hh += int(bit) ^ int(prev_mask[cc])
cc += 1
DIF[mask, prev_mask] = hh
a = mask[:2] + prev_mask[:2]
se = mask[1:] + prev_mask[1:]
if a.count("1") % 2 == 1 and se.count("1") % 2 == 1:
check[mask].append(prev_mask)
for i in range(1, m):
G = dict()
temp = b[0][i] + b[1][i] + b[2][i]
for mask in masks:
G[mask] = float("inf")
h = DIF[mask, temp]
if h < 2:
for prev_mask in check[mask]:
G[mask] = min(G[mask], D[prev_mask] + h)
D = G
ans = float("inf")
for key in D:
ans = min(D[key], ans)
print(ans) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST ASSIGN VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR VAR IF VAR VAR ASSIGN VAR BIN_OP LIST STRING VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST STRING STRING STRING STRING FOR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER ASSIGN VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FOR VAR VAR ASSIGN VAR VAR LIST FOR VAR VAR ASSIGN VAR VAR NUMBER NUMBER FOR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER IF BIN_OP FUNC_CALL VAR STRING NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR BIN_OP VAR NUMBER VAR VAR NUMBER VAR FOR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR STRING ASSIGN VAR VAR VAR VAR IF VAR NUMBER FOR VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR STRING FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR LIST STRING STRING STRING STRING STRING STRING STRING STRING FOR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER ASSIGN VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FOR VAR VAR ASSIGN VAR VAR LIST FOR VAR VAR ASSIGN VAR VAR NUMBER NUMBER FOR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER IF BIN_OP FUNC_CALL VAR STRING NUMBER NUMBER BIN_OP FUNC_CALL VAR STRING NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR FOR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR STRING ASSIGN VAR VAR VAR VAR IF VAR NUMBER FOR VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR STRING FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
l = []
for _ in range(n):
l.append(input().strip())
def witch(s):
out = 0
if s[0] != s[1]:
out += 2
if s[1] != s[2]:
out += 1
return out
if n >= 4 and m >= 4:
print(-1)
else:
if n < m:
n, m = m, n
l = ["".join([l[j][i] for j in range(m)]) for i in range(n)]
if m == 1:
print(0)
elif m == 2:
even = 0
odd = 0
first = l.pop(0)
if first == "00" or first == "11":
odd += 1
else:
even += 1
for nex in l:
if nex == "00" or nex == "11":
odd, even = even + 1, odd
else:
odd, even = even, odd + 1
print(min(even, odd))
elif m == 3:
ll = [0, 0, 0, 0]
for nex in l:
ll.reverse()
ll[witch(nex)] += 1
print(n - max(ll)) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER RETURN VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR FUNC_CALL STRING VAR VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR NUMBER IF VAR STRING VAR STRING VAR NUMBER VAR NUMBER FOR VAR VAR IF VAR STRING VAR STRING ASSIGN VAR VAR BIN_OP VAR NUMBER VAR ASSIGN VAR VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR LIST NUMBER NUMBER NUMBER NUMBER FOR VAR VAR EXPR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = list(map(int, input().split()))
if n >= 4 and m >= 4:
print(-1)
elif n <= 1 or m <= 1:
print(0)
else:
matrix = []
for _ in range(n):
matrix.append(input())
if n > 3:
matrix2 = []
for j in range(m):
row = []
for i in range(n):
row.append(matrix[i][j])
matrix2.append(row)
matrix = matrix2
temp = n
n = m
m = temp
binaries = []
changes = []
for i in range(n - 1):
binary = []
change = []
bit = 0
for j in range(m):
parity = int(matrix[i][j]) ^ int(matrix[i + 1][j])
binary.append(parity)
change.append(parity ^ bit)
bit = 1 - bit
binaries.append(binary)
changes.append(change)
if n == 2:
total = sum(changes[0])
print(min(total, m - total))
else:
total = [0] * 4
for i in range(m):
total[0] += changes[0][i] | changes[1][i]
total[1] += changes[0][i] | 1 - changes[1][i]
total[2] += 1 - changes[0][i] | changes[1][i]
total[3] += 1 - changes[0][i] | 1 - changes[1][i]
print(min(total)) | ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR IF VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR ASSIGN VAR LIST ASSIGN VAR LIST FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR LIST ASSIGN VAR LIST ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR VAR ASSIGN VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER VAR BIN_OP NUMBER VAR NUMBER VAR VAR NUMBER BIN_OP BIN_OP NUMBER VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER BIN_OP BIN_OP NUMBER VAR NUMBER VAR BIN_OP NUMBER VAR NUMBER VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = list(map(int, input().split()))
g = []
for _ in range(n):
g.append(input())
if n < m:
new_g = [[(0) for _ in range(m)] for _ in range(n)]
for i in range(n):
for j in range(m):
new_g[i][j] = int(g[i][j])
else:
new_g = [[(0) for _ in range(n)] for _ in range(m)]
for i in range(n):
for j in range(m):
new_g[j][i] = int(g[i][j])
n, m = m, n
g = new_g
def get_one_count(num):
ans = 0
while num > 0:
ans += num % 2
num //= 2
return ans
def solve(n, m, g):
if n >= 4:
return -1
if n == 1:
return 0
if n == 2:
prev_mask = {(0): [1, 2], (1): [0, 3], (2): [0, 3], (3): [1, 2]}
k = 4
else:
prev_mask = {
(0): [2, 5],
(1): [3, 4],
(2): [0, 7],
(3): [1, 6],
(4): [1, 6],
(5): [0, 7],
(6): [3, 4],
(7): [2, 5],
}
k = 8
dp = [[(0) for _ in range(k)] for _ in range(m)]
for i in range(0, m):
cur_state = g[0][i] + g[1][i] * 2
if n == 3:
cur_state += g[2][i] * 4
for kk in range(k):
prev_states = prev_mask[kk]
change_num = get_one_count(kk ^ cur_state)
if i == 0:
dp[i][kk] = change_num
continue
dp[i][kk] = (
min([dp[i - 1][prev_state] for prev_state in prev_states]) + change_num
)
return min(dp[m - 1])
print(solve(n, m, g)) | ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR IF VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR FUNC_DEF ASSIGN VAR NUMBER WHILE VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER RETURN VAR FUNC_DEF IF VAR NUMBER RETURN NUMBER IF VAR NUMBER RETURN NUMBER IF VAR NUMBER ASSIGN VAR DICT NUMBER NUMBER NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER ASSIGN VAR NUMBER ASSIGN VAR DICT NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR BIN_OP VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP VAR VAR IF VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR VAR VAR VAR RETURN FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | def f(l, a):
i, count = 0, 0
for x in l:
count += x not in a[i]
i = (i + 1) % 2
return count
def g(l, mx):
return min([f(l, mx[i]) for i in range(len(mx))])
def two():
l = [(x[0] + x[1]) for x in zip(input(), input())]
mx = [["00", "11"], ["10", "01"]], [["10", "01"], ["00", "11"]]
return g(l, mx)
def three():
l = [(x[0] + x[1] + x[2]) for x in zip(input(), input(), input())]
mx = (
[["100", "011"], ["110", "001"]],
[["110", "001"], ["100", "011"]],
[["111", "000"], ["010", "101"]],
[["010", "101"], ["000", "111"]],
)
return g(l, mx)
nm = input()
n, m = [int(x) for x in nm.split()]
if n == 1:
print(0)
exit()
if n > 3:
print(-1)
exit()
if n == 2:
print(two())
exit()
if n == 3:
print(three())
exit() | FUNC_DEF ASSIGN VAR VAR NUMBER NUMBER FOR VAR VAR VAR VAR VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER NUMBER RETURN VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_DEF ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR LIST LIST STRING STRING LIST STRING STRING LIST LIST STRING STRING LIST STRING STRING RETURN FUNC_CALL VAR VAR VAR FUNC_DEF ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR LIST LIST STRING STRING LIST STRING STRING LIST LIST STRING STRING LIST STRING STRING LIST LIST STRING STRING LIST STRING STRING LIST LIST STRING STRING LIST STRING STRING RETURN FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
if min(n, m) > 3:
print(-1)
exit()
if min(n, m) == 1:
print(0)
exit()
if n > m:
inp = []
for i in range(n):
inp.append(list(map(int, input().split())))
u = []
n, m = m, n
for i in range(n):
u.append([0] * m)
for i in range(n):
for j in range(m):
u[i][j] = inp[j][i]
else:
u = []
for i in range(n):
u.append(list(map(int, list(input()))))
if n == 2:
d = [0] * m
for j in range(m):
if u[0][j] + u[1][j] == 1:
d[j] = 1
cnt1 = 0
cnt2 = 0
for j in range(m):
if d[j] % 2 == j % 2:
cnt1 += 1
else:
cnt2 += 1
print(min(cnt1, cnt2))
else:
d1 = [0] * m
d2 = [0] * m
for j in range(m):
if u[0][j] + u[1][j] == 1:
d1[j] = 1
if u[1][j] + u[2][j] == 1:
d2[j] = 1
cnt1 = cnt2 = cnt3 = cnt4 = 0
for j in range(m):
r1 = d1[j] % 2 == j % 2
r2 = d2[j] % 2 == j % 2
if r1 and r2:
cnt2 += 1
cnt3 += 1
cnt4 += 1
elif r1:
cnt1 += 1
cnt3 += 1
cnt4 += 1
elif r2:
cnt1 += 1
cnt2 += 1
cnt4 += 1
else:
cnt1 += 1
cnt2 += 1
cnt3 += 1
print(min(cnt1, cnt2, cnt3, cnt4)) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST ASSIGN VAR VAR VAR VAR FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR IF VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER ASSIGN VAR VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP LIST NUMBER VAR ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER ASSIGN VAR VAR NUMBER IF BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER ASSIGN VAR VAR NUMBER ASSIGN VAR VAR VAR VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR BIN_OP VAR VAR NUMBER BIN_OP VAR NUMBER IF VAR VAR VAR NUMBER VAR NUMBER VAR NUMBER IF VAR VAR NUMBER VAR NUMBER VAR NUMBER IF VAR VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
mat = []
for i in range(n):
mat.append([bool(int(i)) for i in input()])
if n >= 4 and m >= 4:
print(-1)
exit(0)
if n == 1 or m == 1:
print(0)
exit(0)
if n > m:
m, n = n, m
mat = [[i[j] for i in mat] for j in range(len(mat[0]))]
if n == 2:
res = []
for i, ni in enumerate(mat[0]):
if i == 0:
continue
if mat[0][i] + mat[1][i] + mat[0][i - 1] + mat[1][i - 1] & 1:
res.append(True)
else:
res.append(False)
ans = 0
status = False
l = 0
pat1 = []
for i in res:
pat1.append(status)
l += 1
if not i:
if status:
ans += l
status = False
else:
status = True
l = 0
pat1.append(status)
if status:
ans += l + 1
print(min(ans, len(res) + 1 - ans))
elif n == 3:
res = []
for i, ni in enumerate(mat[0]):
if i == 0:
continue
if mat[0][i] + mat[1][i] + mat[0][i - 1] + mat[1][i - 1] & 1:
res.append(True)
else:
res.append(False)
ress = []
for i, ni in enumerate(mat[0]):
if i == 0:
continue
if mat[1][i] + mat[2][i] + mat[1][i - 1] + mat[2][i - 1] & 1:
ress.append(True)
else:
ress.append(False)
status = False
l = 0
pat1 = []
for i in res:
pat1.append(status)
l += 1
if not i:
if status:
status = False
else:
status = True
l = 0
pat1.append(status)
status = False
l = 0
pat2 = []
for i in ress:
pat2.append(status)
l += 1
if not i:
if status:
status = False
else:
status = True
l = 0
pat2.append(status)
ans = len(pat1)
a1 = 0
a2 = 0
a3 = 0
a4 = 0
for i in range(len(pat1)):
if pat1[i] == True and pat2[i] == True:
a1 += 1
elif pat1[i] == True and pat2[i] == False:
a2 += 1
elif pat1[i] == False and pat2[i] == True:
a3 += 1
else:
a4 += 1
ans = ans - max(a1, a2, a3, a4)
print(ans) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST FOR VAR VAR FUNC_CALL VAR VAR NUMBER IF VAR NUMBER IF BIN_OP BIN_OP BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR LIST FOR VAR VAR EXPR FUNC_CALL VAR VAR VAR NUMBER IF VAR IF VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER EXPR FUNC_CALL VAR VAR IF VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP BIN_OP FUNC_CALL VAR VAR NUMBER VAR IF VAR NUMBER ASSIGN VAR LIST FOR VAR VAR FUNC_CALL VAR VAR NUMBER IF VAR NUMBER IF BIN_OP BIN_OP BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR LIST FOR VAR VAR FUNC_CALL VAR VAR NUMBER IF VAR NUMBER IF BIN_OP BIN_OP BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR LIST FOR VAR VAR EXPR FUNC_CALL VAR VAR VAR NUMBER IF VAR IF VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR LIST FOR VAR VAR EXPR FUNC_CALL VAR VAR VAR NUMBER IF VAR IF VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
a = [list(input().rstrip()) for i in range(n)]
for i in range(n):
for j in range(m):
a[i][j] = int(a[i][j])
if n >= 4:
print(-1)
exit()
if n == 1:
print(0)
exit()
if n == 2:
a.append(a[0])
r = n * m
for tar in range(4):
tot = 0
for a0, a1, a2 in zip(*a):
if a0 ^ a1 != tar & 1 or a1 ^ a2 != tar >> 1:
tot += 1
tar ^= 3
if r > tot:
r = tot
print(r) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR VAR NUMBER ASSIGN VAR BIN_OP VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR FUNC_CALL VAR VAR IF BIN_OP VAR VAR BIN_OP VAR NUMBER BIN_OP VAR VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER IF VAR VAR ASSIGN VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
if n == 1 or m == 1:
print(0)
exit()
field = []
for _ in range(n):
field.append([int(item) for item in input().rstrip()])
if n < m:
n, m = m, n
nfield = []
for col in zip(*field):
nfield.append(list(col))
field = nfield[:]
nums = []
for line in field:
val = 0
for i, item in enumerate(line):
val += item << i
nums.append(val)
if m == 2:
ans = n * m
for i in range(2):
parity = i
diff = 0
for j, num in enumerate(nums):
if parity == 0:
diff += min(bin(num ^ 3).count("1"), bin(num ^ 0).count("1"))
else:
diff += min(bin(num ^ 1).count("1"), bin(num ^ 2).count("1"))
parity = 1 - parity
ans = min(ans, diff)
elif m == 3:
ans = n * m
for i in range(2):
parity = i
diff = 0
for j, num in enumerate(nums):
if parity == 0:
c1 = bin(num ^ 5).count("1")
c2 = bin(num ^ 2).count("1")
if c1 < c2:
diff += c1
else:
diff += c2
else:
c1 = bin(num ^ 0).count("1")
c2 = bin(num ^ 7).count("1")
if c1 < c2:
diff += c1
else:
diff += c2
parity = 1 - parity
ans = min(ans, diff)
for i in range(2):
parity = i
diff = 0
for j, num in enumerate(nums):
if parity == 0:
c1 = bin(num ^ 1).count("1")
c2 = bin(num ^ 6).count("1")
if c1 < c2:
diff += c1
else:
diff += c2
else:
c1 = bin(num ^ 4).count("1")
c2 = bin(num ^ 3).count("1")
if c1 < c2:
diff += c1
else:
diff += c2
parity = 1 - parity
ans = min(ans, diff)
else:
print(-1)
exit()
print(ans) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR VAR ASSIGN VAR LIST FOR VAR VAR ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING VAR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING IF VAR VAR VAR VAR VAR VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING IF VAR VAR VAR VAR VAR VAR ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING IF VAR VAR VAR VAR VAR VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP VAR NUMBER STRING IF VAR VAR VAR VAR VAR VAR ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | raw = input()
n, m = map(int, raw.split(" "))
mx = []
for ri in range(n):
mx += [input()]
if n >= 4:
print(-1)
if n == 1:
print(0)
if n == 2:
p = m // 2
s = "AB" * (p + 2)
s1 = s[:m]
s2 = s[1 : m + 1]
r1, r2 = 0, 0
for i in range(m):
o1 = int(mx[0][i] != mx[1][i])
letter = "AB"[o1]
if letter != s1[i]:
r1 += 1
if letter != s2[i]:
r2 += 1
print(min(r1, r2))
if n == 3:
p = m // 2
s = "AD" * (p + 2)
s1 = s[:m]
s2 = s[1 : m + 1]
s = "BC" * (p + 2)
s3 = s[:m]
s4 = s[1 : m + 1]
r1, r2, r3, r4 = 0, 0, 0, 0
for i in range(m):
o1 = int(mx[0][i] != mx[1][i])
o2 = int(mx[1][i] != mx[2][i])
letter = "ABCD"[o1 * 2 + o2]
if letter != s1[i]:
r1 += 1
if letter != s2[i]:
r2 += 1
if letter != s3[i]:
r3 += 1
if letter != s4[i]:
r4 += 1
rez = min(min(r1, r2), min(r3, r4))
print(rez) | ASSIGN VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR STRING ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR VAR LIST FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP STRING BIN_OP VAR NUMBER ASSIGN VAR VAR VAR ASSIGN VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER VAR VAR NUMBER VAR ASSIGN VAR STRING VAR IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP STRING BIN_OP VAR NUMBER ASSIGN VAR VAR VAR ASSIGN VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR BIN_OP STRING BIN_OP VAR NUMBER ASSIGN VAR VAR VAR ASSIGN VAR VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR VAR VAR VAR NUMBER NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER VAR VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER VAR VAR NUMBER VAR ASSIGN VAR STRING BIN_OP BIN_OP VAR NUMBER VAR IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
def hasOddCnt2x2(mat, i, j):
cnt = 0
for ii in range(i, i + 2):
for jj in range(j, j + 2):
cnt += mat[ii][jj]
return cnt % 2 == 1
def convertRowToBitMask(row):
b = 0
for i, x in enumerate(row):
if x == 1:
b = b | 1 << i
return b
def nMovesToChangeB1ToB2(b1, b2):
nMoves = 0
for i in range(3):
if (b1 & 1 << i > 0) != (b2 & 1 << i > 0):
nMoves += 1
return nMoves
b1Tob2 = [[(0) for _ in range(2**3)] for __ in range(2**3)]
for b1 in range(8):
for b2 in range(8):
b1Tob2[b1][b2] = nMovesToChangeB1ToB2(b1, b2)
def main():
n, m = readIntArr()
mat = [[(0) for _ in range(n)] for __ in range(m)]
for col in range(n):
s = input()
for row, x in enumerate(s):
mat[row][col] = int(x)
n, m = m, n
if n >= 4 and m >= 4:
print(-1)
else:
if n == 1 or m == 1:
print(0)
return
validMatches = [[] for _ in range(2**m)]
doubleRows = [[(0) for _ in range(m)] for __ in range(2)]
for b1 in range(2**m):
for i in range(m):
if b1 & 1 << i > 0:
doubleRows[0][i] = 1
else:
doubleRows[0][i] = 0
for b2 in range(b1, 2**m):
for i in range(m):
if b2 & 1 << i > 0:
doubleRows[1][i] = 1
else:
doubleRows[1][i] = 0
ok = True
for jj in range(m - 1):
if hasOddCnt2x2(doubleRows, 0, jj) == False:
ok = False
if ok:
validMatches[b1].append(b2)
validMatches[b2].append(b1)
dp = [[float("inf") for _ in range(2**m)] for __ in range(n)]
for row in range(n):
rowB = convertRowToBitMask(mat[row])
for mask in range(2**m):
changeMoves = b1Tob2[rowB][mask]
if row - 1 >= 0:
for prevMask in validMatches[mask]:
dp[row][mask] = min(
dp[row][mask], changeMoves + dp[row - 1][prevMask]
)
else:
dp[row][mask] = min(dp[row][mask], changeMoves)
ans = float("inf")
for mask in range(2**m):
ans = min(ans, dp[n - 1][mask])
print(ans)
return
input = lambda: sys.stdin.readline().rstrip("\r\n")
def oneLineArrayPrint(arr):
print(" ".join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
print("\n".join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
print("\n".join([" ".join([str(x) for x in y]) for y in arr]))
def readIntArr():
return [int(x) for x in input().split()]
def readIntArr2():
return [int(x) for x in input()]
main() | IMPORT FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR VAR VAR VAR RETURN BIN_OP VAR NUMBER NUMBER FUNC_DEF ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP NUMBER VAR RETURN VAR FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER BIN_OP VAR BIN_OP NUMBER VAR NUMBER VAR NUMBER RETURN VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FOR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER RETURN ASSIGN VAR LIST VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER ASSIGN VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER ASSIGN VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR EXPR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR STRING VAR FUNC_CALL VAR BIN_OP NUMBER VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER FOR VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR VAR BIN_OP VAR NUMBER VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR STRING FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER VAR EXPR FUNC_CALL VAR VAR RETURN ASSIGN VAR FUNC_CALL FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR VAR VAR FUNC_DEF RETURN FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR VAR FUNC_CALL VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
def rs():
return sys.stdin.readline().rstrip()
def ri():
return int(sys.stdin.readline())
def ria():
return list(map(int, sys.stdin.readline().split()))
def ws(s):
sys.stdout.write(s)
sys.stdout.write("\n")
def wi(n):
sys.stdout.write(str(n))
sys.stdout.write("\n")
def wia(a, sep=" "):
sys.stdout.write(sep.join([str(x) for x in a]))
sys.stdout.write("\n")
def bit_count(n):
cnt = 0
while n > 0:
cnt += 1
n = n & n - 1
return cnt
def ok(n, mask1, mask2):
for i in range(n - 1):
cnt = (
(1 if mask1 & 1 << i else 0)
+ (1 if mask2 & 1 << i else 0)
+ (1 if mask1 & 1 << i + 1 else 0)
+ (1 if mask2 & 1 << i + 1 else 0)
)
if cnt % 2 == 0:
return False
return True
def solve(n, m, a):
if n == 1:
return 0
if n >= 4:
return -1
p2 = 2**n
inf = float("inf")
b = [0] * m
for j in range(m):
mask = 0
for i in range(n):
if a[i][j] == 1:
mask |= 1 << i
b[j] = mask
dp = [([inf] * p2) for _ in range(m)]
for mask in range(p2):
dp[0][mask] = bit_count(b[0] ^ mask)
masks = [[] for _ in range(p2)]
for mask1 in range(p2):
for mask2 in range(p2):
if ok(n, mask1, mask2):
masks[mask1].append(mask2)
for i in range(1, m):
for prev_mask in range(p2):
for next_mask in masks[prev_mask]:
dp[i][next_mask] = min(
dp[i][next_mask], dp[i - 1][prev_mask] + bit_count(b[i] ^ next_mask)
)
return min(dp[-1])
def main():
n, m = ria()
a = []
for i in range(n):
a.append([int(si) for si in rs()])
wi(solve(n, m, a))
main() | IMPORT FUNC_DEF RETURN FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR STRING FUNC_DEF STRING EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR STRING FUNC_DEF ASSIGN VAR NUMBER WHILE VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP VAR NUMBER RETURN VAR FUNC_DEF FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP BIN_OP VAR BIN_OP NUMBER VAR NUMBER NUMBER BIN_OP VAR BIN_OP NUMBER VAR NUMBER NUMBER BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER NUMBER NUMBER BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER NUMBER NUMBER IF BIN_OP VAR NUMBER NUMBER RETURN NUMBER RETURN NUMBER FUNC_DEF IF VAR NUMBER RETURN NUMBER IF VAR NUMBER RETURN NUMBER ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR STRING ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR NUMBER VAR BIN_OP NUMBER VAR ASSIGN VAR VAR VAR ASSIGN VAR BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR ASSIGN VAR LIST VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR FOR VAR FUNC_CALL VAR VAR FOR VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR VAR VAR RETURN FUNC_CALL VAR VAR NUMBER FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | def gen_changes_table(threes):
table = []
for c, three in enumerate(threes):
line = []
for c2, three2 in enumerate(threes):
total = 0
for i in range(3):
if three[i] != three2[i]:
total += 1
line.append(total)
table.append(line)
return table
def main():
n, m = map(int, input().split())
if n == 1 or n > 3:
for _ in range(n):
__ = input()
if n == 1:
print(0)
else:
print(-1)
return
elif n == 2:
first, second = input(), input()
one_first = one_second = 0
for i in range(m):
line = first[i] + second[i]
num = line.count("0")
if i % 2 == num % 2:
one_first += 1
else:
one_second += 1
print(min(one_first, one_second))
else:
threes_l = ["111", "011", "101", "001", "110", "010", "100", "000"]
threes = {threes_l[x]: x for x in range(8)}
table = gen_changes_table(threes_l)
routes = [0, 0, 0, 0]
first, second, third = input(), input(), input()
for i in range(m):
line = first[i] + second[i] + third[i]
raw_three_num = threes[line]
if i % 2 == 0:
for j in range(4):
routes[j] += min(
table[raw_three_num][j], table[raw_three_num][7 - j]
)
else:
for j in range(4):
new_j = (j + 2) % 4
routes[j] += min(
table[raw_three_num][new_j], table[raw_three_num][7 - new_j]
)
print(min(routes))
main() | FUNC_DEF ASSIGN VAR LIST FOR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR LIST FOR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR RETURN VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER RETURN IF VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR STRING IF BIN_OP VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST STRING STRING STRING STRING STRING STRING STRING STRING ASSIGN VAR VAR VAR VAR VAR FUNC_CALL VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR LIST NUMBER NUMBER NUMBER NUMBER ASSIGN VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER VAR VAR FUNC_CALL VAR VAR VAR VAR VAR VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR VAR FUNC_CALL VAR VAR VAR VAR VAR VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import itertools
n, m = map(int, input().split())
rows = []
for _ in range(n):
rows.append(list(map(int, input())))
if m >= 4 and n >= 4:
print(-1)
exit()
if m == 1 or n == 1:
print(0)
exit()
if n == 2 or m == 2:
if n == 2:
pars = [((rows[0][i] + rows[1][i]) % 2) for i in range(m)]
else:
pars = [((rows[i][0] + rows[i][1]) % 2) for i in range(n)]
best = 10**8
for to_match in [itertools.cycle([0, 1]), itertools.cycle([1, 0])]:
cost = 0
for x, y in zip(pars, to_match):
cost += abs(x - y)
best = min(best, cost)
print(best)
exit()
best = 10**8
if n == 3:
vals = [
((rows[0][i] + rows[1][i]) % 2, (rows[1][i] + rows[2][i]) % 2) for i in range(m)
]
else:
vals = [
((rows[i][0] + rows[i][1]) % 2, (rows[i][1] + rows[i][2]) % 2) for i in range(n)
]
for up, down in itertools.product([0, 1], repeat=2):
cost = 0
for cur_up, cur_down in vals:
up = 1 - up
down = 1 - down
diff = abs(cur_up - up) + abs(cur_down - down)
if diff == 2:
diff = 1
cost += diff
best = min(best, cost)
print(best) | IMPORT ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP NUMBER NUMBER FOR VAR LIST FUNC_CALL VAR LIST NUMBER NUMBER FUNC_CALL VAR LIST NUMBER NUMBER ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR BIN_OP VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR ASSIGN VAR BIN_OP NUMBER NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR FUNC_CALL VAR VAR FOR VAR VAR FUNC_CALL VAR LIST NUMBER NUMBER NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR BIN_OP NUMBER VAR ASSIGN VAR BIN_OP FUNC_CALL VAR BIN_OP VAR VAR FUNC_CALL VAR BIN_OP VAR VAR IF VAR NUMBER ASSIGN VAR NUMBER VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | def solve_two(A, n, m):
B = [((A[0][i] + A[1][i]) % 2) for i in range(m)]
odd = 0
even = 0
for i in range(m):
if B[i] == i % 2:
odd += 1
else:
even += 1
return min(odd, even)
def solve_three(A, n, m):
BU = [((A[0][i] + A[1][i]) % 2) for i in range(m)]
BD = [((A[1][i] + A[2][i]) % 2) for i in range(m)]
oddodd = 0
oddeven = 0
evenodd = 0
eveneven = 0
for i in range(m):
if BU[i] == i % 2:
oddeven += 1
oddodd += 1
else:
eveneven += 1
evenodd += 1
if BD[i] == i % 2:
if BU[i] == i % 2:
evenodd += 1
else:
oddodd += 1
elif BU[i] == i % 2:
eveneven += 1
else:
oddeven += 1
return min([oddodd, oddeven, evenodd, eveneven])
def solve():
n, m = map(int, input().split())
A = [list(map(int, list(input()))) for _ in range(n)]
if n >= 4 and m >= 4:
return -1
if n == 1:
return 0
if n > m:
n, m = m, n
A = list(zip(*A))
ans = 0
if n == 2:
return solve_two(A, n, m)
if n == 3:
return solve_three(A, n, m)
def main():
print(solve())
main() | FUNC_DEF ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER RETURN FUNC_CALL VAR VAR VAR FUNC_DEF ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR NUMBER VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER RETURN FUNC_CALL VAR LIST VAR VAR VAR VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR NUMBER RETURN NUMBER IF VAR NUMBER RETURN NUMBER IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER IF VAR NUMBER RETURN FUNC_CALL VAR VAR VAR VAR IF VAR NUMBER RETURN FUNC_CALL VAR VAR VAR VAR FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
def checkPairable(b1, b2, n):
ok = True
for start in range(n - 1):
cnt = 0
if b1 & 1 << start > 0:
cnt += 1
if b1 & 1 << start + 1 > 0:
cnt += 1
if b2 & 1 << start > 0:
cnt += 1
if b2 & 1 << start + 1 > 0:
cnt += 1
if cnt % 2 == 0:
ok = False
return ok
def nMovesB1toB2(b1, b2, n):
res = 0
for i in range(n):
if (b1 & 1 << i > 0) != (b2 & 1 << i > 0):
res += 1
return res
def main():
n, m = readIntArr()
mat = []
for _ in range(n):
mat.append(input())
if n >= 4:
print(-1)
return
if n == 1:
print(0)
return
cols = []
for j in range(m):
b = 0
for i in range(n):
if mat[i][j] == "1":
b = b | 1 << i
cols.append(b)
pairableCols = [[] for _ in range(2**n)]
for b1 in range(2**n):
for b2 in range(2**n):
if checkPairable(b1, b2, n):
pairableCols[b1].append(b2)
dp = [[float("inf") for _ in range(2**n)] for __ in range(m)]
for b in range(2**n):
dp[0][b] = min(dp[0][b], nMovesB1toB2(cols[0], b, n))
for col in range(1, m):
for b in range(2**n):
moveCnt = nMovesB1toB2(cols[col], b, n)
for matchedPrev in pairableCols[b]:
dp[col][b] = min(dp[col][b], moveCnt + dp[col - 1][matchedPrev])
ans = float("inf")
for b in range(2**n):
ans = min(ans, dp[m - 1][b])
print(ans)
return
input = lambda: sys.stdin.readline().rstrip("\r\n")
def oneLineArrayPrint(arr):
print(" ".join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
print("\n".join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
print("\n".join([" ".join([str(x) for x in y]) for y in arr]))
def readIntArr():
return [int(x) for x in input().split()]
main() | IMPORT FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR NUMBER IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER VAR NUMBER IF BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER VAR NUMBER IF BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR NUMBER NUMBER ASSIGN VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER BIN_OP VAR BIN_OP NUMBER VAR NUMBER VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER RETURN IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER RETURN ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR STRING ASSIGN VAR BIN_OP VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR LIST VAR FUNC_CALL VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR IF FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR STRING VAR FUNC_CALL VAR BIN_OP NUMBER VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR VAR FOR VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR VAR BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR STRING FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER VAR EXPR FUNC_CALL VAR VAR RETURN ASSIGN VAR FUNC_CALL FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR FUNC_DEF EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR VAR VAR FUNC_DEF RETURN FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | from sys import stdin
def inp():
return stdin.buffer.readline().rstrip().decode("utf8")
def itg():
return int(stdin.buffer.readline())
def mpint():
return map(int, stdin.buffer.readline().split())
def clockwise(two_d_array, copy=False):
if copy:
return list(map(list, zip(*two_d_array[::-1])))
two_d_array[:] = map(list, zip(*two_d_array[::-1]))
def get_bit(mask: int, bit_length, index):
return mask >> bit_length - index % bit_length - 1 & 1
def to_binary(iterable):
result = 0
for item in iterable:
result <<= 1
result += item
return result
def mask_differ(mask1, mask2):
if not isinstance(mask1, int):
mask1 = to_binary(mask1)
if not isinstance(mask2, int):
mask2 = to_binary(mask2)
return mask1 ^ mask2
def binary_count_1(binary_num: int):
result = 0
while binary_num:
result += binary_num & 1
binary_num >>= 1
return result
INF = 487639487
def solve():
n, m = mpint()
g = [list(map(lambda b: b == "1", inp())) for _ in range(n)]
if n >= 4:
return -1
if n == 1:
return 0
max_mask = 1 << n
clockwise(g)
n, m = m, n
dp = [([INF] * max_mask) for _ in range(n)]
def is_good(m1, m2):
for i in range(m - 1):
s = (
get_bit(m1, m, i)
+ get_bit(m1, m, i + 1)
+ get_bit(m2, m, i)
+ get_bit(m2, m, i + 1)
)
if s & 1 ^ 1:
return False
return True
is_good_table = [
[is_good(m1, m2) for m2 in range(max_mask)] for m1 in range(max_mask)
]
count_differ_table = [
[binary_count_1(mask_differ(m1, m2)) for m2 in range(max_mask)]
for m1 in range(max_mask)
]
mask1 = to_binary(g[0])
for mask2 in range(max_mask):
dp[0][mask2] = binary_count_1(mask_differ(mask1, mask2))
for i in range(1, n):
mask_i = to_binary(g[i])
for mask1 in range(max_mask):
mask1_cost = dp[i - 1][mask1]
for mask2 in range(max_mask):
if is_good_table[mask1][mask2]:
mask2_cost = count_differ_table[mask_i][mask2]
dp[i][mask2] = min(dp[i][mask2], mask1_cost + mask2_cost)
return min(dp[-1])
print(solve()) | FUNC_DEF RETURN FUNC_CALL FUNC_CALL FUNC_CALL VAR STRING FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF NUMBER IF VAR RETURN FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER FUNC_DEF VAR RETURN BIN_OP BIN_OP VAR BIN_OP BIN_OP VAR BIN_OP VAR VAR NUMBER NUMBER FUNC_DEF ASSIGN VAR NUMBER FOR VAR VAR VAR NUMBER VAR VAR RETURN VAR FUNC_DEF IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR RETURN BIN_OP VAR VAR FUNC_DEF VAR ASSIGN VAR NUMBER WHILE VAR VAR BIN_OP VAR NUMBER VAR NUMBER RETURN VAR ASSIGN VAR NUMBER FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR STRING FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER RETURN NUMBER IF VAR NUMBER RETURN NUMBER ASSIGN VAR BIN_OP NUMBER VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP BIN_OP BIN_OP FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER IF BIN_OP BIN_OP VAR NUMBER NUMBER RETURN NUMBER RETURN NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR BIN_OP VAR NUMBER VAR FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR VAR RETURN FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
data = [list(int(v) for v in input()) for _ in range(n)]
if n > 3 and m > 3:
print(-1)
elif n == 1 or m == 1:
print(0)
else:
if n < m:
n, m = m, n
data = [list(t) for t in zip(*data)]
if m == 2:
x, y = 0, 0
for i, v in enumerate(data):
if i & 1 == sum(v) & 1:
x += 1
else:
y += 1
print(min(x, y))
elif m == 3:
x, y, z, w = 0, 0, 0, 0
for i, v in enumerate(data):
if i & 1 == sum(v[:2]) & 1 or i & 1 == sum(v[1:]) & 1:
x += 1
if i & 1 != sum(v[:2]) & 1 or i & 1 == sum(v[1:]) & 1:
y += 1
if i & 1 == sum(v[:2]) & 1 or i & 1 != sum(v[1:]) & 1:
z += 1
if i & 1 != sum(v[:2]) & 1 or i & 1 != sum(v[1:]) & 1:
w += 1
print(min(x, y, z, w)) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR VAR NUMBER NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR VAR VAR VAR NUMBER NUMBER NUMBER NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = list(map(int, input().split()))
a = []
def f(x, y):
res = 0
if x[0] != y[0]:
res += 1
if x[1] != y[1]:
res += 1
if x[2] != y[2]:
res += 1
return res
if n >= 4 and m >= 4:
for i in range(n):
a.append(list(input()))
print(-1)
elif n == 1 or m == 1:
for i in range(n):
a.append(list(input()))
print(0)
elif n == 2 or m == 2:
c = []
if m == 2:
for i in range(n):
s = list(input())
c.append(s.count("1") % 2)
elif n == 2:
for i in range(n):
a.append(list(input()))
for i in range(m):
tmp = 0
if a[0][i] == "1":
tmp += 1
if a[1][i] == "1":
tmp += 1
c.append(tmp % 2)
res1 = 0
res2 = 0
for i in range(len(c)):
if i % 2 == c[i]:
res1 += 1
else:
res2 += 1
print(min(res1, res2))
else:
a = []
if n == 3:
b = list(input())
c = list(input())
d = list(input())
for i in range(m):
a.append(b[i] + c[i] + d[i])
elif m == 3:
s = input()
a.append(s)
r = max(n, m)
res1 = 0
res2 = 0
res3 = 0
res4 = 0
for i in range(r):
if i % 2 == 0:
res1 += min(f(a[i], "111"), f(a[i], "000"))
res2 += min(f(a[i], "010"), f(a[i], "101"))
res3 += min(f(a[i], "110"), f(a[i], "001"))
res4 += min(f(a[i], "011"), f(a[i], "100"))
else:
res2 += min(f(a[i], "111"), f(a[i], "000"))
res1 += min(f(a[i], "010"), f(a[i], "101"))
res4 += min(f(a[i], "110"), f(a[i], "001"))
res3 += min(f(a[i], "011"), f(a[i], "100"))
print(min(res1, res2, res3, res4)) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FUNC_DEF ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER IF VAR NUMBER VAR NUMBER VAR NUMBER RETURN VAR IF VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR LIST IF VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR STRING NUMBER IF VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER IF VAR NUMBER VAR STRING VAR NUMBER IF VAR NUMBER VAR STRING VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER VAR VAR VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR VAR VAR VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR VAR STRING EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
def dif(x, y):
ans = 0
for i in range(3):
if x % 2 != y % 2:
ans += 1
x //= 2
y //= 2
return ans
def s(x, y):
ans = 0
for i in range(3):
ans += x % 2
ans += y % 2
x //= 2
y //= 2
return ans
def main():
n, m = map(int, sys.stdin.readline().split())
inf = 10**9
if n > 3:
print(-1)
return
if n == 1:
print(0)
return
f = [None] * n
for i in range(n):
f[i] = sys.stdin.readline()
a = [0] * m
d = [([0] * 8) for i in range(8)]
for msk1 in range(8):
for msk2 in range(8):
d[msk1][msk2] = dif(msk1, msk2)
for i in range(m):
cur = 0
for j in range(n):
if f[j][i] == "1":
cur += 2**j
a[i] = cur
if n == 2:
dp = [([inf] * 4) for i in range(m)]
for msk in range(2**2):
dp[0][msk] = d[msk][a[0]]
par = []
for msk in range(2**2):
for msk1 in range(2**2):
if s(msk, msk1) % 2 == 1:
par.append((msk, msk1))
for i in range(1, m):
for msk, msk1 in par:
dp[i][msk] = min(dp[i][msk], dp[i - 1][msk1] + dif(msk, a[i]))
sys.stdout.write(str(min(dp[m - 1])))
if n == 3:
dp = [([inf] * 8) for i in range(m)]
for msk in range(2**3):
dp[0][msk] = d[msk][a[0]]
par = []
for msk in range(2**3):
for msk1 in range(2**3):
if (
s(msk // 2, msk1 // 2) % 2 == 1
and s(msk - msk // 4 * 4, msk1 - msk1 // 4 * 4) % 2 == 1
):
par.append((msk, msk1))
for i in range(1, m):
for msk, msk1 in par:
dp[i][msk] = min(dp[i][msk], dp[i - 1][msk1] + dif(msk, a[i]))
sys.stdout.write(str(min(dp[m - 1])))
main() | IMPORT FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER VAR BIN_OP VAR NUMBER VAR BIN_OP VAR NUMBER VAR NUMBER VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR BIN_OP NUMBER NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER RETURN IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER RETURN ASSIGN VAR BIN_OP LIST NONE VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR BIN_OP LIST NUMBER VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR STRING VAR BIN_OP NUMBER VAR ASSIGN VAR VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP LIST VAR NUMBER VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR VAR VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER IF BIN_OP FUNC_CALL VAR VAR VAR NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR FOR VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP LIST VAR NUMBER VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER ASSIGN VAR NUMBER VAR VAR VAR VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER IF BIN_OP FUNC_CALL VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER NUMBER NUMBER BIN_OP FUNC_CALL VAR BIN_OP VAR BIN_OP BIN_OP VAR NUMBER NUMBER BIN_OP VAR BIN_OP BIN_OP VAR NUMBER NUMBER NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR FOR VAR VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR VAR BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | mod = 10**9 + 7
def solve():
n, m = map(int, input().split())
ans = 0
s = []
for i in range(n):
s.append(list(input()))
if n >= 4 and m > -4:
ans = -1
elif n == 1 or m == 1:
ans = 0
elif n == 2 or m == 2:
vec = []
if n == 2:
for i in range(m):
sm = 0
if s[0][i] == "1":
sm += 1
if s[1][i] == "1":
sm += 1
vec.append(sm)
else:
for i in range(n):
sm = 0
if s[i][0] == "1":
sm += 1
if s[i][1] == "1":
sm += 1
vec.append(sm)
tmp1 = 0
tmp2 = 0
for i in range(len(vec)):
if vec[i] % 2 == i % 2:
tmp1 += 1
if (vec[i] + 1) % 2 == i % 2:
tmp2 += 1
ans = len(vec) - max(tmp1, tmp2)
else:
vec = []
if n == 3:
for i in range(m):
sm1 = (1 if s[0][i] == "1" else 0) + (1 if s[1][i] == "1" else 0)
sm2 = (1 if s[1][i] == "1" else 0) + (1 if s[2][i] == "1" else 0)
vec.append([sm1, sm2])
else:
for i in range(n):
sm1 = (1 if s[i][0] == "1" else 0) + (1 if s[i][1] == "1" else 0)
sm2 = (1 if s[i][1] == "1" else 0) + (1 if s[i][2] == "1" else 0)
vec.append([sm1, sm2])
tmp = [(0) for i in range(4)]
for i in range(len(vec)):
if vec[i][0] % 2 == vec[i][1] % 2:
if vec[i][0] % 2 == i % 2:
tmp[0] += 1
else:
tmp[1] += 1
elif vec[i][0] % 2 == i % 2:
tmp[2] += 1
else:
tmp[3] += 1
ans = len(vec) - max(tmp)
print(ans)
t = 1
for _ in range(t):
solve() | ASSIGN VAR BIN_OP BIN_OP NUMBER NUMBER NUMBER FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR LIST IF VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER IF VAR NUMBER VAR STRING VAR NUMBER IF VAR NUMBER VAR STRING VAR NUMBER EXPR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER IF VAR VAR NUMBER STRING VAR NUMBER IF VAR VAR NUMBER STRING VAR NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR VAR NUMBER BIN_OP VAR NUMBER VAR NUMBER IF BIN_OP BIN_OP VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST IF VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR STRING NUMBER NUMBER VAR NUMBER VAR STRING NUMBER NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR STRING NUMBER NUMBER VAR NUMBER VAR STRING NUMBER NUMBER EXPR FUNC_CALL VAR LIST VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR VAR NUMBER STRING NUMBER NUMBER VAR VAR NUMBER STRING NUMBER NUMBER ASSIGN VAR BIN_OP VAR VAR NUMBER STRING NUMBER NUMBER VAR VAR NUMBER STRING NUMBER NUMBER EXPR FUNC_CALL VAR LIST VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR VAR NUMBER NUMBER BIN_OP VAR VAR NUMBER NUMBER IF BIN_OP VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER IF BIN_OP VAR VAR NUMBER NUMBER BIN_OP VAR NUMBER VAR NUMBER NUMBER VAR NUMBER NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
size = input()[:-1].split(" ")
size[0] = int(size[0])
size[1] = int(size[1])
lines = []
def diffOddDouble(bitList):
flipCount = []
for x in range(2):
for y in range(2):
flipCount.append(
sum(
bitList[i][0] == (i + x) % 2 or bitList[i][1] == (i + y) % 2
for i in range(len(bitList))
)
)
return min(x for x in flipCount)
if size[0] >= 4 and size[1] >= 4:
print(-1)
elif 1 in size:
print(0)
elif 2 in size:
if size[0] == 2:
lines.append(input()[:-1])
lines.append(input()[:-1])
parity = list(lines[0][x] == lines[1][x] for x in range(size[1]))
else:
parity = []
for x in range(size[0]):
line = input()
parity.append(line[0] == line[1])
modify = sum(parity[x] == x % 2 for x in range(size[1]))
if modify > size[1] // 2:
modify = size[1] - modify
print(modify)
else:
parity = []
if size[0] == 3:
lines = [input()[:-1], input()[:-1], input()[:-1]]
for x in range(size[1]):
parity.append([lines[0][x] == lines[1][x], lines[1][x] == lines[2][x]])
else:
for x in range(size[0]):
line = input()
parity.append([lines[x][0] == lines[x][1], lines[x][1] == lines[x][2]])
print(diffOddDouble(parity)) | IMPORT ASSIGN VAR VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR NUMBER STRING ASSIGN VAR NUMBER FUNC_CALL VAR VAR NUMBER ASSIGN VAR NUMBER FUNC_CALL VAR VAR NUMBER ASSIGN VAR LIST FUNC_DEF ASSIGN VAR LIST FOR VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR VAR NUMBER BIN_OP BIN_OP VAR VAR NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR RETURN FUNC_CALL VAR VAR VAR VAR IF VAR NUMBER NUMBER VAR NUMBER NUMBER EXPR FUNC_CALL VAR NUMBER IF NUMBER VAR EXPR FUNC_CALL VAR NUMBER IF NUMBER VAR IF VAR NUMBER NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR NUMBER VAR VAR NUMBER VAR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR NUMBER VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR VAR NUMBER IF VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR LIST IF VAR NUMBER NUMBER ASSIGN VAR LIST FUNC_CALL VAR NUMBER FUNC_CALL VAR NUMBER FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR LIST VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR FOR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR EXPR FUNC_CALL VAR LIST VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = list(map(int, input().split()))
masks = ["000", "001", "010", "011", "100", "101", "110", "111"]
D = {}
x = []
for _ in range(n):
l = input().rstrip()
x.append(l)
if n < 2:
print(0)
if n == 2:
masks = ["00", "01", "10", "11"]
for mask in masks:
D[mask] = 0
c = 0
for bit in mask:
D[mask] += int(bit) ^ int(x[c][0])
c += 1
check = {}
DIF = {}
for mask in masks:
check[mask] = []
for prev_mask in masks:
cc, hh = 0, 0
for bit in mask:
hh += int(bit) ^ int(prev_mask[cc])
cc += 1
DIF[mask, prev_mask] = hh
a = mask[:2] + prev_mask[:2]
if a.count("1") % 2 == 1:
check[mask].append(prev_mask)
for i in range(1, m):
G = {}
temp = x[0][i] + x[1][i]
for mask in masks:
G[mask] = 99999999
h = DIF[mask, temp]
if h < 2:
for prev_mask in check[mask]:
G[mask] = min(G[mask], D[prev_mask] + h)
D = G
ans = 99999999
for key in D:
ans = min(D[key], ans)
print(ans)
if n == 3:
for mask in masks:
D[mask] = 0
c = 0
for bit in mask:
D[mask] += int(bit) ^ int(x[c][0])
c += 1
check = {}
DIF = {}
for mask in masks:
check[mask] = []
for prev_mask in masks:
cc, hh = 0, 0
for bit in mask:
hh += int(bit) ^ int(prev_mask[cc])
cc += 1
DIF[mask, prev_mask] = hh
a = mask[:2] + prev_mask[:2]
b = mask[1:] + prev_mask[1:]
if a.count("1") % 2 == 1 and b.count("1") % 2 == 1:
check[mask].append(prev_mask)
for i in range(1, m):
G = {}
temp = x[0][i] + x[1][i] + x[2][i]
for mask in masks:
G[mask] = 99999999
h = DIF[mask, temp]
if h < 2:
for prev_mask in check[mask]:
G[mask] = min(G[mask], D[prev_mask] + h)
D = G
ans = 99999999
for key in D:
ans = min(D[key], ans)
print(ans)
if n > 3:
print(-1) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST STRING STRING STRING STRING STRING STRING STRING STRING ASSIGN VAR DICT ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST STRING STRING STRING STRING FOR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER ASSIGN VAR DICT ASSIGN VAR DICT FOR VAR VAR ASSIGN VAR VAR LIST FOR VAR VAR ASSIGN VAR VAR NUMBER NUMBER FOR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER IF BIN_OP FUNC_CALL VAR STRING NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR DICT ASSIGN VAR BIN_OP VAR NUMBER VAR VAR NUMBER VAR FOR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR VAR VAR VAR IF VAR NUMBER FOR VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR NUMBER FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER FOR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER ASSIGN VAR DICT ASSIGN VAR DICT FOR VAR VAR ASSIGN VAR VAR LIST FOR VAR VAR ASSIGN VAR VAR NUMBER NUMBER FOR VAR VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER IF BIN_OP FUNC_CALL VAR STRING NUMBER NUMBER BIN_OP FUNC_CALL VAR STRING NUMBER NUMBER EXPR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR DICT ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR FOR VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR VAR VAR VAR IF VAR NUMBER FOR VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR BIN_OP VAR VAR VAR ASSIGN VAR VAR ASSIGN VAR NUMBER FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | from sys import exit, stdin, stdout
def input():
return stdin.readline().strip()
def match_same(col):
if len(set(col)) == 1:
return 0
return 1
def match_exact(p, q):
ret = 0
for a, b in zip(p, q):
if a != b:
ret += 1
return ret
def match_diff(col):
if len(set(col)) == 1:
return 1
if len(col) == 2:
return 0
return min(match_exact(col, (0, 1, 0)), match_exact(col, (1, 0, 1)))
def match_sd(col):
return min(match_exact(col, (1, 1, 0)), match_exact(col, (0, 0, 1)))
def match_ds(col):
return min(match_exact(col, (0, 1, 1)), match_exact(col, (1, 0, 0)))
def match(col, is_same):
if is_same:
return match_same(col)
else:
return match_diff(col)
def match_3(col, at_sd):
if at_sd:
return match_sd(col)
else:
return match_ds(col)
def ans_s(A):
is_same = True
ret = 0
for col in A:
ret += match(col, is_same)
is_same = not is_same
return ret
def ans_d(A):
is_same = False
ret = 0
for col in A:
ret += match(col, is_same)
is_same = not is_same
return ret
def ans_sd(A):
if len(A[0]) != 3:
return float("inf")
at_sd = True
ret = 0
for col in A:
ret += match_3(col, at_sd)
at_sd = not at_sd
return ret
def ans_ds(A):
if len(A[0]) != 3:
return float("inf")
at_sd = False
ret = 0
for col in A:
ret += match_3(col, at_sd)
at_sd = not at_sd
return ret
def ans(A):
return min(ans_s(A), ans_d(A), ans_sd(A), ans_ds(A))
n, m = input().split()
n = int(n)
m = int(m)
A = []
for _ in range(n):
A += [input()]
if n >= 4:
A = [tuple(map(int, row)) for row in A]
print(-1)
exit(0)
if n == 1:
print(0)
exit(0)
A = zip(*A)
A = [list(map(int, row)) for row in A]
print(ans(A)) | FUNC_DEF RETURN FUNC_CALL FUNC_CALL VAR FUNC_DEF IF FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER RETURN NUMBER RETURN NUMBER FUNC_DEF ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR VAR IF VAR VAR VAR NUMBER RETURN VAR FUNC_DEF IF FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER RETURN NUMBER IF FUNC_CALL VAR VAR NUMBER RETURN NUMBER RETURN FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER NUMBER NUMBER FUNC_CALL VAR VAR NUMBER NUMBER NUMBER FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER NUMBER NUMBER FUNC_CALL VAR VAR NUMBER NUMBER NUMBER FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER NUMBER NUMBER FUNC_CALL VAR VAR NUMBER NUMBER NUMBER FUNC_DEF IF VAR RETURN FUNC_CALL VAR VAR RETURN FUNC_CALL VAR VAR FUNC_DEF IF VAR RETURN FUNC_CALL VAR VAR RETURN FUNC_CALL VAR VAR FUNC_DEF ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR RETURN VAR FUNC_DEF ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR RETURN VAR FUNC_DEF IF FUNC_CALL VAR VAR NUMBER NUMBER RETURN FUNC_CALL VAR STRING ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR RETURN VAR FUNC_DEF IF FUNC_CALL VAR VAR NUMBER NUMBER RETURN FUNC_CALL VAR STRING ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR RETURN VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR VAR LIST FUNC_CALL VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | n, m = map(int, input().split())
if n > 3 and m > 3:
print(-1)
else:
arr = [[] for i in range(n)]
for i in range(n):
arr[i] = list(map(int, list(input())))
if n < m:
arr1 = [[(0) for i in range(n)] for i in range(m)]
for i in range(n):
for j in range(m):
arr1[j][i] = arr[i][j]
arr = arr1
if n == 1 or m == 1:
print(0)
elif n == 2 or m == 2:
ans1 = 0
for i in range(len(arr)):
if i % 2 == 0:
if arr[i][0] + arr[i][1] != 1:
ans1 += 1
elif arr[i][0] + arr[i][1] == 1:
ans1 += 1
ans2 = 0
for i in range(len(arr)):
if i % 2 == 0:
if arr[i][0] + arr[i][1] == 1:
ans2 += 1
elif arr[i][0] + arr[i][1] != 1:
ans2 += 1
print(min(ans1, ans2))
else:
oo = [[0, 1, 0], [1, 0, 1]]
oe = [[1, 0, 0], [0, 1, 1]]
eo = [[0, 0, 1], [1, 1, 0]]
ee = [[0, 0, 0], [1, 1, 1]]
ans1 = 0
for i in range(len(arr)):
if i % 2 == 0:
if arr[i] not in oo:
ans1 += 1
elif arr[i] not in ee:
ans1 += 1
ans2 = 0
for i in range(len(arr)):
if i % 2 == 0:
if arr[i] not in oe:
ans2 += 1
elif arr[i] not in eo:
ans2 += 1
ans3 = 0
for i in range(len(arr)):
if i % 2 == 0:
if arr[i] not in eo:
ans3 += 1
elif arr[i] not in oe:
ans3 += 1
ans4 = 0
for i in range(len(arr)):
if i % 2 == 0:
if arr[i] not in ee:
ans4 += 1
elif arr[i] not in oo:
ans4 += 1
print(min(ans1, ans2, ans3, ans4)) | ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER ASSIGN VAR LIST VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR IF VAR VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR NUMBER IF BIN_OP VAR VAR NUMBER VAR VAR NUMBER NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR LIST LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | from itertools import chain, product
def find_cells_to_fix_n(matrix):
if len(matrix) < 2 or len(matrix[0]) < 2:
return 0
if not len(matrix) <= len(matrix[0]):
matrix = tuple(zip(*matrix))
len_y, len_x = len(matrix), len(matrix[0])
if len_y >= 4:
result = None
elif len_y == 3:
result = _solve_for_3(matrix)
elif len_y == 2:
result = _solve_for_2(matrix)
else:
raise AssertionError("can't get here")
return result
def _compress_2xn(matrix):
assert len(matrix) == 2
parity_line = tuple(map(int.__add__, *matrix))
parity_line = map(int.__add__, parity_line, parity_line[1:])
parity_line = map((2).__rmod__, parity_line)
parity_line = tuple(parity_line)
return parity_line
def _compress_3xn(matrix):
assert len(matrix) == 3
first_row = _compress_2xn(matrix[0:2])
second_row = _compress_2xn(matrix[1:3])
result = first_row, second_row
return result
def _get_zeros_pairs(zeros_positions, line_length, is_first_towards_left):
if not zeros_positions:
return []
if is_first_towards_left:
zeros_pairs = [(-1, zeros_positions[0])]
else:
zeros_pairs = []
i_start_zero = 1 if is_first_towards_left else 0
for i_first_zero in range(i_start_zero, len(zeros_positions), 2):
i_second_zero = i_first_zero + 1
first_zero_pos = zeros_positions[i_first_zero]
if i_second_zero < len(zeros_positions):
second_zero_pos = zeros_positions[i_second_zero]
else:
second_zero_pos = line_length
zeros_pairs.append((first_zero_pos, second_zero_pos))
return zeros_pairs
def _find_zeros_pairs_costs(zeros_pairs):
return sum(second_pos - first_pos for first_pos, second_pos in zeros_pairs)
def _solve_for_2(matrix):
parity_line = _compress_2xn(matrix)
zeros_positions = tuple(i for i, value in enumerate(parity_line) if value == 0)
line_length = len(parity_line)
min_cost = min(
_how_much_costs_tactic_for_2xn(
zeros_positions, line_length, is_first_towards_left
)
for is_first_towards_left in (True, False)
)
return min_cost
def _how_much_costs_tactic_for_2xn(zeros_positions, line_length, is_first_towards_left):
zeros_pairs = _get_zeros_pairs(zeros_positions, line_length, is_first_towards_left)
return _find_zeros_pairs_costs(zeros_pairs)
def _solve_for_3(matrix):
parity_lines = _compress_3xn(matrix)
zeros_positions = tuple(
tuple(i for i, value in enumerate(parity_line) if value == 0)
for parity_line in parity_lines
)
line_length = len(parity_lines[0])
min_cost = min(
_how_much_costs_tactic_for_3xn(
zeros_positions, line_length, is_first_towards_left
)
for is_first_towards_left in product((True, False), repeat=2)
)
return min_cost
def _how_much_costs_tactic_for_3xn(zeros_positions, line_length, is_first_towards_left):
zeros_pairs = tuple(
_get_zeros_pairs(_zeros_positions, line_length, _is_first_towards_left)
for _zeros_positions, _is_first_towards_left in zip(
zeros_positions, is_first_towards_left
)
)
first_row_pairs, second_row_pairs = zeros_pairs
walked = [0] * (line_length + 1)
for pair_first, pair_last in chain(first_row_pairs, second_row_pairs):
for i in range(pair_first, pair_last):
walked[i + 1] = 1
return sum(walked)
def main():
n, m = map(int, input().split())
matrix = tuple(tuple(map(int, input())) for i in range(n))
cells_to_fix_n = find_cells_to_fix_n(matrix)
if cells_to_fix_n is None:
cells_to_fix_n = -1
print(cells_to_fix_n)
main() | FUNC_DEF IF FUNC_CALL VAR VAR NUMBER FUNC_CALL VAR VAR NUMBER NUMBER RETURN NUMBER IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER IF VAR NUMBER ASSIGN VAR NONE IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR STRING RETURN VAR FUNC_DEF FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR RETURN VAR FUNC_DEF FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR NUMBER NUMBER ASSIGN VAR VAR VAR RETURN VAR FUNC_DEF IF VAR RETURN LIST IF VAR ASSIGN VAR LIST NUMBER VAR NUMBER ASSIGN VAR LIST ASSIGN VAR VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR VAR VAR IF VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR VAR EXPR FUNC_CALL VAR VAR VAR RETURN VAR FUNC_DEF RETURN FUNC_CALL VAR BIN_OP VAR VAR VAR VAR VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR NUMBER NUMBER RETURN VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR VAR VAR RETURN FUNC_CALL VAR VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR NUMBER VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR FUNC_CALL VAR NUMBER NUMBER NUMBER RETURN VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR BIN_OP LIST NUMBER BIN_OP VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER NUMBER RETURN FUNC_CALL VAR VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF VAR NONE ASSIGN VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
def input():
return sys.stdin.readline().strip()
def list2d(a, b, c):
return [([c] * b) for i in range(a)]
def list3d(a, b, c, d):
return [[([d] * c) for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e):
return [[[([e] * d) for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1):
return int(-(-x // y))
def INT():
return int(input())
def MAP():
return map(int, input().split())
def LIST(N=None):
return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes():
print("Yes")
def No():
print("No")
def YES():
print("YES")
def NO():
print("NO")
INF = 10**19
MOD = 10**9 + 7
def popcount(x):
x -= x >> 1 & 85
x = (x & 51) + (x >> 2 & 51)
x = x + (x >> 4) & 15
return x & 15
H, W = MAP()
grid = [[]] * H
for i in range(H):
grid[i] = list(map(int, input()))
if H >= 4 and W >= 4:
print(-1)
exit()
if H == 1 or W == 1:
print(0)
exit()
if W > H:
grid = list(zip(*grid))
H, W = W, H
cur = 0
dp = list2d(H, 2**W, INF)
for j in range(W):
if grid[0][j]:
k = W - j - 1
cur += 1 << k
if W == 2:
for nxt in range(2**W):
dp[0][nxt] = popcount(cur ^ nxt)
for i in range(1, H):
cur = 0
for j in range(W):
if grid[i][j]:
k = W - j - 1
cur += 1 << k
for k in range(2**W):
if k in (1, 2):
dp[i][0] = min(dp[i][0], dp[i - 1][k] + popcount(cur ^ 0))
dp[i][3] = min(dp[i][3], dp[i - 1][k] + popcount(cur ^ 3))
else:
dp[i][2] = min(dp[i][2], dp[i - 1][k] + popcount(cur ^ 2))
dp[i][1] = min(dp[i][1], dp[i - 1][k] + popcount(cur ^ 1))
else:
for nxt in range(2**W):
dp[0][nxt] = popcount(cur ^ nxt)
for i in range(1, H):
cur = 0
for j in range(W):
if grid[i][j]:
k = W - j - 1
cur += 1 << k
dp[i][0] = min(dp[i][0], dp[i - 1][5] + popcount(cur ^ 0))
dp[i][0] = min(dp[i][0], dp[i - 1][2] + popcount(cur ^ 0))
dp[i][1] = min(dp[i][1], dp[i - 1][3] + popcount(cur ^ 1))
dp[i][1] = min(dp[i][1], dp[i - 1][4] + popcount(cur ^ 1))
dp[i][2] = min(dp[i][2], dp[i - 1][7] + popcount(cur ^ 2))
dp[i][2] = min(dp[i][2], dp[i - 1][0] + popcount(cur ^ 2))
dp[i][3] = min(dp[i][3], dp[i - 1][6] + popcount(cur ^ 3))
dp[i][3] = min(dp[i][3], dp[i - 1][1] + popcount(cur ^ 3))
dp[i][4] = min(dp[i][4], dp[i - 1][1] + popcount(cur ^ 4))
dp[i][4] = min(dp[i][4], dp[i - 1][6] + popcount(cur ^ 4))
dp[i][5] = min(dp[i][5], dp[i - 1][7] + popcount(cur ^ 5))
dp[i][5] = min(dp[i][5], dp[i - 1][0] + popcount(cur ^ 5))
dp[i][6] = min(dp[i][6], dp[i - 1][4] + popcount(cur ^ 6))
dp[i][6] = min(dp[i][6], dp[i - 1][3] + popcount(cur ^ 6))
dp[i][7] = min(dp[i][7], dp[i - 1][5] + popcount(cur ^ 7))
dp[i][7] = min(dp[i][7], dp[i - 1][2] + popcount(cur ^ 7))
ans = min(dp[-1])
print(ans) | IMPORT FUNC_DEF RETURN FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF RETURN BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF RETURN BIN_OP LIST VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR FUNC_DEF NUMBER RETURN FUNC_CALL VAR BIN_OP VAR VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF NONE RETURN VAR NONE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_DEF EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR STRING FUNC_DEF EXPR FUNC_CALL VAR STRING ASSIGN VAR BIN_OP NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP NUMBER NUMBER NUMBER FUNC_DEF VAR BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP BIN_OP VAR BIN_OP VAR NUMBER NUMBER RETURN BIN_OP VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR ASSIGN VAR BIN_OP LIST LIST VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR IF VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR BIN_OP NUMBER VAR VAR FOR VAR FUNC_CALL VAR VAR IF VAR NUMBER VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER VAR BIN_OP NUMBER VAR IF VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER VAR BIN_OP NUMBER VAR FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR IF VAR NUMBER NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR BIN_OP VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR NUMBER VAR BIN_OP NUMBER VAR ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER BIN_OP VAR BIN_OP VAR NUMBER NUMBER FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | from sys import stdin
input = stdin.readline
n, m = map(int, input().split())
a = []
for x in range(n):
a.append(input().rstrip())
if n == 1:
print(0)
elif n >= 4:
print(-1)
elif n == 2:
cnt1, cnt2 = 0, 0
for x in range(m):
if x % 2 == 0:
cnt1 += a[0][x] == a[1][x]
cnt2 += a[0][x] != a[1][x]
else:
cnt1 += a[0][x] != a[1][x]
cnt2 += a[0][x] == a[1][x]
print(min(cnt1, cnt2))
elif n == 3:
cnt1, cnt2, cnt3, cnt4 = 0, 0, 0, 0
for x in range(m):
if x % 2 == 0:
if a[0][x] == a[1][x] == a[2][x]:
cnt1 += 0
else:
cnt1 += 1
if a[0][x] == a[2][x] and a[0][x] != a[1][x]:
cnt2 += 0
else:
cnt2 += 1
else:
if a[0][x] == a[2][x] and a[0][x] != a[1][x]:
cnt1 += 0
else:
cnt1 += 1
if a[0][x] == a[1][x] == a[2][x]:
cnt2 += 0
else:
cnt2 += 1
if x % 2 == 0:
if a[0][x] == a[1][x] and a[0][x] != a[2][x]:
cnt3 += 0
else:
cnt3 += 1
if a[1][x] == a[2][x] and a[0][x] != a[1][x]:
cnt4 += 0
else:
cnt4 += 1
else:
if a[1][x] == a[2][x] and a[0][x] != a[1][x]:
cnt3 += 0
else:
cnt3 += 1
if a[0][x] == a[1][x] and a[0][x] != a[2][x]:
cnt4 += 0
else:
cnt4 += 1
print(min(cnt1, cnt2, cnt3, cnt4)) | ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL FUNC_CALL VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR VAR NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR NUMBER VAR VAR VAR NUMBER VAR VAR NUMBER VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR VAR VAR VAR NUMBER NUMBER NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR IF BIN_OP VAR NUMBER NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF BIN_OP VAR NUMBER NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR |
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings — refer to the Notes section for their formal definitions.
-----Input-----
The first line of input contains two integers $n$ and $m$ ($1 \leq n \leq m \leq 10^6$ and $n\cdot m \leq 10^6$) — the number of rows and columns in $a$, respectively.
The following $n$ lines each contain $m$ characters, each of which is one of 0 and 1. If the $j$-th character on the $i$-th line is 1, then $a_{i,j} = 1$. Similarly, if the $j$-th character on the $i$-th line is 0, then $a_{i,j} = 0$.
-----Output-----
Output the minimum number of cells you need to change to make $a$ good, or output $-1$ if it's not possible at all.
-----Examples-----
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
-----Note-----
In the first case, changing $a_{1,1}$ to $0$ and $a_{2,2}$ to $1$ is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions — A binary matrix is one in which every element is either $1$ or $0$. A sub-matrix is described by $4$ parameters — $r_1$, $r_2$, $c_1$, and $c_2$; here, $1 \leq r_1 \leq r_2 \leq n$ and $1 \leq c_1 \leq c_2 \leq m$. This sub-matrix contains all elements $a_{i,j}$ that satisfy both $r_1 \leq i \leq r_2$ and $c_1 \leq j \leq c_2$. A sub-matrix is, further, called an even length square if $r_2-r_1 = c_2-c_1$ and $r_2-r_1+1$ is divisible by $2$. | import sys
input = sys.stdin.readline
n, m = map(int, input().split())
matrix = [0] * n
for i in range(n):
line = input()
matrix[i] = [0] * m
for j in range(m):
matrix[i][j] = int(line[j])
if n > m:
matrix2 = [0] * m
for i in range(m):
matrix2[i] = [0] * n
for j in range(n):
matrix2[i][j] = matrix[i][j]
n, m = m, n
matrix = [0] * n
for i in range(n):
matrix[i] = [0] * m
for j in range(m):
matrix[i][j] = matrix2[i][j]
if n > 3:
print(-1)
elif n == 1:
print(0)
elif n == 2:
poss = [[0, 0], [1, 0], [1, 1], [0, 1]]
costs = [0] * 4
for i in range(m):
newcosts = [0] * 4
for p in range(4):
bc = 0
for foo in range(2):
if poss[p][foo] != matrix[foo][i]:
bc += 1
newcosts[p] = min(costs[p - 1], costs[(p + 1) % 4])
newcosts[p] += bc
for p in range(4):
costs[p] = newcosts[p]
print(min(costs))
else:
poss1 = [[0, 0, 0], [0, 1, 0], [1, 1, 1], [1, 0, 1]]
poss2 = [[1, 0, 0], [1, 1, 0], [0, 1, 1], [0, 0, 1]]
costs1 = [0] * 4
costs2 = [0] * 4
for i in range(m):
newcosts1 = [0] * 4
newcosts2 = [0] * 4
for p in range(4):
bc1 = 0
bc2 = 0
for foo in range(3):
if poss1[p][foo] != matrix[foo][i]:
bc1 += 1
if poss2[p][foo] != matrix[foo][i]:
bc2 += 1
newcosts1[p] = min(costs1[p - 1], costs1[(p + 1) % 4])
newcosts1[p] += bc1
newcosts2[p] = min(costs2[p - 1], costs2[(p + 1) % 4])
newcosts2[p] += bc2
for p in range(4):
costs1[p] = newcosts1[p]
costs2[p] = newcosts2[p]
print(min(min(costs1), min(costs2))) | IMPORT ASSIGN VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR VAR IF VAR VAR ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR ASSIGN VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR BIN_OP LIST NUMBER VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR NUMBER IF VAR NUMBER ASSIGN VAR LIST LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER LIST NUMBER NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR VAR VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR LIST LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER ASSIGN VAR LIST LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER LIST NUMBER NUMBER NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR VAR VAR VAR VAR VAR NUMBER IF VAR VAR VAR VAR VAR VAR VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR BIN_OP BIN_OP VAR NUMBER NUMBER VAR VAR VAR FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
from sys import stdin
def solve(n, k):
s = set()
ans = []
for i in range(len(n)):
dig = n[i]
if len(s) == k and dig not in s:
bigmin = None
for c in s:
if dig < c:
if bigmin == None:
bigmin = c
else:
bigmin = min(bigmin, c)
if bigmin == None:
divser = 10 ** (len(n) - i)
nex = (int(n) // divser + 1) * divser
return solve(str(nex), k)
else:
ans.append(bigmin)
allmin = min(s)
while len(ans) < len(n):
ans.append(allmin)
return "".join(ans)
s.add(dig)
ans.append(dig)
return "".join(ans)
tt = int(stdin.readline())
ANS = []
for loop in range(tt):
n, k = stdin.readline()[:-1].split()
k = int(k)
ANS.append(solve(n, k))
print("\n".join(ANS)) | IMPORT FUNC_DEF ASSIGN VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR IF FUNC_CALL VAR VAR VAR VAR VAR ASSIGN VAR NONE FOR VAR VAR IF VAR VAR IF VAR NONE ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NONE ASSIGN VAR BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR RETURN FUNC_CALL VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR WHILE FUNC_CALL VAR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR RETURN FUNC_CALL STRING VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR RETURN FUNC_CALL STRING VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL STRING VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
input = sys.stdin.readline
tests = int(input())
for test in range(tests):
tInt, k = map(int, input().split())
t = [int(x) for x in str(tInt)]
foundInts = 0
ints = []
firstOccurence = {}
pos = 0
while pos < len(t):
char = t[pos]
if char not in ints:
if foundInts < k:
ints.append(char)
ints.sort()
firstOccurence[char] = pos
foundInts += 1
else:
break
pos += 1
if pos == len(t):
print("".join(str(x) for x in t))
else:
fixed = False
largerThanPos = list(filter(lambda val: val > t[pos], ints))
if largerThanPos:
t[pos] = largerThanPos[0]
fixed = True
while not fixed:
pos -= 1
largerThanPos = list(filter(lambda val: val > t[pos], ints))
if firstOccurence[t[pos]] == pos:
ints.remove(t[pos])
if t[pos] + 1 in ints:
ints.append(0)
else:
ints.append(t[pos] + 1)
t[pos] = t[pos] + 1
fixed = True
elif largerThanPos:
t[pos] = largerThanPos[0]
fixed = True
ints.sort()
pos += 1
while pos < len(t):
t[pos] = ints[0]
pos += 1
print("".join(str(x) for x in t)) | IMPORT ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR LIST ASSIGN VAR DICT ASSIGN VAR NUMBER WHILE VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR IF VAR VAR IF VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR ASSIGN VAR VAR VAR VAR NUMBER VAR NUMBER IF VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR IF VAR ASSIGN VAR VAR VAR NUMBER ASSIGN VAR NUMBER WHILE VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR VAR IF VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR IF BIN_OP VAR VAR NUMBER VAR EXPR FUNC_CALL VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR VAR NUMBER ASSIGN VAR VAR BIN_OP VAR VAR NUMBER ASSIGN VAR NUMBER IF VAR ASSIGN VAR VAR VAR NUMBER ASSIGN VAR NUMBER EXPR FUNC_CALL VAR VAR NUMBER WHILE VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
def solve():
n, k = map(int, input().split())
s = str(n)
se = set()
for i in range(len(s)):
se.add(s[i])
if len(se) <= k:
return s
se = set()
i = 0
while True:
se.add(s[i])
if len(se) > k:
break
i += 1
se.remove(s[i])
arr = sorted(se)
while True:
cur = set(c for c in s[:i])
if len(cur) == k:
if s[i] >= arr[-1]:
i -= 1
continue
j = 0
while arr[j] <= s[i]:
j += 1
return s[:i] + arr[j] + arr[0] * (len(s) - i - 1)
c = str(int(s[i]) + 1)
cur.add(c)
r = min(cur) if len(cur) == k else "0"
return s[:i] + c + r * (len(s) - i - 1)
input = lambda: sys.stdin.readline().rstrip()
t = int(input())
for i in range(t):
print(solve()) | IMPORT FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR RETURN VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR NUMBER WHILE NUMBER EXPR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR WHILE NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR VAR VAR IF FUNC_CALL VAR VAR VAR IF VAR VAR VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER WHILE VAR VAR VAR VAR VAR NUMBER RETURN BIN_OP BIN_OP VAR VAR VAR VAR BIN_OP VAR NUMBER BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR STRING RETURN BIN_OP BIN_OP VAR VAR VAR BIN_OP VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for i in range(int(input())):
n, k = map(int, input().split())
x = n
while len(set(str(x))) > k:
x = x // 10 if x % 10 == 0 else x + 1
p = str(x)
d = "0" if len(set(p)) < k else min(p)
print(p + d * (len(str(n)) - len(p))) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR VAR WHILE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER NUMBER BIN_OP VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR BIN_OP VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | times = int(input())
for _ in range(times):
n, k = map(int, input().split())
num = n
while len(set(str(num))) > k:
if num % 10 == 0:
num = num // 10
else:
num += 1
last = str(min(str(num))) * (len(str(n)) - len(str(num)))
print(str(num) + last) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR VAR WHILE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for _ in range(int(input())):
n, k = input().split()
k = int(k)
a = []
ans = 0
it = False
for i in range(len(n)):
if it:
if k:
ans = ans * 10
else:
ans = ans * 10 + min(a)
continue
j = i
while j < len(n):
if n[j] > n[i]:
j += 1
break
j += 1
j -= 1
kk = j
while kk < len(n):
if n[kk] < n[j]:
kk += 1
break
kk += 1
kk -= 1
if (
n[i] == max(n[i:])
or k > 1
or k > 0
and int(n[i]) in a
or a
and max(a) >= int(max(n[j : kk + 1]))
or i == len(n) - 1
or a
and min([int(n[x]) for x in range(i + 1, j + 1)]) < max(a)
or min([int(n[x]) for x in range(i + 1, j + 1)]) < int(n[i])
):
d = int(n[i])
else:
d = int(n[i]) + 1
if d not in a and k:
k -= 1
a.append(d)
a.sort()
ans = ans * 10 + d
else:
for x in a:
if x >= d:
ans = ans * 10 + x
break
if ans % 10 > int(n[i]):
it = True
print(ans) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR LIST ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR IF VAR ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER FUNC_CALL VAR VAR ASSIGN VAR VAR WHILE VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR VAR NUMBER VAR NUMBER VAR NUMBER ASSIGN VAR VAR WHILE VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR VAR NUMBER VAR NUMBER VAR NUMBER IF VAR VAR FUNC_CALL VAR VAR VAR VAR NUMBER VAR NUMBER FUNC_CALL VAR VAR VAR VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER VAR BIN_OP FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER IF VAR VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR FOR VAR VAR IF VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR IF BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR ASSIGN VAR NUMBER EXPR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for _ in range(int(input())):
n, k = map(int, input().split())
tmp = n
while len(set(str(tmp))) > k:
if tmp % 10 == 0:
tmp //= 10
else:
tmp += 1
if len(set(str(tmp))) < k:
print(str(tmp) + "0" * (len(str(n)) - len(str(tmp))))
else:
print(str(tmp) + min(str(tmp)) * (len(str(n)) - len(str(tmp)))) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR VAR WHILE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER VAR NUMBER VAR NUMBER IF FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR BIN_OP STRING BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for _ in range(int(input())):
x, k = input().split()
k = int(k)
n = len(x)
while len(set(x)) > k:
x = str(int(x) + 1).rstrip("0")
print(x + (min(x) if len(set(x)) == k else "0") * (n - len(x))) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR WHILE FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR NUMBER STRING EXPR FUNC_CALL VAR BIN_OP VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR STRING BIN_OP VAR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for i in range(int(input())):
a, k = input().split()
k = int(k)
k0 = k
b = [0] * 10
a = [int(i) for i in a]
j = 0
m = 9
mx = 0
for i in a:
if b[i] == 0:
k -= 1
if k < 0:
break
j += 1
b[i] += 1
m = min(m, i)
mx = max(mx, i)
if j == len(a):
print(*a, sep="")
continue
for i in range(a[j] + 1, 10):
if b[i]:
a[j] = i
for k in range(j + 1, len(a)):
a[k] = m
break
else:
b1 = [0] * 10
j1 = j
for i in range(j1):
if b1[a[i]] == 0 or a[i] != mx:
j = i + 1
b1[a[i]] = 1
if b[a[j - 1]] == 1 or a[j - 1] == mx:
a[j - 1] += 1
else:
while b[a[j - 1] + 1] == 0:
a[j - 1] += 1
a[j - 1] += 1
b = [0] * 10
for i in range(j):
b[a[i]] += 1
if 10 - b.count(0) < k0:
for i in range(j, len(a)):
a[i] = 0
else:
m = 9
for i in range(10):
if b[i]:
m = min(m, i)
for i in range(j, len(a)):
a[i] = m
print(*a, sep="") | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR IF VAR VAR NUMBER VAR NUMBER IF VAR NUMBER VAR NUMBER VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR STRING FOR VAR FUNC_CALL VAR BIN_OP VAR VAR NUMBER NUMBER IF VAR VAR ASSIGN VAR VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR BIN_OP LIST NUMBER NUMBER ASSIGN VAR VAR FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR NUMBER VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR VAR VAR NUMBER IF VAR VAR BIN_OP VAR NUMBER NUMBER VAR BIN_OP VAR NUMBER VAR VAR BIN_OP VAR NUMBER NUMBER WHILE VAR BIN_OP VAR BIN_OP VAR NUMBER NUMBER NUMBER VAR BIN_OP VAR NUMBER NUMBER VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR VAR VAR VAR NUMBER IF BIN_OP NUMBER FUNC_CALL VAR NUMBER VAR FOR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER IF VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR EXPR FUNC_CALL VAR VAR STRING |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def lower_bound(nums, x):
for i in range(len(nums)):
if nums[i] >= x:
return i
return -1
def check(n, k, num, pos, _n, wid):
x = num
nums = dict()
while x > 0:
nums.setdefault(x % 10, 0)
x //= 10
nums = list(nums.keys())
nums.sort()
flag = 0
for i in range(pos, wid):
tmp = int(_n[i])
x = lower_bound(nums, tmp) if flag == 0 else 0
if x == -1:
return -1
if flag == 0 and nums[x] > tmp:
flag = 1
num = num * 10 + nums[x]
return num
def work(n, k):
res = 10**11
_n = str(n)
wid = len(_n)
vis = dict()
tmp = 0
cnt = 0
for i in range(wid):
num = int(_n[i])
vis.setdefault(num, 0)
if vis[num] == 1:
tmp = tmp * 10 + num
continue
if cnt == k:
res = check(n, k, tmp, i, _n, wid)
if res == -1:
return work((tmp + 1) * 10 ** (wid - i), k)
return res
cnt += 1
vis[num] = 1
tmp = tmp * 10 + num
return tmp
_t = int(input())
for _c in range(_t):
n, k = map(int, input().split())
print(work(n, k)) | FUNC_DEF FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR VAR RETURN VAR RETURN NUMBER FUNC_DEF ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR WHILE VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR NUMBER FUNC_CALL VAR VAR VAR NUMBER IF VAR NUMBER RETURN NUMBER IF VAR NUMBER VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR VAR RETURN VAR FUNC_DEF ASSIGN VAR BIN_OP NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR NUMBER IF VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR IF VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR VAR VAR VAR VAR IF VAR NUMBER RETURN FUNC_CALL VAR BIN_OP BIN_OP VAR NUMBER BIN_OP NUMBER BIN_OP VAR VAR VAR RETURN VAR VAR NUMBER ASSIGN VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR NUMBER VAR RETURN VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def find_nearest(s, k):
ln = len(s)
if max(s[: ln - 1]) > s[ln - 1]:
x = list(set(s[: ln - 1]))
x.sort()
for it in x:
if it > s[-1]:
s = s[: ln - 1] + it
return s
else:
for i in range(ln - 1, -1, -1):
x = s[:i]
while x[-1] < "9":
x = str(int(x) + 1)
if len(set(x)) <= k:
if len(set(x)) == k:
x = x + (ln - len(x)) * min(set(x))
return x
else:
x = x + (ln - len(x)) * "0"
return x
def solve(s, k):
if len(set(str(s))) <= k:
return s
s = str(s)
for i in range(len(s)):
if len(set(s[: i + 1])) > k:
break
i += 1
x = s[:i]
x = find_nearest(x, k)
ans = x + (len(s) - i) * min(set(x))
return ans
n = int(input())
for _ in range(n):
s, k = [int(i) for i in input().split()]
print(solve(s, k)) | FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FOR VAR VAR IF VAR VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP VAR NUMBER VAR RETURN VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER NUMBER ASSIGN VAR VAR VAR WHILE VAR NUMBER STRING ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR NUMBER IF FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP BIN_OP VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR RETURN VAR ASSIGN VAR BIN_OP VAR BIN_OP BIN_OP VAR FUNC_CALL VAR VAR STRING RETURN VAR FUNC_DEF IF FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR RETURN VAR ASSIGN VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR VAR NUMBER ASSIGN VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR RETURN VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def getBeautiful(num, k):
if len(set(str(num))) <= k:
return num
unstableIdx = k
st = str(num)
digits = set(map(int, set(st[:unstableIdx])))
while int(st[unstableIdx]) in digits or len(digits) < k:
if unstableIdx != len(st) - 1:
digits.add(int(st[unstableIdx]))
unstableIdx += 1
else:
return num
n = int(st[unstableIdx])
while n not in digits:
n += 1
if n == 10:
break
if n in digits:
return int(
st[:unstableIdx] + str(n) + str(min(digits)) * (len(st) - unstableIdx - 1)
)
else:
return getBeautiful(
(int(st[:unstableIdx]) + 1) * 10 ** (len(st) - unstableIdx), k
)
for t in range(int(input())):
n, k = map(int, input().split())
print(getBeautiful(n, k)) | FUNC_DEF IF FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR RETURN VAR ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR WHILE FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR VAR IF VAR BIN_OP FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR NUMBER RETURN VAR ASSIGN VAR FUNC_CALL VAR VAR VAR WHILE VAR VAR VAR NUMBER IF VAR NUMBER IF VAR VAR RETURN FUNC_CALL VAR BIN_OP BIN_OP VAR VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER RETURN FUNC_CALL VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER BIN_OP NUMBER BIN_OP FUNC_CALL VAR VAR VAR VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for _ in range(int(input())):
n, k = map(int, input().split())
s = str(n)
if k == 1:
if int(s[0] * len(s)) >= n:
print(s[0] * len(s))
else:
print(str(int(s[0]) + 1) * len(s))
continue
dg, prob = set(), False
for i, v in enumerate(s):
if v not in dg:
if len(dg) < k:
dg.add(v)
else:
prob = i
break
if not prob:
print(n)
else:
res, g = s[prob:], max(dg)
if int(str(g) * len(res)) >= int(res):
ans = s[:prob]
for i in range(prob, len(s)):
if s[i] in dg:
ans += s[i]
else:
ans += min(d for d in dg if d > s[i])
omp = len(s) - len(ans)
ans += min(dg) * omp
break
print(ans)
else:
for i in range(prob - 1, -1, -1):
if s[i] < g:
prob = i
break
if s[prob] in s[:prob]:
ans = s[:prob]
ans += min(d for d in dg if d > s[prob])
omp = len(s) - len(ans)
ans += min(dg) * omp
else:
dg.remove(s[prob])
ans = s[:prob]
nou = str(int(s[prob]) + 1)
ans += nou
if nou in dg:
dg.add("0")
omp = len(s) - len(ans)
ans += min(dg) * omp
dg, k = set(), k - 1
for i, v in enumerate(s):
if v not in dg:
if len(dg) < k:
dg.add(v)
else:
prob = i
break
ans2 = s[:prob]
nou = str(int(s[prob]) + 1)
ans2 += nou
dg.add(nou)
omp = len(s) - len(ans2)
ans2 += min(dg) * omp
print(min(ans, ans2)) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR IF VAR NUMBER IF FUNC_CALL VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR NUMBER NUMBER FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR VAR IF VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR FOR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR VAR VAR VAR FUNC_CALL VAR VAR VAR VAR VAR VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR BIN_OP FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER NUMBER IF VAR VAR VAR ASSIGN VAR VAR IF VAR VAR VAR VAR ASSIGN VAR VAR VAR VAR FUNC_CALL VAR VAR VAR VAR VAR VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR BIN_OP FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR VAR IF VAR VAR EXPR FUNC_CALL VAR STRING ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR BIN_OP FUNC_CALL VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR BIN_OP FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | from sys import stdin, stdout
def find_next_big(d, dic):
for i in range(d + 1, 10):
if dic[i] > 0:
return i
return -1
def find_min(dic):
for i in range(0, 10):
if dic[i] > 0:
return i
return -1
def find_cnt(dic):
cnt = 0
for i in range(0, 10):
if dic[i] > 0:
cnt += 1
return cnt
def solve(n, k):
dic = {}
for i in range(10):
dic[i] = 0
sn = str(n)
ck = 0
for i in range(len(sn)):
d = ord(sn[i]) - ord("0")
if dic[d] == 0:
if ck == k:
nb = find_next_big(d, dic)
if nb >= 0:
cm = find_min(dic)
res = sn[:i] + str(nb) + str(cm) * (len(sn) - i - 1)
return res
else:
j = i - 1
tv = -1
while dic[ord(sn[j]) - ord("0")] != 1:
tv = find_next_big(ord(sn[j]) - ord("0"), dic)
if tv != -1:
break
dic[ord(sn[j]) - ord("0")] -= 1
j -= 1
pv = ord(sn[j]) - ord("0")
if tv == -1:
tv = pv + 1
dic[tv] += 1
dic[pv] -= 1
if find_cnt(dic) < k:
res = sn[:j] + str(tv) + "0" * (len(sn) - j - 1)
else:
cm = find_min(dic)
res = sn[:j] + str(tv) + str(cm) * (len(sn) - j - 1)
return res
ck += 1
dic[d] += 1
return sn
t = int(stdin.readline())
for _ in range(t):
n, k = map(int, stdin.readline().split())
r = solve(n, k)
stdout.write(r + "\n") | FUNC_DEF FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER IF VAR VAR NUMBER RETURN VAR RETURN NUMBER FUNC_DEF FOR VAR FUNC_CALL VAR NUMBER NUMBER IF VAR VAR NUMBER RETURN VAR RETURN NUMBER FUNC_DEF ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER NUMBER IF VAR VAR NUMBER VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR DICT FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR FUNC_CALL VAR STRING IF VAR VAR NUMBER IF VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER RETURN VAR ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR NUMBER WHILE VAR BIN_OP FUNC_CALL VAR VAR VAR FUNC_CALL VAR STRING NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR FUNC_CALL VAR STRING VAR IF VAR NUMBER VAR BIN_OP FUNC_CALL VAR VAR VAR FUNC_CALL VAR STRING NUMBER VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR FUNC_CALL VAR STRING IF VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR VAR NUMBER VAR VAR NUMBER IF FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR FUNC_CALL VAR VAR BIN_OP STRING BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER RETURN VAR VAR NUMBER VAR VAR NUMBER RETURN VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR STRING |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def main(t):
n, k = map(int, input().split())
s = str(n)
m = len(s)
dic = {}
ans = ""
for i in range(m):
if s[i] in dic:
dic[s[i]] += 1
else:
dic[s[i]] = 1
if len(dic) == k and i < m - 1:
if s[i + 1 :] > max(dic) * (m - i - 1):
dic[s[i]] -= 1
if dic[s[i]] == 0:
del dic[s[i]]
if str(int(s[i]) + 1) in dic and len(dic) < k:
ans += str(int(s[i]) + 1)
ans += "0" * (m - i - 1)
else:
dic[str(int(s[i]) + 1)] = 1
ans += str(int(s[i]) + 1)
ans += min(dic) * (m - i - 1)
break
else:
ans += s[i]
broken = i + 1
flag = True
for j in range(i + 1, m):
if s[j] < max(dic):
broken = j
if s[j] not in dic:
flag = False
break
if flag:
broken = m
ans += s[i + 1 : broken]
if broken == m:
break
for d in range(int(s[broken]) + 1, 10):
if str(d) in dic:
break
dic[str(d)] = 1
ans += str(d)
ans += min(dic) * (m - len(ans))
break
ans += s[i]
print(ans)
T = int(input())
t = 1
while t <= T:
main(t)
t += 1 | FUNC_DEF ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR DICT ASSIGN VAR STRING FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR VAR VAR NUMBER ASSIGN VAR VAR VAR NUMBER IF FUNC_CALL VAR VAR VAR VAR BIN_OP VAR NUMBER IF VAR BIN_OP VAR NUMBER BIN_OP FUNC_CALL VAR VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR VAR NUMBER IF VAR VAR VAR NUMBER VAR VAR VAR IF FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR BIN_OP STRING BIN_OP BIN_OP VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER NUMBER VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR BIN_OP FUNC_CALL VAR VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR IF VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR IF VAR VAR VAR ASSIGN VAR NUMBER IF VAR ASSIGN VAR VAR VAR VAR BIN_OP VAR NUMBER VAR IF VAR VAR FOR VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER NUMBER IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER VAR FUNC_CALL VAR VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP VAR FUNC_CALL VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR NUMBER WHILE VAR VAR EXPR FUNC_CALL VAR VAR VAR NUMBER |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for _ in range(int(input())):
n, k = map(int, input().split())
d = [int(x) for x in str(n)]
l = len(d)
if n == 1000000000:
print(1111111111 if k == 1 else 1000000000)
continue
if k >= len(set(d)):
print(n)
continue
mn = 10**15
for i in range(l):
for v in range(d[i] + 1, 10):
uniq = set(d[:i]) | {v}
if len(uniq) > k:
continue
elif len(uniq) < k:
uniq |= {0}
nd = d[:i] + [v] + [min(uniq)] * (l - i - 1)
nn = int("".join(map(str, nd)))
if nn < mn:
mn = nn
print(mn) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR VAR NUMBER NUMBER NUMBER IF VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP NUMBER NUMBER FOR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR VAR NUMBER NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR VAR IF FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR VAR LIST VAR BIN_OP LIST FUNC_CALL VAR VAR BIN_OP BIN_OP VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR IF VAR VAR ASSIGN VAR VAR EXPR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | from sys import stdin, stdout
input = stdin.readline
t = int(input())
for _ in range(t):
n, k = map(int, input().split())
arr = [i for i in str(n)]
l = len(arr)
if len(set(arr)) <= k:
print(n)
continue
ans = -1
for i in range(0, l):
s = set()
vals = []
for j in arr[:i]:
s.add(j)
vals.append(j)
p = len(s)
if p > k or arr[i] == "9":
continue
if p < k:
vals.append(str(int(arr[i]) + 1))
s.add(str(int(arr[i]) + 1))
else:
mi = float("inf")
for j in s:
if int(j) > int(arr[i]):
mi = min(mi, int(j))
if mi == float("inf"):
continue
vals.append(str(mi))
mi = 0
p = len(s)
if p == k:
mi = float("inf")
for j in s:
mi = min(mi, int(j))
mi = str(mi)
for j in arr[i + 1 :]:
vals.append(str(mi))
ans = "".join(vals)
try:
ans = int(ans)
print(ans)
except:
print(n, k, ans) | ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF VAR VAR VAR VAR STRING IF VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR STRING FOR VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF VAR FUNC_CALL VAR STRING EXPR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR IF VAR VAR ASSIGN VAR FUNC_CALL VAR STRING FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FOR VAR VAR BIN_OP VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL STRING VAR ASSIGN VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | t = int(input())
some_list = []
for i in range(t):
some_list.append(input())
for i in range(t):
n_k = some_list[i].split()
n = int(n_k[0])
k = int(n_k[1])
x = n
while len(set(str(n))) > k:
if n % 10 == 0:
n = n // 10
else:
n += 1
end = str(min(str(n))) * (len(str(x)) - len(str(n)))
print(int(str(n) + end)) | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR VAR WHILE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER ASSIGN VAR BIN_OP VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys as _sys
def _main():
[tests_n] = _read_ints()
for i_test in range(tests_n):
[n, k] = _read_ints()
result = find_nearest_beautiful_number(lower_bound=n, k_parameter=k)
print(result)
def find_nearest_beautiful_number(lower_bound: int, k_parameter: int):
prefix = lower_bound
while not _is_beautiful(prefix, k_parameter):
if prefix % 10 == 0:
prefix //= 10
else:
prefix += 1
zeros_n = len(str(lower_bound)) - len(str(prefix))
tail_digit = "0" if _measure_k(prefix) < k_parameter else min(str(prefix))
tail = int(tail_digit * zeros_n) if zeros_n > 0 else 0
return prefix * 10**zeros_n + tail
def _is_beautiful(x: int, k_parameter: int):
return _measure_k(x) <= k_parameter
def _measure_k(x: int):
assert x >= 1
return len(set(str(x)))
def _read_ints():
return map(int, _sys.stdin.readline().split())
_main() | IMPORT FUNC_DEF ASSIGN LIST VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN LIST VAR VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR FUNC_DEF VAR VAR ASSIGN VAR VAR WHILE FUNC_CALL VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER FUNC_CALL VAR BIN_OP VAR VAR NUMBER RETURN BIN_OP BIN_OP VAR BIN_OP NUMBER VAR VAR FUNC_DEF VAR VAR RETURN FUNC_CALL VAR VAR VAR FUNC_DEF VAR VAR NUMBER RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
input = sys.stdin.readline
def inp():
return int(input())
def input_list():
return list(map(int, input().split()))
def input_string():
s = input()
return list(s[: len(s) - 1])
def input_int_gen():
return map(int, input().split())
def largest(using, n_digits):
return (10**n_digits - 1) // 9 * max(using)
def smallest(using, n_digits, zero_allowed=False):
if zero_allowed:
return 0
return (10**n_digits - 1) // 9 * min(using)
def lowest_greater_single(using, n):
return min([x for x in using if x > n], default=-1)
def lowest_greater(using, mini, n_digits):
highest = mini // 10 ** (n_digits - 1)
rem = mini % 10 ** (n_digits - 1)
if n_digits == 1:
return mini if mini in using else lowest_greater_single(using, mini)
if highest in using:
if rem > largest(using, n_digits - 1):
if lowest_greater_single(using, highest) == -1:
return -1
return lowest_greater_single(using, highest) * 10 ** (
n_digits - 1
) + smallest(using, n_digits - 1)
else:
return highest * 10 ** (n_digits - 1) + lowest_greater(
using, rem, n_digits - 1
)
else:
if lowest_greater_single(using, highest) == -1:
return -1
return lowest_greater_single(using, highest) * 10 ** (n_digits - 1) + smallest(
using, n_digits - 1
)
def nbn(mini, using, n_digits, k):
if n_digits == 1:
if mini in using or k > len(using):
return mini
return lowest_greater_single(using, mini)
if len(using) == k:
return lowest_greater(using, mini, n_digits)
else:
highest = mini // 10 ** (n_digits - 1)
rem = mini % 10 ** (n_digits - 1)
if highest in using:
res = nbn(rem, using, n_digits - 1, k)
return highest * 10 ** (n_digits - 1) + res
else:
res = nbn(rem, using | {highest}, n_digits - 1, k)
if res != -1:
return highest * 10 ** (n_digits - 1) + res
else:
return (highest + 1) * 10 ** (n_digits - 1) + smallest(
using | {highest + 1}, n_digits - 1, len(using | {highest + 1}) < k
)
tests = inp()
for _ in range(tests):
n, k = input_int_gen()
print(nbn(n, set(), len(str(n)), k)) | IMPORT ASSIGN VAR VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR FUNC_DEF RETURN FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR RETURN FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR NUMBER FUNC_DEF RETURN FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR FUNC_DEF RETURN BIN_OP BIN_OP BIN_OP BIN_OP NUMBER VAR NUMBER NUMBER FUNC_CALL VAR VAR FUNC_DEF NUMBER IF VAR RETURN NUMBER RETURN BIN_OP BIN_OP BIN_OP BIN_OP NUMBER VAR NUMBER NUMBER FUNC_CALL VAR VAR FUNC_DEF RETURN FUNC_CALL VAR VAR VAR VAR VAR VAR NUMBER FUNC_DEF ASSIGN VAR BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER IF VAR NUMBER RETURN VAR VAR VAR FUNC_CALL VAR VAR VAR IF VAR VAR IF VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR VAR NUMBER RETURN NUMBER RETURN BIN_OP BIN_OP FUNC_CALL VAR VAR VAR BIN_OP NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER RETURN BIN_OP BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER IF FUNC_CALL VAR VAR VAR NUMBER RETURN NUMBER RETURN BIN_OP BIN_OP FUNC_CALL VAR VAR VAR BIN_OP NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR VAR BIN_OP VAR NUMBER FUNC_DEF IF VAR NUMBER IF VAR VAR VAR FUNC_CALL VAR VAR RETURN VAR RETURN FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR RETURN FUNC_CALL VAR VAR VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER IF VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR BIN_OP VAR NUMBER VAR RETURN BIN_OP BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR BIN_OP VAR VAR BIN_OP VAR NUMBER VAR IF VAR NUMBER RETURN BIN_OP BIN_OP VAR BIN_OP NUMBER BIN_OP VAR NUMBER VAR RETURN BIN_OP BIN_OP BIN_OP VAR NUMBER BIN_OP NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR BIN_OP VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER FUNC_CALL VAR BIN_OP VAR BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def first_bad(A, k):
seen = [0] * 10
for i, a in enumerate(A):
if seen[a] == 0:
k -= 1
seen[a] = 1
if k < 0:
return i
return -1
t = int(input())
for _ in range(t):
n, k = [int(x) for x in input().split()]
A = [(ord(c) - ord("0")) for c in str(n)]
while True:
i = first_bad(A, k)
if i == -1:
break
A[i] += 1
while i and A[i] == 10:
i -= 1
A[i] += 1
for j in range(i + 1, len(A)):
A[j] = 0
print("".join(str(x) for x in A)) | FUNC_DEF ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER VAR NUMBER ASSIGN VAR VAR NUMBER IF VAR NUMBER RETURN VAR RETURN NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR STRING VAR FUNC_CALL VAR VAR WHILE NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER VAR VAR NUMBER WHILE VAR VAR VAR NUMBER VAR NUMBER VAR VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER FUNC_CALL VAR VAR ASSIGN VAR VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def find_lsb(mask):
if mask == 0:
return -1
lsb = 0
while True:
if mask & 1 << lsb:
break
lsb += 1
return lsb
def solve(n, k):
mask = 0
cnt = 0
for c in n:
if mask & 1 << int(c):
continue
cnt += 1
mask |= 1 << int(c)
if cnt <= k:
return True
else:
return False
def main():
t = int(input())
for tc in range(t):
n, k = map(int, input().split())
n = str(n)
backup_k = k
if k == 1:
res = "1" * (len(n) + 1)
for i in range(10):
cur = str(i) * len(n)
if int(cur) >= int(n):
res = cur
break
print(res)
continue
res = "1" + "0" * len(n)
mask = 0
cur = ""
for i in range(len(n)):
c = int(n[i])
for j in range(c + 1, 10):
rem_k = k
if mask & 1 << j == 0:
rem_k -= 1
if rem_k < 0:
continue
nmask = mask | 1 << j
if rem_k > 0:
nmask |= 1 << 0
temp = cur + str(j)
temp = temp + str(find_lsb(nmask)) * (len(n) - len(temp))
if int(temp) >= int(n) and int(temp) <= int(res):
res = temp
if mask & 1 << c:
cur = cur + n[i]
continue
if k > 0:
k -= 1
mask = mask | 1 << c
cur = cur + n[i]
else:
for i in range(c + 1, 10):
if mask & 1 << i:
cur = cur + str(i)
cur = cur + str(find_lsb(mask)) * (len(n) - len(cur))
if int(cur) >= int(n) and int(cur) <= int(res):
res = cur
break
if int(cur) >= int(n) and int(cur) <= int(res):
res = cur
print(res)
main() | FUNC_DEF IF VAR NUMBER RETURN NUMBER ASSIGN VAR NUMBER WHILE NUMBER IF BIN_OP VAR BIN_OP NUMBER VAR VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR IF BIN_OP VAR BIN_OP NUMBER FUNC_CALL VAR VAR VAR NUMBER VAR BIN_OP NUMBER FUNC_CALL VAR VAR IF VAR VAR RETURN NUMBER RETURN NUMBER FUNC_DEF ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR VAR IF VAR NUMBER ASSIGN VAR BIN_OP STRING BIN_OP FUNC_CALL VAR VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP STRING BIN_OP STRING FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR STRING FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER ASSIGN VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR NUMBER VAR NUMBER IF VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP NUMBER VAR IF VAR NUMBER VAR BIN_OP NUMBER NUMBER ASSIGN VAR BIN_OP VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR IF BIN_OP VAR BIN_OP NUMBER VAR ASSIGN VAR BIN_OP VAR VAR VAR IF VAR NUMBER VAR NUMBER ASSIGN VAR BIN_OP VAR BIN_OP NUMBER VAR ASSIGN VAR BIN_OP VAR VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER IF BIN_OP VAR BIN_OP NUMBER VAR ASSIGN VAR BIN_OP VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
def main(N, K):
S = str(N)
d = len(S)
if d <= K:
return N
if len(set(S)) <= K:
return N
for i in range(d - 1, -1, -1):
up = set(S[:i])
if len(up) > K:
continue
if len(up) == K:
n = int(S[i])
for m in sorted(up):
if int(m) > n:
break
else:
continue
res = S[:i] + m
mn = min(up)
for _ in range(i + 1, d):
res += mn
return int(res)
n = int(S[i])
if n == 9:
continue
m = str(n + 1)
res = S[:i] + m
up.add(m)
if len(up) == K:
mn = min(up)
for _ in range(i + 1, d):
res += mn
return int(res)
for _ in range(i + 1, d):
res += "0"
return int(res)
input = sys.stdin.readline
T = int(input())
for _ in range(T):
N, K = map(int, input().split())
print(main(N, K)) | IMPORT FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR IF VAR VAR RETURN VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR VAR RETURN VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR VAR RETURN FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP VAR VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR VAR RETURN FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR VAR STRING RETURN FUNC_CALL VAR VAR ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
input = sys.stdin.readline
bits = [[] for _ in range(11)]
for bit in range(1 << 10):
se = set()
for i in range(10):
if bit >> i & 1:
se.add(i)
bits[len(se)].append(se)
def main():
n, k = input().strip().split()
k = int(k)
l = len(n)
times = (10**l - 1) // 9
min_ = 10**20
N = int(n)
se_ = set()
ans_ = []
for s in n:
if len(se_) >= k - 2:
break
s = int(s)
se_.add(s)
ans_.append(s)
if len(ans_) == l:
print(n)
return
n = n[len(ans_) :]
l = len(n)
for se2 in bits[min(k, 2)]:
se = se2 | se_
if max(se) * times < N:
continue
tmp = -1
nex = [-1] * 10
for i in range(9, -1, -1):
if i in se:
tmp = i
nex[i] = tmp
ans = ans_.copy()
flg = False
for i in range(l):
if flg:
ans.append(nex[0])
continue
s = int(n[i])
t = nex[s]
if t == s:
ans.append(s)
elif t != -1:
ans.append(t)
flg = True
else:
cnt = 1
while 1:
s = ans[-1]
ans.pop()
if nex[s + 1] != -1:
ans.append(nex[s + 1])
break
cnt += 1
for _ in range(cnt):
ans.append(nex[0])
flg = True
min_ = min(min_, int("".join(map(str, ans))))
print(min_)
for _ in range(int(input())):
main() | IMPORT ASSIGN VAR VAR ASSIGN VAR LIST VAR FUNC_CALL VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR NUMBER IF BIN_OP BIN_OP VAR VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_DEF ASSIGN VAR VAR FUNC_CALL FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP BIN_OP NUMBER VAR NUMBER NUMBER ASSIGN VAR BIN_OP NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR VAR IF FUNC_CALL VAR VAR BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR RETURN ASSIGN VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FOR VAR VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR BIN_OP VAR VAR IF BIN_OP FUNC_CALL VAR VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER FOR VAR FUNC_CALL VAR NUMBER NUMBER NUMBER IF VAR VAR ASSIGN VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR EXPR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR VAR VAR IF VAR VAR EXPR FUNC_CALL VAR VAR IF VAR NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER WHILE NUMBER ASSIGN VAR VAR NUMBER EXPR FUNC_CALL VAR IF VAR BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR NUMBER ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR EXPR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for s in [*open(0)][1:]:
prefix, k = map(int, s.split())
n = str(prefix)
while len(set(str(prefix))) > k:
prefix = prefix // 10 if not prefix % 10 else prefix + 1
prefix = str(prefix)
x = len(n) - len(prefix)
suffix = str(min(prefix) * x)
print(prefix + suffix) | FOR VAR LIST FUNC_CALL VAR NUMBER NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR WHILE FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR BIN_OP VAR NUMBER BIN_OP VAR NUMBER BIN_OP VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
input = sys.stdin.readline
for _ in range(int(input())):
n, k = [int(i) for i in input().split()]
sn = [int(i) for i in str(n)]
s = set()
ans = []
for i in sn:
if i in s:
ans.append(i)
elif len(s) < k:
s.add(i)
ans.append(i)
else:
flag = 0
for j in range(1, 10):
if i + j in s:
ans.append(i + j)
flag = 1
break
if flag:
ans.extend([min(ans)] * (len(sn) - len(ans)))
else:
while len(ans):
if ans.count(ans[-1]) == 1:
s.remove(ans[-1])
s.add(ans[-1] + 1)
ans.append(ans.pop() + 1)
break
else:
flag1 = 0
for j in range(1, 10):
if ans[-1] + j in s:
flag1 = ans[-1] + j
break
if flag1:
ans.pop()
ans.append(flag1)
break
else:
ans.pop()
if len(s) == k:
ans.extend([min(ans)] * (len(sn) - len(ans)))
else:
ans.extend([0] * (len(sn) - len(ans)))
break
for i in ans:
print(i, end="")
print() | IMPORT ASSIGN VAR VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR LIST FOR VAR VAR IF VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER NUMBER IF BIN_OP VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR VAR ASSIGN VAR NUMBER IF VAR EXPR FUNC_CALL VAR BIN_OP LIST FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR WHILE FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR NUMBER NUMBER EXPR FUNC_CALL VAR VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR NUMBER NUMBER IF BIN_OP VAR NUMBER VAR VAR ASSIGN VAR BIN_OP VAR NUMBER VAR IF VAR EXPR FUNC_CALL VAR EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP LIST FUNC_CALL VAR VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP LIST NUMBER BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR FOR VAR VAR EXPR FUNC_CALL VAR VAR STRING EXPR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def number(L):
r = 0
for d in L:
r = r * 10 + int(d)
return r
def go(n, i, D, eq):
if i == len(n):
return True, []
if eq:
for d in D:
if n[i] == d:
flag, x = go(n, i + 1, D, True)
if flag:
return True, [d] + x
if n[i] < d:
flag, x = go(n, i + 1, D, False)
if flag:
return True, [d] + x
return False, []
else:
flag, x = go(n, i + 1, D, False)
return True, [D[0]] + x
def find(n, k):
if len(set(n)) == 1:
return n
D = []
for d in map(int, n):
if d not in D:
D.append(d)
if len(D) <= k:
return n
U = [D[:k]]
E = D[:k]
if E[-1] + 1 in E:
E[-1] = 0
else:
E[-1] = (E[-1] + 1) % 10
U.append(E)
r = 10**20
for digits in U:
x = []
digits.sort()
flag, x = go(list(map(int, n)), 0, digits, True)
if flag:
r = min(r, number(x))
return r
T = int(input())
for _ in range(T):
n, k = input().split(" ")
k = int(k)
print(find(n, k)) | FUNC_DEF ASSIGN VAR NUMBER FOR VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR NUMBER FUNC_CALL VAR VAR RETURN VAR FUNC_DEF IF VAR FUNC_CALL VAR VAR RETURN NUMBER LIST IF VAR FOR VAR VAR IF VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR RETURN NUMBER BIN_OP LIST VAR VAR IF VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR NUMBER IF VAR RETURN NUMBER BIN_OP LIST VAR VAR RETURN NUMBER LIST ASSIGN VAR VAR FUNC_CALL VAR VAR BIN_OP VAR NUMBER VAR NUMBER RETURN NUMBER BIN_OP LIST VAR NUMBER VAR FUNC_DEF IF FUNC_CALL VAR FUNC_CALL VAR VAR NUMBER RETURN VAR ASSIGN VAR LIST FOR VAR FUNC_CALL VAR VAR VAR IF VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR RETURN VAR ASSIGN VAR LIST VAR VAR ASSIGN VAR VAR VAR IF BIN_OP VAR NUMBER NUMBER VAR ASSIGN VAR NUMBER NUMBER ASSIGN VAR NUMBER BIN_OP BIN_OP VAR NUMBER NUMBER NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP NUMBER NUMBER FOR VAR VAR ASSIGN VAR LIST EXPR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER IF VAR ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR RETURN VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR STRING ASSIGN VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | t = int(input())
while t:
num, k = [int(tok) for tok in input().split()]
ans = 111111111111111
num = str(num)
n = len(num)
s = set()
for ch in num:
s.add(ch)
if len(s) <= k:
print(int(num))
else:
for ind in range(0, n):
if num[ind] == "9":
continue
done = set()
for i in range(0, ind):
done.add(num[i])
if len(done) > k:
continue
elif len(done) == k:
to_fill = None
mi = "9"
for el in done:
mi = min(mi, el)
if el > num[ind]:
if to_fill is None:
to_fill = el
else:
to_fill = min(to_fill, el)
if to_fill is not None:
ans = min(ans, int(num[:ind] + to_fill + mi * (n - ind - 1)))
else:
mi = "9"
for i in range(0, 9):
if str(i) > num[ind]:
mi = str(i)
break
done.add(mi)
if len(done) == k:
ans = min(ans, int(num[:ind] + mi + min(done) * (n - ind - 1)))
else:
ans = min(ans, int(num[:ind] + mi + "0" * (n - ind - 1)))
print(ans)
t -= 1 | ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR WHILE VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FOR VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR NUMBER VAR IF VAR VAR STRING ASSIGN VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR NUMBER VAR EXPR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR NONE ASSIGN VAR STRING FOR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR VAR VAR IF VAR NONE ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR IF VAR NONE ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR VAR BIN_OP VAR BIN_OP BIN_OP VAR VAR NUMBER ASSIGN VAR STRING FOR VAR FUNC_CALL VAR NUMBER NUMBER IF FUNC_CALL VAR VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP BIN_OP VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR FUNC_CALL VAR BIN_OP BIN_OP VAR VAR VAR BIN_OP STRING BIN_OP BIN_OP VAR VAR NUMBER EXPR FUNC_CALL VAR VAR VAR NUMBER |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
import time
input = sys.stdin.readline
def main():
t = int(input())
for _ in range(t):
n, k = list(map(int, input().split()))
digits = len(str(n))
first = str(n)[0]
if digits == 1:
print(n)
continue
if k == 1:
if int(first * digits) >= n:
print(first * digits)
else:
print(str(int(first) + 1) * digits)
continue
m = str(n)
picked = [first]
picked_list = [(i == int(first)) for i in range(10)]
left = k - 1
res = ""
big = 0
maxx = int(first)
for i in range(digits):
if big:
if left == 1:
res += (digits - i) * "0"
else:
res += (digits - i) * str(min([int(j) for j in picked]))
break
if left == 0:
minpicked = str(min([int(j) for j in picked if int(j) >= int(m[i])]))
if int(minpicked) > int(m[i]):
res += minpicked
big = 1
continue
if int(res + m[i] + str(maxx) * (digits - i - 1)) >= n:
res += minpicked
continue
else:
res += str(
sorted([int(j) for j in picked if int(j) >= int(m[i])])[1]
)
big = 1
continue
if picked_list[int(m[i])]:
res += m[i]
continue
if left >= 2:
maxx = max(int(m[i]), maxx)
picked.append(m[i])
picked_list[int(m[i])] = True
left -= 1
res += m[i]
continue
if left == 1:
if int(res + m[i] + str(max(maxx, int(m[i]))) * (digits - i - 1)) >= n:
maxx = max(int(m[i]), maxx)
picked.append(m[i])
picked_list[int(m[i])] = True
left = 0
res += m[i]
continue
else:
big = 1
if picked_list[int(m[i]) + 1]:
res += str(int(m[i]) + 1)
else:
left -= 1
picked.append(str(int(m[i]) + 1))
picked_list[int(m[i]) + 1] = True
maxx = max(int(m[i]) + 1, maxx)
res += str(int(m[i]) + 1)
continue
print(res)
main() | IMPORT IMPORT ASSIGN VAR VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER IF VAR NUMBER EXPR FUNC_CALL VAR VAR IF VAR NUMBER IF FUNC_CALL VAR BIN_OP VAR VAR VAR EXPR FUNC_CALL VAR BIN_OP VAR VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR LIST VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER ASSIGN VAR STRING ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR VAR IF VAR IF VAR NUMBER VAR BIN_OP BIN_OP VAR VAR STRING VAR BIN_OP BIN_OP VAR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR VAR VAR ASSIGN VAR NUMBER IF FUNC_CALL VAR BIN_OP BIN_OP VAR VAR VAR BIN_OP FUNC_CALL VAR VAR BIN_OP BIN_OP VAR VAR NUMBER VAR VAR VAR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR NUMBER IF VAR FUNC_CALL VAR VAR VAR VAR VAR VAR IF VAR NUMBER ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER VAR VAR VAR IF VAR NUMBER IF FUNC_CALL VAR BIN_OP BIN_OP VAR VAR VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR BIN_OP BIN_OP VAR VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR VAR EXPR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR NUMBER VAR VAR VAR ASSIGN VAR NUMBER IF VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER ASSIGN VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER VAR VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
def get_digits(n):
digits = []
while n != 0:
digits.append(n % 10)
n = n // 10
return digits[::-1]
def construct(digits):
result = 0
power = 1
for d in digits[::-1]:
result += power * d
power *= 10
return result
def solve(n, k):
digits = get_digits(n)
if len(set(digits)) <= k:
return n
met = [(False) for _ in range(10)]
counter = 0
for i, d in enumerate(digits):
if met[d] == True:
continue
if counter == k:
break
met[d] = True
counter += 1
for t in range(digits[i] + 1, 10):
if met[t] == True:
answer = digits[:i] + [t] + [min(digits[:i])] * (len(digits) - i - 1)
return construct(answer)
prefix = construct(digits[:i])
sub_answer = get_digits(solve(prefix + 1, k))
sub_k = len(set(sub_answer))
if sub_k < k:
filler = 0
else:
filler = min(sub_answer)
answer = sub_answer + [filler] * (len(digits) - len(sub_answer))
return construct(answer)
def main():
outputs = []
fin = sys.stdin
N = int(fin.readline())
for _ in range(N):
n, k = map(int, fin.readline().split())
outputs.append(solve(n, k))
print("\n".join(map(str, outputs)))
main() | IMPORT FUNC_DEF ASSIGN VAR LIST WHILE VAR NUMBER EXPR FUNC_CALL VAR BIN_OP VAR NUMBER ASSIGN VAR BIN_OP VAR NUMBER RETURN VAR NUMBER FUNC_DEF ASSIGN VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR NUMBER VAR BIN_OP VAR VAR VAR NUMBER RETURN VAR FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR VAR RETURN VAR ASSIGN VAR NUMBER VAR FUNC_CALL VAR NUMBER ASSIGN VAR NUMBER FOR VAR VAR FUNC_CALL VAR VAR IF VAR VAR NUMBER IF VAR VAR ASSIGN VAR VAR NUMBER VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR VAR NUMBER NUMBER IF VAR VAR NUMBER ASSIGN VAR BIN_OP BIN_OP VAR VAR LIST VAR BIN_OP LIST FUNC_CALL VAR VAR VAR BIN_OP BIN_OP FUNC_CALL VAR VAR VAR NUMBER RETURN FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR VAR ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP LIST VAR BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR RETURN FUNC_CALL VAR VAR FUNC_DEF ASSIGN VAR LIST ASSIGN VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL STRING FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | for _ in range(int(input())):
n, k = input().split()
k = int(k)
m = len(n)
d = {}
i = 0
for i in range(m):
if n[i] not in d:
if len(d) == k:
break
d[n[i]] = 0
d[n[i]] += 1
else:
print(n)
continue
n = list(n)
while True:
if n[i] == "9" or len(d) == k and max(d) <= n[i]:
i -= 1
d[n[i]] -= 1
if d[n[i]] == 0:
del d[n[i]]
else:
if len(d) < k:
n[i] = str(int(n[i]) + 1)
if n[i] not in d:
d[n[i]] = 0
d[n[i]] += 1
p = "0" if len(d) < k else min(d)
for i in range(i + 1, m):
n[i] = p
else:
n[i] = min(j for j in d if j > n[i])
for i in range(i + 1, m):
n[i] = min(d)
break
print("".join(n)) | FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR DICT ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR VAR IF VAR VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR VAR VAR NUMBER VAR VAR VAR NUMBER EXPR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR WHILE NUMBER IF VAR VAR STRING FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR VAR VAR VAR NUMBER VAR VAR VAR NUMBER IF VAR VAR VAR NUMBER VAR VAR VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR NUMBER IF VAR VAR VAR ASSIGN VAR VAR VAR NUMBER VAR VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR STRING FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR ASSIGN VAR VAR VAR ASSIGN VAR VAR FUNC_CALL VAR VAR VAR VAR VAR VAR VAR FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER VAR ASSIGN VAR VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR FUNC_CALL STRING VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
n = ""
k = l = 0
d = [0] * 9
def dfs(cur, dset):
p = len(cur)
if p == l:
return cur
if cur > n:
nd = 0
else:
nd = int(n[p])
for i in range(nd, 10):
if i in dset:
r = dfs(cur + str(i), dset)
if r != -1:
return r
elif len(dset) < k:
r = dfs(cur + str(i), dset | set([i]))
if r != -1:
return r
return -1
for _ in range(int(sys.stdin.readline())):
n, k = sys.stdin.readline().split()
k = int(k)
l = len(n)
sys.stdout.write(dfs("", set()) + "\n") | IMPORT ASSIGN VAR STRING ASSIGN VAR VAR NUMBER ASSIGN VAR BIN_OP LIST NUMBER NUMBER FUNC_DEF ASSIGN VAR FUNC_CALL VAR VAR IF VAR VAR RETURN VAR IF VAR VAR ASSIGN VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR VAR FOR VAR FUNC_CALL VAR VAR NUMBER IF VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP VAR FUNC_CALL VAR VAR VAR IF VAR NUMBER RETURN VAR IF FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP VAR FUNC_CALL VAR VAR BIN_OP VAR FUNC_CALL VAR LIST VAR IF VAR NUMBER RETURN VAR RETURN NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR VAR EXPR FUNC_CALL VAR BIN_OP FUNC_CALL VAR STRING FUNC_CALL VAR STRING |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def solve(n, k):
a = sorted((n.index(x), int(x)) for x in set(n))
if len(a) <= k:
return n
d = {x[1] for x in a[:k]}
for i in range(a[k][1], 10):
if i in d:
m = n[: a[k][0]] + str(i)
break
else:
m = solve(str(int(n[: a[k][0]]) + 1), k)
return m + (min(m) if len(set(m)) == k else "0") * (len(n) - len(m))
for _ in range(int(input())):
n, k = input().split()
print(solve(n, int(k))) | FUNC_DEF ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR RETURN VAR ASSIGN VAR VAR NUMBER VAR VAR VAR FOR VAR FUNC_CALL VAR VAR VAR NUMBER NUMBER IF VAR VAR ASSIGN VAR BIN_OP VAR VAR VAR NUMBER FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR VAR VAR NUMBER NUMBER VAR RETURN BIN_OP VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR VAR FUNC_CALL VAR VAR STRING BIN_OP FUNC_CALL VAR VAR FUNC_CALL VAR VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | import sys
t = int(input())
for i in range(t):
n, k = sys.stdin.readline().split()
n = n.lstrip("000000000")
k = int(k)
L = []
for s in n:
if int(s) not in L:
L.append(int(s))
if len(L) <= k:
print(n)
else:
L = L[:k]
Num = list(map(int, n))
ind = Num.index(L[-1])
maxL = max(L)
bada = False
i = 0
while i < len(n):
if bada:
Num[i] = 0
elif Num[i] > maxL:
bada = True
while Num[i] + 1 > maxL and i > ind:
i -= 1
Num[i] += 1
if i == ind:
L[-1] += 1
if L[-1] in L[:-1]:
L[-1] = 0
elif Num[i] not in L:
bada = True
i += 1
L.sort()
Go = dict()
ind = 0
for i in range(L[-1] + 1):
while i > L[ind]:
ind += 1
Go[i] = str(L[ind])
minL = str(L[0])
bada = False
for i in range(len(Num)):
if bada == True:
Num[i] = minL
else:
if Num[i] not in L:
bada = True
Num[i] = Go[Num[i]]
print(int("".join(Num))) | IMPORT ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR FOR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR STRING ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR LIST FOR VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR VAR EXPR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR ASSIGN VAR FUNC_CALL VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR NUMBER ASSIGN VAR NUMBER WHILE VAR FUNC_CALL VAR VAR IF VAR ASSIGN VAR VAR NUMBER IF VAR VAR VAR ASSIGN VAR NUMBER WHILE BIN_OP VAR VAR NUMBER VAR VAR VAR VAR NUMBER VAR VAR NUMBER IF VAR VAR VAR NUMBER NUMBER IF VAR NUMBER VAR NUMBER ASSIGN VAR NUMBER NUMBER IF VAR VAR VAR ASSIGN VAR NUMBER VAR NUMBER EXPR FUNC_CALL VAR ASSIGN VAR FUNC_CALL VAR ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR BIN_OP VAR NUMBER NUMBER WHILE VAR VAR VAR VAR NUMBER ASSIGN VAR VAR FUNC_CALL VAR VAR VAR ASSIGN VAR FUNC_CALL VAR VAR NUMBER ASSIGN VAR NUMBER FOR VAR FUNC_CALL VAR FUNC_CALL VAR VAR IF VAR NUMBER ASSIGN VAR VAR VAR IF VAR VAR VAR ASSIGN VAR NUMBER ASSIGN VAR VAR VAR VAR VAR EXPR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL STRING VAR |
It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \le 2$, F2: $k \le 10$).
You are given an integer $n$. Find the minimum integer $x$ such that $x \ge n$ and the number $x$ is $k$-beautiful.
A number is called $k$-beautiful if its decimal representation having no leading zeroes contains no more than $k$ different digits. E.g. if $k = 2$, the numbers $3434443$, $55550$, $777$ and $21$ are $k$-beautiful whereas the numbers $120$, $445435$ and $998244353$ are not.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.
Each test case consists of one line containing two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
-----Output-----
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
-----Examples-----
Input
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678
-----Note-----
None | def f(n, k):
dig_set = set()
pre = ""
for x in n:
dig_set.add(x)
if len(dig_set) > int(k):
post_head = x
dig_set.remove(x)
break
pre += x
post_head = ""
post = n[len(pre) :]
if post_head:
min_dig = min(dig_set)
poss_digs = {i for i in dig_set if i > x}
if poss_digs:
min_poss_dig = min(poss_digs)
ans = pre + min_poss_dig + min_dig * (len(post) - 1)
else:
pre = str(int(pre) + 1)
if len(set(pre)) == int(k):
ans = pre + min(set(pre)) * len(post)
elif len(set(pre)) < int(k):
ans = pre + "0" * len(post)
else:
ans = f(pre + "0" * len(post), k)
else:
ans = pre
return ans
for i in range(int(input())):
n, k = input().split()
print(f(n, k)) | FUNC_DEF ASSIGN VAR FUNC_CALL VAR ASSIGN VAR STRING FOR VAR VAR EXPR FUNC_CALL VAR VAR IF FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR VAR EXPR FUNC_CALL VAR VAR VAR VAR ASSIGN VAR STRING ASSIGN VAR VAR FUNC_CALL VAR VAR IF VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR VAR VAR VAR VAR VAR IF VAR ASSIGN VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP BIN_OP VAR VAR BIN_OP VAR BIN_OP FUNC_CALL VAR VAR NUMBER ASSIGN VAR FUNC_CALL VAR BIN_OP FUNC_CALL VAR VAR NUMBER IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR IF FUNC_CALL VAR FUNC_CALL VAR VAR FUNC_CALL VAR VAR ASSIGN VAR BIN_OP VAR BIN_OP STRING FUNC_CALL VAR VAR ASSIGN VAR FUNC_CALL VAR BIN_OP VAR BIN_OP STRING FUNC_CALL VAR VAR VAR ASSIGN VAR VAR RETURN VAR FOR VAR FUNC_CALL VAR FUNC_CALL VAR FUNC_CALL VAR ASSIGN VAR VAR FUNC_CALL FUNC_CALL VAR EXPR FUNC_CALL VAR FUNC_CALL VAR VAR VAR |
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