message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD | instruction | 0 | 9,708 | 16 | 19,416 |
"Correct Solution:
```
n = int(input())
grid = [list(map(int, input().split())) for i in range(n)]
for i in range(n - 1):
if (grid[i][0] + grid[i][1]) % 2 != (grid[i + 1][0] + grid[i + 1][1]) % 2:
print(-1)
exit()
m = 31
D = [2 ** i for i in range(m)]
if (grid[0][0] + grid[0][1]) % 2 == 0:
D.insert(0, 1)
m += 1
w = [[] for i in range(n)]
for i, g in enumerate(grid):
x, y = g
for d in D[::-1]:
if abs(x) >= abs(y):
if x > 0:
x -= d
w[i].append('R')
else:
x += d
w[i].append('L')
else:
if y > 0:
y -= d
w[i].append('U')
else:
y += d
w[i].append('D')
print(m)
print(*D)
for ans in w:
print(*ans[::-1], sep='')
``` | output | 1 | 9,708 | 16 | 19,417 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD | instruction | 0 | 9,709 | 16 | 19,418 |
"Correct Solution:
```
N = int(input())
XY = []
parity = []
for _ in range(N):
xy = list(map(int, input().split()))
XY.append(xy)
parity.append(sum(xy))
def check(ds, l, xy):
x = 0
y = 0
for i in range(len(ds)):
if l[i] == "R":
x += ds[i]
elif l[i] == "L":
x -= ds[i]
elif l[i] == "U":
y += ds[i]
elif l[i] == "D":
y -= ds[i]
else:
raise Exception
return (x == xy[0]) & (y == xy[1])
if len(list(set([i % 2 for i in parity]))) == 2:
print(-1)
elif parity[0] % 2 == 0:
print(33)
ds = [1, 1] + [2 ** k for k in range(1, 32)]
print(*ds)
for xy in XY:
rev_ans = ""
curr_x, curr_y = 0, 0
for d in ds[::-1]:
x_diff = xy[0] - curr_x
y_diff = xy[1] - curr_y
if abs(x_diff) >= abs(y_diff):
if x_diff >= 0:
rev_ans += "R"
curr_x += d
else:
rev_ans += "L"
curr_x -= d
else:
if y_diff >= 0:
rev_ans += "U"
curr_y += d
else:
rev_ans += "D"
curr_y -= d
print(rev_ans[::-1])
# print(check(ds, list(rev_ans[::-1]), xy))
else: # odd
print(32)
ds = [2 ** k for k in range(32)]
print(*ds)
for xy in XY:
rev_ans = ""
curr_x, curr_y = 0, 0
for d in ds[::-1]:
x_diff = xy[0] - curr_x
y_diff = xy[1] - curr_y
if abs(x_diff) >= abs(y_diff):
if x_diff >= 0:
rev_ans += "R"
curr_x += d
else:
rev_ans += "L"
curr_x -= d
else:
if y_diff >= 0:
rev_ans += "U"
curr_y += d
else:
rev_ans += "D"
curr_y -= d
print(rev_ans[::-1])
# print(check(ds, list(rev_ans[::-1]), xy))
``` | output | 1 | 9,709 | 16 | 19,419 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD | instruction | 0 | 9,710 | 16 | 19,420 |
"Correct Solution:
```
N = int(input())
point = [tuple(map(int, input().split())) for i in range(N)]
point_farthest = max(point, key=lambda p: abs(p[0]) + abs(p[1]))
mod = sum(point_farthest) % 2
D = [1, 1] if mod == 0 else [1]
while sum(D) < abs(point_farthest[0]) + abs(point_farthest[1]):
D.append(D[-1] * 2)
D.reverse()
W = []
for x, y in point:
if (x + y) % 2 != mod:
print(-1)
exit()
w = ''
for d in D:
if abs(x) >= abs(y):
if x > 0:
w += 'R'
x -= d
else:
w += 'L'
x += d
else:
if y > 0:
w += 'U'
y -= d
else:
w += 'D'
y += d
W.append(w)
print(len(D))
print(*D)
print(*W, sep='\n')
``` | output | 1 | 9,710 | 16 | 19,421 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD | instruction | 0 | 9,711 | 16 | 19,422 |
"Correct Solution:
```
import sys
def f(s,t):
if s>=t and -s<=t:
return 0
elif s<=t and -s<=t:
return 1
elif s<=t and -s>=t:
return 2
else:
return 3
n=int(input())
xy=[list(map(int,input().split())) for i in range(n)]
for i in range(1,n):
if sum(xy[i])%2!=sum(xy[i-1])%2:
print(-1)
sys.exit()
data_1=["R","U","L","D"]
data_2=[[1,0],[0,1],[-1,0],[0,-1]]
arms=[2**i for i in range(32)]
if sum(xy[0])%2==1:
print(len(arms))
print(*arms)
for X,Y in xy:
x,y=X,Y
ans=[]
i=31
while i>=0:
c=f(x,y)
ans.append(data_1[c])
x-=arms[i]*data_2[c][0]
y-=arms[i]*data_2[c][1]
i-=1
print("".join(ans[::-1]))
else:
arms=[1]+arms
print(len(arms))
print(*arms)
for X,Y in xy:
x,y=X,Y
ans=[]
i=32
while i>=1:
c=f(x,y)
ans.append(data_1[c])
x-=arms[i]*data_2[c][0]
y-=arms[i]*data_2[c][1]
i-=1
if x==1:
ans.append("R")
elif x==-1:
ans.append("L")
elif y==1:
ans.append("U")
else:
ans.append("D")
print("".join(ans[::-1]))
``` | output | 1 | 9,711 | 16 | 19,423 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD | instruction | 0 | 9,712 | 16 | 19,424 |
"Correct Solution:
```
N, *XY = map(int, open(0).read().split())
XY = list(zip(*[iter(XY)] * 2))
mod = sum(XY[0]) % 2
if any((x + y) % 2 != mod for x, y in XY):
print(-1)
quit()
D = [2 ** i for i in reversed(range(32))] + [1] * (mod == 0)
print(len(D))
print(*D)
for x, y in XY:
A = []
for d in D:
if 0 <= x - y and 0 <= x + y:
A.append("R")
x -= d
elif x - y < 0 and 0 <= x + y:
A.append("U")
y -= d
elif 0 <= x - y and x + y < 0:
A.append("D")
y += d
else:
A.append("L")
x += d
print("".join(A))
``` | output | 1 | 9,712 | 16 | 19,425 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
n=int(input())
xy=[list(map(int,input().split()))for _ in range(n)]
g=39
a=[]
if sum(xy[0])%2==0:a.append(1)
for i in range(g):a.append(1<<i)
g=len(a)
for x,y in xy:
if (x+y)%2!=sum(xy[0])%2:exit(print(-1))
print(g)
print(*a)
def f(s):
t=s
ans=[]
for i in a[::-1]:
if abs(t-i)<abs(t+i):
ans.append(-i)
t-=i
else:
ans.append(i)
t+=i
return ans[::-1]
for x,y in xy:
xpy=f(-(x+y))
xmy=f(-(x-y))
ans=""
for p,m in zip(xpy,xmy):
if 0<p and 0<m:ans+="R"
if p<0 and m<0:ans+="L"
if 0<p and m<0:ans+="U"
if p<0 and 0<m:ans+="D"
print(ans)
``` | instruction | 0 | 9,713 | 16 | 19,426 |
Yes | output | 1 | 9,713 | 16 | 19,427 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
def cal(i,j):
if i==1 and j==1: return "R"
elif i==1 and j==0: return "U"
elif i==0 and j==1: return "D"
elif i==0 and j==0: return "L"
import sys
N=int(input())
a=[list(map(int,input().split())) for i in range(N)]
mod=sum(a[0])%2
for i in range(N):
if sum(a[i])%2!=mod:
print(-1)
sys.exit()
if mod==0:
a=[[ a[i][0]-1 ,a[i][1] ] for i in range(N)]
if mod==0:
print(32)
print(1,end=" ")
for i in range(30): print(2**i, end=" ")
print(2**30)
else:
print(31)
for i in range(30): print(2**i, end=" ")
print(2**30)
for i in range(N):
[x,y]=a[i]
u=bin((x+y+2**31-1)//2)[2:].zfill(31)
v=bin((x-y+2**31-1)//2)[2:].zfill(31)
if mod==0: s="R"
else: s=""
for i in range(30,-1,-1): s=s+cal( int(u[i]),int(v[i]) )
print(s)
``` | instruction | 0 | 9,714 | 16 | 19,428 |
Yes | output | 1 | 9,714 | 16 | 19,429 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = []
mx = 0
for _ in range(N):
x, y = map(int, input().split())
u = x + y
v = x - y
a.append((u, v))
mx = max(mx, max(abs(u), abs(v)))
t = a[0][0] % 2
for u, _ in a:
if u % 2 != t:
print(-1)
exit(0)
d = [pow(2, i) for i in range(mx.bit_length())]
if t == 0: d = [1] + d
print(len(d))
print(*d)
for u, v in a:
s = [0] * len(d)
t = [0] * len(d)
x = 0
y = 0
res = []
for i in range(len(d) - 1, -1, -1):
z = d[i]
if u < x:
x -= z
s[i] = -1
else:
x += z
s[i] = 1
if v < y:
y -= z
t[i] = -1
else:
y += z
t[i] = 1
for i in range(len(d)):
if s[i] == 1 and (t[i] == 1):
res.append("R")
elif s[i] == -1 and (t[i] == -1):
res.append("L")
elif s[i] == 1 and (t[i] == -1):
res.append("U")
elif s[i] == -1 and (t[i] == 1):
res.append("D")
print("".join(res))
``` | instruction | 0 | 9,715 | 16 | 19,430 |
Yes | output | 1 | 9,715 | 16 | 19,431 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
def main():
"""
ロボットアーム
腕、関節
arm_1, arm_2,...,arm_m
k_0, k_1, k_2,..., k_m
k_i-1, arm_i, k_i
arm_i_length: d_i
mode: L, R, D, U
(x0, y0) = (0, 0)
L: (x_i, y_i) = (x_i-1 - d_i, y_i-1)
R: (x_i, y_i) = (x_i-1 + d_i, y_i-1)
U: (x_i, y_i) = (x_i-1, y_i-1 - d_i)
D: (x_i, y_i) = (x_i-1, y_i-1 + d_i)
input:
1 <= N <= 10^3
-10^9 <= Xi <= 10^9
-10^9 <= Yi <= 10^9
output:
NG: -1
OK:
m
d1 d2 ... dm
w1
w2
...
wN
1 <= m <= 40
1 <= d_i <= 10^12
w_i: {L, R, U, D}, w_i_lenght = m
動かし方の例は、入力例1参照
"""
N = int(input())
X, Y = zip(*(
map(int, input().split())
for _ in range(N)
))
# m, d, w = part_300(N, X, Y)
m, d, w = ref(N, X, Y)
if m == -1:
print(-1)
else:
print(m)
print(*d)
print(*w, sep="\n")
def ex1(N, X, Y):
m = 2
d = [1, 2]
w = ["RL", "UU", "DR"]
return m, d, w
def part_300(N, X, Y):
"""
1つ1つのクエリに対する操作は独立
ただし、使うパラメータm, d は共通
部分点は以下の制約
-10 <= i <= 10
-10 <= i <= 10
探索範囲
20 * 20
この範囲においてm<=40で到達するためのd
d=1のとき|X|+|Y|の偶奇
揃っている場合、mは最大に合わせる、余っているときはRLのように移動なしにできる
揃っていない場合, d=1では不可能？
2と1およびLR,UDを駆使して-1を再現して偶奇を揃える?
無理っぽい: 奇数しか作れない
"""
dists = []
for x, y in zip(X, Y):
dist = abs(x) + abs(y)
dists.append(dist)
m = -1
d = []
w = []
mod = list(map(lambda x: x % 2, dists))
if len(set(mod)) == 1:
m = max(dists)
d = [1] * m
for x, y, dist in zip(X, Y, dists):
x_dir = "R" if x > 0 else "L"
y_dir = "U" if y > 0 else "D"
_w = x_dir * abs(x) + y_dir * abs(y)
rest = m - len(_w)
if rest > 0:
_w += "LR" * (rest // 2)
w.append(_w)
return m, d, w
def editorial(N, X, Y):
"""
2冪の数の組合せにより、どの点にでも移動できるようになる
※ただし、奇数のみ。偶数に対応させたいときは１での移動を追加する
1, 2, 4, 8,
2^0, 2^1, 2^2, 2^3, ...
{1} だけでの移動、原点からの1の距離。当たり前
x: 原点
b
-------cxa------
d
{1, 2} での移動、原点から1の距離から2移動できる
a-d を基準に考えると
a-d をa方向に2移動: a方向に菱形の移動範囲が増える
a-d をb方向に2移動: b
a-d をc方向に2移動: c
a-d をd方向に2移動: d
b
b b
c b a
c cxa a
c d a
d d
d
https://twitter.com/CuriousFairy315/status/1046073372315209728
https://twitter.com/schwarzahl/status/1046031849221316608
どうして(u, v)=(x+y, x-y)的な変換を施す必要があるのか？
https://twitter.com/ILoveTw1tter/status/1046062363831660544
http://drken1215.hatenablog.com/entry/2018/09/30/002900
x 座標, y 座標両方頑張ろうと思うと、60 個くらい欲しくなる。で、困っていた。
U
|
L----o----R
|
D
# TODO
U＼ ／R
＼ ／
＼／
／ ＼
／ ＼
L／ ＼D
"""
pass
def ref(N, X, Y):
dists = []
for x, y in zip(X, Y):
dist = (abs(x) + abs(y)) % 2
dists.append(dist)
m = -1
d = []
w = []
mod = set(map(lambda x: x % 2, dists))
if len(mod) != 1:
return m, d, w
for i in range(30, 0-1, -1):
d.append(1 << i)
if 0 in mod:
d.append(1)
m = len(d)
w1 = transform_xy(N, X, Y, d)
# w2 = no_transform_xy(N, X, Y, d)
# assert w1 == w2
return m, d, w1
def transform_xy(N, X, Y, d):
"""
http://kagamiz.hatenablog.com/entry/2014/12/21/213931
"""
# 変換: θ=45°, 分母は共通の√2 なので払ってしまうと下記の式になる
trans_x = []
trans_y = []
for x, y in zip(X, Y):
trans_x.append(x + y)
trans_y.append(x - y)
plot = False
if plot:
import matplotlib.pyplot as plt
plt.axhline(0, linestyle="--")
plt.axvline(0, linestyle="--")
# denominator: 分母
deno = 2 ** 0.5
plt.scatter(X, Y, label="src")
plt.scatter([x / deno for x in trans_x],
[y / deno for y in trans_y],
label="trans")
for x, y, x_src, y_src in zip(trans_x, trans_y, X, Y):
plt.text(x_src, y_src, str((x_src, y_src)))
plt.text(x / deno, y / deno, str((x_src, y_src)))
plt.legend()
plt.show()
# print(*zip(X, Y))
# print(*zip(trans_x, trans_y))
w = []
dirs = {
# dir: x', y'
(-1, -1): "L", # 本来の座標(x, y): (-1, 0), 変換後: (-1+0, -1-0)
(+1, +1): "R", # 本来の座標(x, y): (+1, 0), 変換後: (+1+0, +1-0)
# 感覚と違うのは、変換の仕方
(+1, -1): "U", # 本来の座標(x, y): ( 0, +1), 変換後: ( 0+1, 0-(-1))
(-1, +1): "D", # 本来の座標(x, y): ( 0, -1), 変換後: ( 0-1, 0-(+1))
}
for x, y in zip(trans_x, trans_y):
x_sum = 0
y_sum = 0
_w = ""
for _d in d:
# 変換後の座標でx',y'を独立に求めている
if x_sum <= x:
x_dir = 1
x_sum += _d
else:
x_dir = -1
x_sum -= _d
if y_sum <= y:
y_dir = 1
y_sum += _d
else:
y_dir = -1
y_sum -= _d
_w += dirs[(x_dir, y_dir)]
w.append(_w)
return w
def no_transform_xy(N, X, Y, d):
w = []
for x, y in zip(X, Y):
x_sum, y_sum = 0, 0
_w = ""
for _d in d:
# 変化量の大きい方を優先する
if abs(x_sum - x) >= abs(y_sum - y):
if x_sum >= x:
x_sum -= _d
_w += "L"
else:
x_sum += _d
_w += "R"
else:
if y_sum >= y:
y_sum -= _d
_w += "D"
else:
y_sum += _d
_w += "U"
w.append(_w)
return w
if __name__ == '__main__':
main()
``` | instruction | 0 | 9,716 | 16 | 19,432 |
Yes | output | 1 | 9,716 | 16 | 19,433 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
N = int(input())
point = []
dist = []
for _ in range(N) :
x, y = map(int, input().split())
point.append((x, y))
dist.append(abs(x) + abs(y))
distSort = sorted(dist)
maxDist = dist[-1]
for d in distSort :
if (maxDist - d) % 2 == 1 : # 実現不可能
print(-1)
break
else : # 実現可能
print(maxDist) # 腕の数
for _ in range(maxDist) :
print('1 ', end='')
print('')
for x, y in point :
for _ in range(abs(x)) :
if x < 0 :
print('L', end='')
else :
print('R', end='')
for _ in range(abs(y)) :
if y < 0 :
print('D', end='')
else :
print('U', end='')
for i in range((maxDist - (abs(x) + abs(y))) // 2) :
print('LR', end='')
print('')
``` | instruction | 0 | 9,717 | 16 | 19,434 |
No | output | 1 | 9,717 | 16 | 19,435 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
import sys
N = int(input())
XY = [[int(_) for _ in input().split()] for i in range(N)]
mc = [0, 0]
maxl = 0
for x, y in XY:
l = abs(x) + abs(y)
maxl = max(maxl, l)
mc[l % 2] += 1
if mc[0] > 0 and mc[1] > 0:
print(-1)
sys.exit()
#if maxl > 20:
# raise
def calc(sx, sy, dx, dy, d):
#print("#", sx, sy, dx, dy)
x = dx - sx
y = dy - sy
tx = x + 3 * d - y
ty = x + 3 * d + y
dirs = ("LL", "LD", "DD"), ("LU", "UD", "RD"), ("UU", "RU", "RR")
ds = {"R": (+d, 0), "L": (-d, 0), "U": (0, +d), "D": (0, -d)}
dir = dirs[ty // (2 * d)][tx // (2 * d)]
ex, ey = sx, sy
for d in dir:
ex += ds[d][0]
ey += ds[d][1]
#print("*", dir, ex, ey)
return dir, ex, ey
ds = []
ds0 = []
for i in range(19):
d = 3 ** (19 - i)
ds.append(d)
ds0.append(d)
ds0.append(d)
w0 = ""
x0, y0 = 0, 0
if mc[1] > 0:
ds0 = [1] + ds0
w0 += "R"
x0 += 1
print(len(ds0))
print(*ds0)
for i in range(N):
w = w0
x, y = x0, y0
for j, d in enumerate(ds):
wc, x, y = calc(x, y, XY[i][0], XY[i][1], d)
w += wc
print(w)
``` | instruction | 0 | 9,718 | 16 | 19,436 |
No | output | 1 | 9,718 | 16 | 19,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
from collections import defaultdict
N = int(input())
XY = [list(map(int, input().split())) for _ in [0] * N]
md = lambda xy: sum(map(abs,xy))
s = md(XY[0]) % 2
for xy in XY:
if s != md(xy) % 2:
print(-1)
exit()
mdxy = [md(xy) for xy in XY]
m = max(mdxy)
print(m)
print(*[1] * m)
for x, y in XY:
res = []
for i in range(m):
if x:
if x > 0:
res += ['R']
x -= 1
elif x < 0:
res += ['L']
x += 1
elif y:
if y > 0:
res += ['U']
y += 1
elif y < 0:
res += ['D']
y -= 1
else:
if i % 2:
res += ['R']
else:
res += ['L']
print(''.join(res))
``` | instruction | 0 | 9,719 | 16 | 19,438 |
No | output | 1 | 9,719 | 16 | 19,439 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is introducing a robot arm with the following properties to his factory:
* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).
Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).
Constraints
* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.
m
d_1 d_2 ... d_m
w_1
w_2
:
w_N
m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.
w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.
Examples
Input
3
-1 0
0 3
2 -1
Output
2
1 2
RL
UU
DR
Input
5
0 0
1 0
2 0
3 0
4 0
Output
-1
Input
2
1 1
1 1
Output
2
1 1
RU
UR
Input
3
-7 -3
7 3
-3 -7
Output
5
3 1 4 1 5
LRDUL
RDULR
DULRD
Submitted Solution:
```
n = int(input())
x = [list(map(int, input().split())) for _ in range(n)]
a = [abs(p[0])+abs(p[1]) for p in x]
t = max(a)
b = [q%2 for q in a]
if len(set(b)) != 1:
print(-1)
exit()
print(t)
for i in range(t):
print("1 ", end="")
print()
for i in range(n):
ch1 = ch2 = ""
if x[i][0] >= 0:
ch1 = "R"
else:
ch1 = "L"
if x[i][1] >= 0:
ch2 = "U"
else:
ch2 = "D"
for j in range((t-a[i])//2):
print("RL", end="")
for j in range(abs(x[i][0])):
print(ch1, end="")
for j in range(abs(x[i][1])):
print(ch2, end="")
print()
``` | instruction | 0 | 9,720 | 16 | 19,440 |
No | output | 1 | 9,720 | 16 | 19,441 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
from collections import deque
class MaxFlow:
"""
Example.
mf = MaxFlow(N)
mf.add_edge(0, 1, 1)
mf.add_edge(1, 2, 3)
print(mf.max_flow(0, 2))
for fr, to, cap, flow in mf.edges():
print(fr, to, flow)
"""
def __init__(self, n):
self.n = n
self.graph = [[] for _ in range(n)]
self.pos = []
def add_edge(self, fr, to, cap):
m = len(self.pos)
self.pos.append((fr, len(self.graph[fr])))
self.graph[fr].append([to, len(self.graph[to]), cap])
self.graph[to].append([fr, len(self.graph[fr]) - 1, 0])
return m
def get_edge(self, idx):
to, rev, cap = self.graph[self.pos[idx][0]][self.pos[idx][1]]
rev_to, rev_rev, rev_cap = self.graph[to][rev]
return rev_to, to, cap + rev_cap, rev_cap
def edges(self):
m = len(self.pos)
for i in range(m):
yield self.get_edge(i)
def change_edge(self, idx, new_cap, new_flow):
to, rev, cap = self.graph[self.pos[idx][0]][self.pos[idx][1]]
self.graph[self.pos[idx][0]][self.pos[idx][1]][2] = new_cap - new_flow
self.graph[to][rev][2] = new_flow
def dfs(self, s, v, up):
if v == s:
return up
res = 0
lv = self.level[v]
for i in range(self.iter[v], len(self.graph[v])):
to, rev, cap = self.graph[v][i]
if lv <= self.level[to] or self.graph[to][rev][2] == 0:
continue
d = self.dfs(s, to, min(up - res, self.graph[to][rev][2]))
if d <= 0:
continue
self.graph[v][i][2] += d
self.graph[to][rev][2] -= d
res += d
if res == up:
break
self.iter[v] += 1
return res
def max_flow(self, s, t):
return self.max_flow_with_limit(s, t, 2 ** 63 - 1)
def max_flow_with_limit(self, s, t, limit):
flow = 0
while flow < limit:
self.level = [-1] * self.n
self.level[s] = 0
queue = deque()
queue.append(s)
while queue:
v = queue.popleft()
for to, rev, cap in self.graph[v]:
if cap == 0 or self.level[to] >= 0:
continue
self.level[to] = self.level[v] + 1
if to == t:
break
queue.append(to)
if self.level[t] == -1:
break
self.iter = [0] * self.n
while flow < limit:
f = self.dfs(s, t, limit - flow)
if not f:
break
flow += f
return flow
def min_cut(self, s):
visited = [0] * self.n
queue = deque()
queue.append(s)
while queue:
p = queue.popleft()
visited[p] = True
for to, rev, cap in self.graph[p]:
if cap and not visited[to]:
visited[to] = True
queue.append(to)
return visited
H, W = map(int, input().split())
a = [list(input().rstrip()) for _ in range(H)]
mf = MaxFlow(H + W + 2)
start = H + W
terminal = H + W + 1
INF = 10**6
for i in range(H):
for j in range(W):
if a[i][j] == 'S':
mf.add_edge(start, i, INF)
mf.add_edge(start, H + j, INF)
elif a[i][j] == 'T':
mf.add_edge(i, terminal, INF)
mf.add_edge(H + j, terminal, INF)
elif a[i][j] == 'o':
mf.add_edge(i, H + j, 1)
mf.add_edge(H + j, i, 1)
ans = mf.max_flow(start, terminal)
if ans >= INF:
print(-1)
else:
print(ans)
``` | instruction | 0 | 9,745 | 16 | 19,490 |
Yes | output | 1 | 9,745 | 16 | 19,491 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
from collections import deque
INF = 10**9
class Dinic:
def __init__(self, n):
self.n = n
self.edge = [[] for _ in range(n)]
self.level = [None] * self.n
self.it = [None] * self.n
def add_edge(self, fr, to, cap):
# edge consists of [dest, cap, id of reverse edge]
forward = [to, cap, None]
backward = [fr, 0, forward]
forward[2] = backward
self.edge[fr].append(forward)
self.edge[to].append(backward)
def add_bidirect_edge(self, v1, v2, cap1, cap2):
edge1 = [v2, cap1, None]
edge2 = [v1, cap2, edge1]
edge1[2] = edge2
self.edge[v1].append(edge1)
self.edge[v2].append(edge2)
# takes start node and terminal node
# create new self.level, return you can flow more or not
def bfs(self, s, t):
self.level = [None] * self.n
dq = deque([s])
self.level[s] = 0
while dq:
v = dq.popleft()
lv = self.level[v] + 1
for dest, cap, _ in self.edge[v]:
if cap > 0 and self.level[dest] is None:
self.level[dest] = lv
dq.append(dest)
return self.level[t] is not None
# takes vertex, terminal, flow in vertex
def dfs(self, v, t, f):
if v == t:
return f
for e in self.it[v]:
to, cap, rev = e
if cap and self.level[v] < self.level[to]:
ret = self.dfs(to, t, min(f, cap))
# find flow
if ret:
e[1] -= ret
rev[1] += ret
return ret
# no more flow
return 0
def flow(self, s, t):
flow = 0
while self.bfs(s, t):
for i in range(self.n):
self.it[i] = iter(self.edge[i])
# *self.it, = map(iter, self.edge)
f = INF
while f > 0:
f = self.dfs(s, t, INF)
flow += f
return flow
N, M = [int(item) for item in input().split()]
n = N + M + 2
dinic = Dinic(n)
for i in range(N):
line = input().rstrip()
for j, ch in enumerate(line):
if ch == ".":
pass
elif ch == "o":
v1 = i + 1
v2 = N + j + 1
dinic.add_bidirect_edge(v1, v2, 1, 1)
elif ch == "S":
v1 = i + 1
v2 = N + j + 1
dinic.add_edge(0, v1, INF)
dinic.add_edge(0, v2, INF)
elif ch == "T":
v1 = i + 1
v2 = N + j + 1
dinic.add_edge(v1, n-1, INF)
dinic.add_edge(v2, n-1, INF)
ans = dinic.flow(0, n-1)
if ans >= INF:
print(-1)
else:
print(ans)
``` | instruction | 0 | 9,746 | 16 | 19,492 |
Yes | output | 1 | 9,746 | 16 | 19,493 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
from pprint import pprint
from copy import deepcopy
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
from pprint import pprint
sys.setrecursionlimit(2147483647)
INF = 10 ** 15
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007
class Dinic:
def __init__(self, n):
self.n = n
self.G = [[] for _ in range(n)]
self.level = None
self.it = None
def add_edge(self, fr, to, cap):
forward = [to, cap, None]
forward[2] = backward = [fr, 0, forward]
self.G[fr].append(forward)
self.G[to].append(backward)
def add_multi_edge(self, v1, v2, cap1, cap2):
edge1 = [v2, cap1, None]
edge1[2] = edge2 = [v1, cap2, edge1]
self.G[v1].append(edge1)
self.G[v2].append(edge2)
def bfs(self, s, t):
self.level = level = [-1] * self.n
deq = deque([s])
level[s] = 0
G = self.G
while deq:
v = deq.popleft()
lv = level[v] + 1
for w, cap, _ in G[v]:
if cap and level[w] == -1:
level[w] = lv
deq.append(w)
return level[t] != -1
def dfs(self, v, t, f):
if v == t:
return f
for e in self.it[v]:
w, cap, rev = e
if cap and self.level[v] < self.level[w]:
d = self.dfs(w, t, min(f, cap))
if d:
e[1] -= d
rev[1] += d
return d
return 0
def flow(self, s, t):
flow = 0
INF = 10 ** 18
while self.bfs(s, t):
*self.it, = map(iter, self.G)
f = INF
while f:
f = self.dfs(s, t, INF)
flow += f
return flow
h, w = LI()
dinic = Dinic(h + w + 2)
s = SR(h)
for i in range(h):
for j in range(w):
if s[i][j] == 'o':
dinic.add_multi_edge(i, h + j, 1, 1)
elif s[i][j] == 'S':
dinic.add_edge(h + w, i, INF)
dinic.add_edge(h + w, h + j, INF)
elif s[i][j] == 'T':
dinic.add_edge(i, h + w + 1, INF)
dinic.add_edge(h + j, h + w + 1, INF)
ans = dinic.flow(h + w, h + w + 1)
print(ans if ans < INF else -1)
``` | instruction | 0 | 9,747 | 16 | 19,494 |
Yes | output | 1 | 9,747 | 16 | 19,495 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
from collections import deque
class Dinic:
def __init__(self, n: int):
self.INF = 10**9 + 7
self.n = n
self.graph = [[] for _ in range(n)]
def add_edge(self, _from: int, to: int, capacity: int):
"""残余グラフを構築
1. _fromからtoへ向かう容量capacityの辺をグラフに追加する
2. toから_fromへ向かう容量0の辺をグラフに追加する
"""
forward = [to, capacity, None]
forward[2] = backward = [_from, 0, forward]
self.graph[_from].append(forward)
self.graph[to].append(backward)
def bfs(self, s: int, t: int):
"""capacityが正の辺のみを通ってsからtに移動可能かどうかBFSで探索
level: sからの最短路の長さ
"""
self.level = [-1] * self.n
q = deque([s])
self.level[s] = 0
while q:
_from = q.popleft()
for to, capacity, _ in self.graph[_from]:
if capacity > 0 and self.level[to] < 0:
self.level[to] = self.level[_from] + 1
q.append(to)
def dfs(self, _from: int, t: int, f: int) -> int:
"""流量が増加するパスをDFSで探索
BFSによって作られた最短路に従ってfを更新する
"""
if _from == t:
return f
for edge in self.itr[_from]:
to, capacity, reverse_edge = edge
if capacity > 0 and self.level[_from] < self.level[to]:
d = self.dfs(to, t, min(f, capacity))
if d > 0:
edge[1] -= d
reverse_edge[1] += d
return d
return 0
def max_flow(self, s: int, t: int):
"""s-tパス上の最大流を求める
計算量: O(|E||V|^2)
"""
flow = 0
while True:
self.bfs(s, t)
if self.level[t] < 0:
break
self.itr = list(map(iter, self.graph))
f = self.dfs(s, t, self.INF)
while f > 0:
flow += f
f = self.dfs(s, t, self.INF)
return flow
h, w = map(int, input().split())
a = [list(input()) for i in range(h)]
di = Dinic(h + w + 2)
for i in range(h):
for j in range(w):
if a[i][j] == "o":
di.add_edge(i, h + j, 1)
di.add_edge(h + j, i, 1)
if a[i][j] == "S":
di.add_edge(h + w, i, 10 ** 5)
di.add_edge(h + w, h + j, 10 ** 5)
if a[i][j] == "T":
di.add_edge(i, h + w + 1, 10 ** 5)
di.add_edge(h + j, h + w + 1, 10 ** 5)
ans = di.max_flow(h + w, h + w + 1)
if ans >= 10 ** 5:
print(-1)
else:
print(ans)
``` | instruction | 0 | 9,748 | 16 | 19,496 |
Yes | output | 1 | 9,748 | 16 | 19,497 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
from pprint import pprint
from copy import deepcopy
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
from pprint import pprint
sys.setrecursionlimit(2147483647)
INF = 10 ** 15
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007
class Dinic():
def __init__(self, G, source, sink):
self.G = G
self.sink = sink
self.source = source
def add_edge(self, u, v, cap):
self.G[u][v] = cap
self.G[v][u] = 0
def bfs(self):
level = defaultdict(int)
q = [self.source]
level[self.source] = 1
d = 1
while q:
if level[self.sink]:
break
qq = []
d += 1
for u in q:
for v, cap in self.G[u].items():
if cap == 0:
continue
if level[v]:
continue
level[v] = d
qq += [v]
q = qq
self.level = level
def dfs(self, u, f):
if u == self.sink:
return f
for v, cap in self.iter[u]:
if cap == 0 or self.level[v] != self.level[u] + 1:
continue
d = self.dfs(v, min(f, cap))
if d:
self.G[u][v] -= d
self.G[v][u] += d
return d
return 0
def max_flow(self):
flow = 0
while True:
self.bfs()
if self.level[self.sink] == 0:
break
self.iter = {u: iter(self.G[u].items()) for u in self.G}
while True:
f = self.dfs(self.source, INF)
if f == 0:
break
flow += f
return flow
h, w = LI()
s = SR(h)
G = defaultdict(lambda:defaultdict(int))
for i in range(h):
for j in range(w):
if s[i][j] == 'o':
G[i][h + j] = 1
G[h + j][i] = 1
elif s[i][j] == 'S':
G[h + w][i] = INF
G[h + w][h + j] = INF
elif s[i][j] == 'T':
G[i][h + w + 1] = INF
G[h + j][h + w + 1] = INF
ans = Dinic(G, h + w, h + w + 1).max_flow()
if ans == INF:
print(-1)
else:
print(ans)
``` | instruction | 0 | 9,749 | 16 | 19,498 |
No | output | 1 | 9,749 | 16 | 19,499 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
class FordFulkerson:
"""max-flow-min-cut
O(F|E|)
"""
def __init__(self,V:int):
"""
Arguments:
V:num of vertex
adj:adjedscent list(adj[from]=(to,capacity,id))
"""
self.V = V
self.adj=[[] for _ in range(V)]
self.used=[False]*V
def add_edge(self,fro:int,to:int,cap:int):
"""
Arguments:
fro:from
to: to
cap: capacity of the edge
f: max flow value
"""
#edge
self.adj[fro].append([to,cap,len(self.adj[to])])
#rev edge
self.adj[to].append([fro,0,len(self.adj[fro])-1])
def dfs(self,v,t,f):
"""
search increasing path
"""
if v==t:
return f
self.used[v]=True
for i in range(len(self.adj[v])):
(nex_id,nex_cap,nex_rev) = self.adj[v][i]
if not self.used[nex_id] and nex_cap>0:
d = self.dfs(nex_id,t,min(f,nex_cap))
if d>0:
#decrease capacity to denote use it with d flow
self.adj[v][i][1]-=d
self.adj[nex_id][nex_rev][1]+=d
return d
return 0
def max_flow(self,s:int,t:int):
"""calculate maxflow from s to t
"""
flow=0
self.used = [False]*self.V
#while no increasing path is found
while True:
self.used = [False]*self.V
f = self.dfs(s,t,float("inf"))
if f==0:
return flow
else:
flow+=f
H,W = map(int,input().split())
grid=[[v for v in input()] for _ in range(H)]
F = FordFulkerson(H*W*2)
for i in range(H):
for j in range(W):
if grid[i][j]=="S":
sy,sx = i,j
grid[i][j]="o"
if grid[i][j]=="T":
gy,gx=i,j
grid[i][j]="o"
if grid[i][j]=="o":
#in node and out node
F.add_edge(i*W+j+H*W,i*W+j,1)
for i in range(H):
for j in range(W):
for k in range(j+1,W):
if grid[i][j]=="o" and grid[i][k]=="o":
#out->in
F.add_edge(i*W+j,i*W+k+H*W,float("inf"))
F.add_edge(i*W+k,i*W+j+H*W,float("inf"))
for i in range(W):
for j in range(H):
for k in range(j+1,H):
if grid[j][i]=="o" and grid[k][i]=="o":
F.add_edge(j*W+i,k*W+i+H*W,float("inf"))
F.add_edge(k*W+i,j*W+i+H*W,float("inf"))
if sy==gy or sx==gx:
print(-1)
exit()
print(F.max_flow(sy*W+sx,gy*W+gx+H*W))
``` | instruction | 0 | 9,750 | 16 | 19,500 |
No | output | 1 | 9,750 | 16 | 19,501 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
def examC():
ans = 0
print(ans)
return
def examD():
ans = 0
print(ans)
return
def examE():
ans = 0
print(ans)
return
def examF():
# 引用
# https://ikatakos.com/pot/programming_algorithm/graph_theory/maximum_flow
class Dinic:
def __init__(self, n):
self.n = n
self.links = [[] for _ in range(n)]
self.depth = None
self.progress = None
def add_link(self, _from, to, cap):
self.links[_from].append([cap, to, len(self.links[to])])
self.links[to].append([0, _from, len(self.links[_from]) - 1])
def bfs(self, s):
depth = [-1] * self.n
depth[s] = 0
q = deque([s])
while q:
v = q.popleft()
for cap, to, rev in self.links[v]:
if cap > 0 and depth[to] < 0:
depth[to] = depth[v] + 1
q.append(to)
self.depth = depth
def dfs(self, v, t, flow):
if v == t:
return flow
links_v = self.links[v]
for i in range(self.progress[v], len(links_v)):
self.progress[v] = i
cap, to, rev = link = links_v[i]
if cap == 0 or self.depth[v] >= self.depth[to]:
continue
d = self.dfs(to, t, min(flow, cap))
if d == 0:
continue
link[0] -= d
self.links[to][rev][0] += d
return d
return 0
def max_flow(self, s, t):
flow = 0
while True:
self.bfs(s)
if self.depth[t] < 0:
return flow
self.progress = [0] * self.n
current_flow = self.dfs(s, t, inf)
while current_flow > 0:
flow += current_flow
current_flow = self.dfs(s, t, inf)
H, W = LI()
A = [SI()for _ in range(H)]
din = Dinic(H+W+2)
for h in range(H):
for w in range(W):
if A[h][w]==".":
continue
if A[h][w]=="S":
din.add_link(0, h + W + 1, H * W)
din.add_link(h + W + 1, 0, H * W)
din.add_link(0, w + 1, H * W)
din.add_link(w + 1, 0, H * W)
continue
if A[h][w]=="T":
din.add_link(H + W + 1, h + W + 1, H * W)
din.add_link(h + W + 1, H + W + 1, H * W)
din.add_link(H + W + 1, w + 1, H * W)
din.add_link(w + 1, H + W + 1, H * W)
continue
din.add_link(h+W+1,w+1,1)
din.add_link(w+1,h+W+1,1)
ans = din.max_flow(0,H+W+1)
if ans==H*W:
ans = -1
print(ans)
return
from decimal import getcontext,Decimal as dec
import sys,bisect,itertools,heapq,math,random
from copy import deepcopy
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
def I(): return int(input())
def LI(): return list(map(int,sys.stdin.readline().split()))
def DI(): return dec(input())
def LDI(): return list(map(dec,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = dec("0.000000000001")
alphabet = [chr(ord('a') + i) for i in range(26)]
alphabet_convert = {chr(ord('a') + i): i for i in range(26)}
getcontext().prec = 28
sys.setrecursionlimit(10**7)
if __name__ == '__main__':
examF()
"""
142
12 9 1445 0 1
asd dfg hj o o
aidn
"""
``` | instruction | 0 | 9,751 | 16 | 19,502 |
No | output | 1 | 9,751 | 16 | 19,503 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a pond with a rectangular shape. The pond is divided into a grid with H rows and W columns of squares. We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).
Some of the squares in the pond contains a lotus leaf floating on the water. On one of those leaves, S, there is a frog trying to get to another leaf T. The state of square (i,\ j) is given to you by a character a_{ij}, as follows:
* `.` : A square without a leaf.
* `o` : A square with a leaf floating on the water.
* `S` : A square with the leaf S.
* `T` : A square with the leaf T.
The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."
Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T. Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.
Constraints
* 2 ≤ H, W ≤ 100
* a_{ij} is `.`, `o`, `S` or `T`.
* There is exactly one `S` among a_{ij}.
* There is exactly one `T` among a_{ij}.
Input
Input is given from Standard Input in the following format:
H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}
Output
If the objective is achievable, print the minimum necessary number of leaves to remove. Otherwise, print `-1` instead.
Examples
Input
3 3
S.o
.o.
o.T
Output
2
Input
3 4
S...
.oo.
...T
Output
0
Input
4 3
.S.
.o.
.o.
.T.
Output
-1
Input
10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo
Output
5
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**9)
def dfs(v,t,f,used,graph):
if v==t:
return f
used[v] = True
for to in graph[v]:
c = graph[v][to]
if used[to] or c==0:
continue
d = dfs(to,t,min(f,c),used,graph)
if d>0:
graph[v][to] -= d
graph[to][v] += d
return d
return 0
def max_flow(s,t,graph):
flow = 0
while True:
used = [False]*len(graph)
f = dfs(s,t,float('inf'),used,graph)
flow += f
if f==0 or f==float('inf'):
return flow
H,W = map(int,input().split())
a = [input() for _ in range(H)]
a = [[s for s in a[i]] for i in range(H)]
def encode(h,w):
return h*W+w
def decode(d):
return (d//W,d%W)
for h in range(H):
for w in range(W):
if a[h][w]=='S':
s = encode(h,w)
a[h][w]='o'
if a[h][w]=='T':
t = encode(h,w)
a[h][w]='o'
ans = 0
for h in range(H):
for w in range(W):
if a[h][w]=='o':
if (h==decode(s)[0] or w==decode(s)[1]) and (h==decode(t)[0] or w==decode(t)[1]):
ans += 1
a[h][w] = '.'
graph = [{} for _ in range(H*W)]
for h in range(H):
for w in range(W):
if a[h][w]=='.':
continue
for i in range(H):
if i==h:
continue
if a[i][w]=='.':
continue
graph[encode(h,w)][encode(i,w)] = 1
graph[encode(i,w)][encode(h,w)] = 1
for j in range(W):
if j==w:
continue
if a[h][j]=='.':
continue
graph[encode(h,w)][encode(h,j)] = 1
graph[encode(h,j)][encode(h,w)] = 1
for d in graph[s]:
graph[s][d] = float('inf')
graph[d][s] = 0
for d in graph[t]:
graph[t][d] = 0
graph[d][t] = float('inf')
ans += max_flow(s,t,graph)
if ans == float('inf'):
ans = -1
print(ans)
``` | instruction | 0 | 9,752 | 16 | 19,504 |
No | output | 1 | 9,752 | 16 | 19,505 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,753 | 16 | 19,506 |
"Correct Solution:
```
def main():
from bisect import bisect_left as bl
n = int(input())
a = [int(input()) for _ in [0]*n]
b = [int(input()) for _ in [0]*n]
a.sort()
b.sort()
for i in range(n):
if a[i] > b[i]:
a[i], b[i] = b[i], a[i]
# print(a)
# print(b)
mod = 10**9+7
ans = 1
for i in range(n):
ans = ans*(i+1-bl(b, a[i])) % mod
print(ans)
main()
``` | output | 1 | 9,753 | 16 | 19,507 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,754 | 16 | 19,508 |
"Correct Solution:
```
N=int(input())
A=[]
mod=10**9+7
for i in range(N):
a=int(input())
A.append((a,-1))
for i in range(N):
a=int(input())
A.append((a,1))
A.sort()
a=0
s=A[0][1]
ans=1
for i in range(2*N):
if A[i][1]==s:
a+=1
else:
ans*=a
ans%=mod
a-=1
if a==0 and i<2*N-1:
s=A[i+1][1]
#print(a,s,ans)
print(ans)
``` | output | 1 | 9,754 | 16 | 19,509 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,755 | 16 | 19,510 |
"Correct Solution:
```
N = int(input())
src = []
for i in range(2*N):
src.append((int(input()), i//N))
ans = 1
MOD = 10**9+7
mem = [0, 0]
for a,t in sorted(src):
if mem[1-t] > 0:
ans = (ans * mem[1-t]) % MOD
mem[1-t] -= 1
else:
mem[t] += 1
print(ans)
``` | output | 1 | 9,755 | 16 | 19,511 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,756 | 16 | 19,512 |
"Correct Solution:
```
import sys
n = int(input())
lines = sys.stdin.readlines()
aaa = list(map(int, lines[:n]))
bbb = list(map(int, lines[n:]))
coords = [(a, 0) for a in aaa] + [(b, 1) for b in bbb]
coords.sort()
MOD = 10 ** 9 + 7
remain_type = 0
remain_count = 0
ans = 1
for x, t in coords:
if remain_type == t:
remain_count += 1
continue
if remain_count == 0:
remain_type = t
remain_count = 1
continue
ans = ans * remain_count % MOD
remain_count -= 1
print(ans)
``` | output | 1 | 9,756 | 16 | 19,513 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,757 | 16 | 19,514 |
"Correct Solution:
```
N = int(input())
A = [(int(input()), 0) for i in range(N)]
B = [(int(input()), 1) for i in range(N)]
mod = 10 ** 9 + 7
X = A + B
X.sort()
ans = 1
Ar, Br = 0, 0
for x, i in X:
if i == 0:
if Br > 0:
ans *= Br
ans %= mod
Br -= 1
else:
Ar += 1
else:
if Ar > 0:
ans *= Ar
ans %= mod
Ar -= 1
else:
Br += 1
print(ans)
``` | output | 1 | 9,757 | 16 | 19,515 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,758 | 16 | 19,516 |
"Correct Solution:
```
N = int(input())
Q = sorted([[int(input()), i//N] for i in range(2*N)])
mod = 10**9 + 7
ans = 1
S = [0, 0]
for i in Q:
if S[1-i[1]] == 0:
S[i[1]] += 1
else:
ans = (ans*S[1-i[1]]) % mod
S[1-i[1]] -= 1
print(ans)
``` | output | 1 | 9,758 | 16 | 19,517 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,759 | 16 | 19,518 |
"Correct Solution:
```
mod = 10 ** 9 + 7
N = int(input())
A = [(int(input()), -1) for _ in range(N)]
B = [(int(input()), 1) for _ in range(N)]
C = sorted(A + B)
res = 1
cnt = 0
for _, delta in C:
if cnt != 0 and cnt * delta < 0:
res *= abs(cnt)
res %= mod
cnt += delta
print(res)
``` | output | 1 | 9,759 | 16 | 19,519 |
Provide a correct Python 3 solution for this coding contest problem.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1 | instruction | 0 | 9,760 | 16 | 19,520 |
"Correct Solution:
```
N = int(input())
E = []
for _ in range(N):
E += [(int(input()), 1)]
for _ in range(N):
E += [(int(input()), -1)]
E.sort()
mod = 10**9 + 7
ans = 1
ab = 0
for e in E:
if e[1] * ab < 0:
ans *= abs(ab)
ans %= mod
ab += e[1]
print(ans)
``` | output | 1 | 9,760 | 16 | 19,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
N = int(input())
mod = int(1e9+7)
A = []
for _ in range(N):
A.append([int(input()),1])
for _ in range(N):
A.append([int(input()),2])
A.sort()
ans = 1
ca,cb = 0,0
for a in A:
if a[1] == 1:
if cb == 0:
ca += 1
else:
ans = ans * cb % mod
cb -= 1
else:
if ca == 0:
cb += 1
else:
ans = ans * ca % mod
ca -= 1
print(ans)
``` | instruction | 0 | 9,761 | 16 | 19,522 |
Yes | output | 1 | 9,761 | 16 | 19,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
n=int(input())
ans=1
mod=10**9+7
A=[0,0]
AB=[]
for i in range(n):
a=int(input())
AB.append((a,0))
for i in range(n):
b=int(input())
AB.append((b,1))
AB.sort(key=lambda x:x[0])
for i in range(2*n):
a,b=AB[i]
if b==0:
if A[1]>0:
ans=(ans*A[1])%mod
A[1]-=1
else:
A[0]+=1
else:
if A[0]>0:
ans=(ans*A[0])%mod
A[0]-=1
else:
A[1]+=1
print(ans)
``` | instruction | 0 | 9,762 | 16 | 19,524 |
Yes | output | 1 | 9,762 | 16 | 19,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())
N = int(input())
points = []
for i in range(N):
a = int(input())
points.append([a,True])
for i in range(N):
b = int(input())
points.append([b,False])
points.sort()
ans = 1
an = bn = 0
for x,c in points:
if c:
if bn > 0:
ans = (ans*bn)%mod
bn -= 1
else:
an += 1
else:
if an > 0:
ans = (ans*an)%mod
an -= 1
else:
bn += 1
print(ans%mod)
``` | instruction | 0 | 9,763 | 16 | 19,526 |
Yes | output | 1 | 9,763 | 16 | 19,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
n = int(input())
M = 10**9+7
L = []
for _ in range(n):
a = int(input())
L.append((a, 1))
for _ in range(n):
b = int(input())
L.append((b, 0))
L.sort()
C = [0, 0]
ans = 1
for d, f in L:
if C[f^1]:
ans *= C[f^1]
ans %= M
C[f^1] -= 1
else:
C[f] += 1
print(ans)
``` | instruction | 0 | 9,764 | 16 | 19,528 |
Yes | output | 1 | 9,764 | 16 | 19,529 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
N = int(input())
mod = 10**9 + 7
fac = [1 for _ in range(N+1)]
for i in range(N):
fac[i+1] = (i+1)*fac[i]%mod
a = sorted([int(input()) for _ in range(N)])
b = sorted([int(input()) for _ in range(N)])
ab = list(zip(a,b))
X = [-2, -1]
ctr = 1
H = []
for i, j in ab:
if i < X[1]:
X = [i,X[1]]
ctr += 1
else:
H.append(ctr)
ctr = 1
X = i, j
ans = fac[ctr]
for i in H:
ans = ans*fac[i]%mod
print(ans%mod)
``` | instruction | 0 | 9,765 | 16 | 19,530 |
No | output | 1 | 9,765 | 16 | 19,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
N = int(input())
mod = 10**9 + 7
fac = [1 for _ in range(N+1)]
for i in range(N):
fac[i+1] = (i+1)*fac[i]%mod
a = sorted([int(input()) for _ in range(N)])
b = sorted([int(input()) for _ in range(N)])
ab = list(zip(a,b))
X = [-2, -1]
ctr = 1
H = []
for i, j in ab:
if i > j:
i, j = j, i
if i < X[1]:
X = [i,X[1]]
ctr += 1
else:
H.append(ctr)
ctr = 1
X = i, j
ans = fac[ctr]
for i in H:
ans = ans*fac[i]%mod
print(ans%mod)
``` | instruction | 0 | 9,766 | 16 | 19,532 |
No | output | 1 | 9,766 | 16 | 19,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
a = [(int(input()),1) for i in range(n)]
a += [(int(input()),2) for i in range(n)]
a.sort()
b = list(zip(*a))[1]
mod = 10**9+7
cnt = 0
ans = 1
prv = -1
for i in range(2*n):
if b[i] == 1:
cnt += 1
else:
cnt -= 1
if cnt == 0:
ans *= ((i-prv)//2)**2
ans %= mod
prv = i
print(ans)
``` | instruction | 0 | 9,767 | 16 | 19,534 |
No | output | 1 | 9,767 | 16 | 19,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.
Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.
In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.
Constraints
* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.
Input
The input is given from Standard Input in the following format:
N
a_1
:
a_N
b_1
:
b_N
Output
Print the number of ways to minimize the total length of the cables, modulo 10^9+7.
Examples
Input
2
0
10
20
30
Output
2
Input
3
3
10
8
7
12
5
Output
1
Submitted Solution:
```
# -*- coding: utf-8 -*-
import sys
from math import factorial
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 ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7
N=INT()
A=sorted([INT() for i in range(N)])
B=sorted([INT() for i in range(N)])
i=j=cur=cnt=0
L=[]
if A[0]>B[0]:
cur=1
while i<N and j<N:
if cur==0 and A[i]<B[j]:
i+=1
cnt+=1
elif cur==1 and A[i]<B[j]:
i=j
if cnt:
L.append(cnt)
cnt=0
cur=0
elif cur==1 and A[i]>B[j]:
j+=1
cnt+=1
elif cur==0 and A[i]>B[j]:
j=i
if cnt:
L.append(cnt)
cnt=0
cur=1
if cnt!=0:
L.append(cnt)
ans=1
for a in L:
ans=(ans*factorial(a))%MOD
print(ans)
``` | instruction | 0 | 9,768 | 16 | 19,536 |
No | output | 1 | 9,768 | 16 | 19,537 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2 | instruction | 0 | 10,640 | 16 | 21,280 |
"Correct Solution:
```
from collections import Counter
N,M = map(int,input().split())
A = list(map(int,input().split()))
src = [tuple(map(int,input().split())) for i in range(M)]
ctr = Counter(A)
cover = [0] * (2*N+1)
for k,v in ctr.items():
for i in range(k,k-v,-1):
cover[i+N] += 1
ans = cover[N+1:].count(0)
for x,y in src:
ctr[A[x-1]] -= 1
ai = A[x-1]+N - ctr[A[x-1]]
cover[ai] -= 1
if ai > N and cover[ai] == 0: ans += 1
A[x-1] = y
bi = y+N - ctr[y]
if bi > N and cover[bi] == 0: ans -= 1
cover[bi] += 1
ctr[y] += 1
print(ans)
``` | output | 1 | 10,640 | 16 | 21,281 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2 | instruction | 0 | 10,641 | 16 | 21,282 |
"Correct Solution:
```
import sys
from collections import Counter
# sys.stdin = open('c1.in')
def read_int_list():
return list(map(int, input().split()))
def read_int():
return int(input())
def read_str_list():
return input().split()
def read_str():
return input()
def vanish(p, details=False):
while p:
if details:
print(p)
n = len(p)
q = [x for x in p if x != n]
if len(q) == len(p):
return False
p = q[:]
return True
def check(n):
if n == 3:
for i in range(1, n + 1):
for j in range(i, n + 1):
for k in range(j, n + 1):
p = [i, j, k]
if vanish(p):
print(p)
# print()
# vanish(p, details=True)
if n == 5:
for i in range(1, n + 1):
for j in range(i, n + 1):
for k in range(j, n + 1):
for l in range(k, n + 1):
p = [i, j, k, l]
if vanish(p):
print(p)
# print()
# vanish(p, details=True)
if n == 5:
for i in range(1, n + 1):
for j in range(i, n + 1):
for k in range(j, n + 1):
for l in range(k, n + 1):
for m in range(l, n + 1):
p = [i, j, k, l, m]
if vanish(p):
print(p)
# print()
# vanish(p, details=True)
def solve_small():
# check(3)
# check(4)
# check(5)
n, m = read_int_list()
a = read_int_list()
p = [read_int_list() for _ in range(m)]
c = Counter(a)
res = []
for x, y in p:
c[a[x - 1]] -= 1
a[x - 1] = y
c[a[x - 1]] += 1
covered = set(range(n))
for i, ni in c.items():
for j in range(i - ni, i):
if j in covered:
covered.remove(j)
r = len(covered)
res.append(r)
return '\n'.join(map(str, res))
def solve():
n, m = read_int_list()
a = read_int_list()
p = [read_int_list() for _ in range(m)]
c = Counter(a)
covered = Counter({i: 0 for i in range(n)})
for i, ni in c.items():
for j in range(i - ni, i):
if 0 <= j:
covered[j] += 1
r = 0
for i, v in covered.items():
if 0 <= i:
if v == 0:
r += 1
res = []
for x, y in p:
x -= 1
i = a[x] - c[a[x]]
covered[i] -= 1
if 0 <= i:
if covered[i] == 0:
r += 1
c[a[x]] -= 1
a[x] = y
c[a[x]] += 1
i = a[x] - c[a[x]]
if 0 <= i:
if covered[i] == 0:
r -= 1
covered[i] += 1
res.append(r)
return '\n'.join(map(str, res))
def main():
res = solve()
print(res)
if __name__ == '__main__':
main()
``` | output | 1 | 10,641 | 16 | 21,283 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2 | instruction | 0 | 10,642 | 16 | 21,284 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
"""
・とりあえず部分点解法：各クエリに対してO(N)
・いくつかを残していくつかを自由に埋める
・残すもの：被覆区間がoverlapしないように残す
・つまり、区間で覆えている点が処理できて、区間で覆えていない点が他所から持ってこないといけない。
"""
N,M = map(int,input().split())
A = [int(x) for x in input().split()]
XY = [tuple(int(x) for x in input().split()) for _ in range(M)]
def subscore_solution():
from collections import Counter
for x,y in XY:
A[x-1] = y
covered = [False] * (N+N+10)
for key,cnt in Counter(A).items():
for i in range(cnt):
covered[max(0,key-i)] = True
print(sum(not bl for bl in covered[1:N+1]))
counter = [0] * (N+1)
covered = [0] * (N+N+10)
for a in A:
counter[a] += 1
covered[a-counter[a]+1] += 1
magic = sum(x==0 for x in covered[1:N+1])
for i,y in XY:
x = A[i-1]
A[i-1] = y
rem = x - counter[x] + 1
counter[x] -= 1
counter[y] += 1
add = y - counter[y] + 1
covered[rem] -= 1
if 1<=rem<=N and covered[rem] == 0:
magic += 1
if 1<=add<=N and covered[add] == 0:
magic -= 1
covered[add] += 1
print(magic)
``` | output | 1 | 10,642 | 16 | 21,285 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2 | instruction | 0 | 10,643 | 16 | 21,286 |
"Correct Solution:
```
from collections import Counter
n, m = map(int, input().split())
an = list(map(int, input().split()))
ac_ = Counter(an)
ac = {i: ac_[i] if i in ac_ else 0 for i in range(1, n + 1)}
ad = [0] * n
for a, c in ac.items():
for i in range(max(0, a - c), a):
ad[i] += 1
ans = ad.count(0)
anss = []
for x, y in (map(int, input().split()) for _ in range(m)):
ax = an[x - 1]
xdi = ax - ac[ax]
if xdi >= 0:
ad[xdi] -= 1
if ad[xdi] == 0:
ans += 1
ac[ax] -= 1
ac[y] += 1
ydi = y - ac[y]
if ydi >= 0:
ad[ydi] += 1
if ad[ydi] == 1:
ans -= 1
an[x - 1] = y
anss.append(ans)
print('\n'.join(map(str, anss)))
``` | output | 1 | 10,643 | 16 | 21,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2
Submitted Solution:
```
import sys
from collections import Counter
# sys.stdin = open('c1.in')
def read_int_list():
return list(map(int, input().split()))
def read_int():
return int(input())
def read_str_list():
return input().split()
def read_str():
return input()
def vanish(p, details=False):
while p:
if details:
print(p)
n = len(p)
q = [x for x in p if x != n]
if len(q) == len(p):
return False
p = q[:]
return True
def check(n):
if n == 3:
for i in range(1, n+1):
for j in range(i, n+1):
for k in range(j, n+1):
p = [i, j, k]
if vanish(p):
print(p)
# print()
# vanish(p, details=True)
if n == 5:
for i in range(1, n+1):
for j in range(i, n+1):
for k in range(j, n+1):
for l in range(k, n+1):
p = [i, j, k, l]
if vanish(p):
print(p)
# print()
# vanish(p, details=True)
if n == 5:
for i in range(1, n+1):
for j in range(i, n+1):
for k in range(j, n+1):
for l in range(k, n+1):
for m in range(l, n+1):
p = [i, j, k, l, m]
if vanish(p):
print(p)
# print()
# vanish(p, details=True)
def solve():
# check(3)
# check(4)
# check(5)
n, m = read_int_list()
a = read_int_list()
p = [read_int_list() for _ in range(m)]
c = Counter(a)
res = []
for x, y in p:
c[a[x-1]] -= 1
a[x-1] = y
c[a[x-1]] += 1
covered = set(range(n))
for i, ni in c.items():
for j in range(i - ni, i):
if j in covered:
covered.remove(j)
r = len(covered)
res.append(r)
return '\n'.join(map(str, res))
def main():
res = solve()
print(res)
if __name__ == '__main__':
main()
``` | instruction | 0 | 10,644 | 16 | 21,288 |
No | output | 1 | 10,644 | 16 | 21,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2
Submitted Solution:
```
import sys
input = sys.stdin.readline
"""
・とりあえず部分点解法：各クエリに対してO(N)
・いくつかを残していくつかを自由に埋める
・残すもの：被覆区間がoverlapしないように残す
・つまり、区間で覆えている点が処理できて、区間で覆えていない点が他所から持ってこないといけない。
"""
N,M = map(int,input().split())
A = [int(x) for x in input().split()]
XY = [tuple(int(x) for x in input().split()) for _ in range(M)]
def subscore_solution():
from collections import Counter
for x,y in XY:
A[x-1] = y
covered = [False] * (N+N+10)
for key,cnt in Counter(A).items():
for i in range(cnt):
covered[max(0,key-i)] = True
print(sum(not bl for bl in covered[1:N+1]))
if N <= 200 and M <= 200:
subscore_solution()
exit()
raise Exception
``` | instruction | 0 | 10,645 | 16 | 21,290 |
No | output | 1 | 10,645 | 16 | 21,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2
Submitted Solution:
```
from collections import Counter, defaultdict
n, m = map(int, input().split())
an = list(map(int, input().split()))
ac = defaultdict(int, Counter(an))
ad = [0] * (n * 2)
for a, c in ac.items():
for i in range(a - c, a):
ad[i] += 1
ans = ad[:n].count(0)
for _ in range(m):
x, y = map(int, input().split())
ax = an[x - 1]
xdi = ax - ac[ax]
ad[xdi] -= 1
if xdi >= 0 and ad[xdi] == 0:
ans += 1
ac[ax] -= 1
ac[y] += 1
ydi = y - ac[y]
ad[ydi] += 1
if ydi >= 0 and ad[ydi] == 1:
ans -= 1
an[x - 1] = y
print(ans)
``` | instruction | 0 | 10,646 | 16 | 21,292 |
No | output | 1 | 10,646 | 16 | 21,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in a row. Initially, the i-th ball from the left has the integer A_i written on it.
When Snuke cast a spell, the following happens:
* Let the current number of balls be k. All the balls with k written on them disappear at the same time.
Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.
By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.
After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.
Constraints
* 1 \leq N \leq 200000
* 1 \leq M \leq 200000
* 1 \leq A_i \leq N
* 1 \leq X_j \leq N
* 1 \leq Y_j \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M
Output
Print M lines. The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.
Examples
Input
5 3
1 1 3 4 5
1 2
2 5
5 4
Output
0
1
1
Input
4 4
4 4 4 4
4 1
3 1
1 1
2 1
Output
0
1
2
3
Input
10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7
Output
1
0
1
2
2
3
3
3
3
2
Submitted Solution:
```
from collections import Counter
N,M = map(int,input().split())
arr = list(map(int,input().split()))
for i in range(M):
X,Y = map(int,input().split())
arr[X-1] = Y
counter = Counter(arr)
balls = N
count = 0
for n in range(N,0,-1):
if n > balls: continue
if balls in counter:
balls -= counter[balls]
else:
count += 1
balls -= 1
print(count)
``` | instruction | 0 | 10,647 | 16 | 21,294 |
No | output | 1 | 10,647 | 16 | 21,295 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083 | instruction | 0 | 10,664 | 16 | 21,328 |
"Correct Solution:
```
from functools import reduce
mod = 924844033
frac = [1]*5555
for i in range(2,5555):
frac[i] = i * frac[i-1]%mod
fraci = [None]*5555
fraci[-1] = pow(frac[-1], mod -2, mod)
for i in range(-2, -5555, -1):
fraci[i] = fraci[i+1] * (5555 + i + 1) % mod
N, K = map(int, input().split())
dp = [[[0]*3 for _ in range(N)] for _ in range(-(-N//(2*K)) + 1)]
def merge(A, B):
C = [0]*(len(A) + len(B) - 1)
for i in range(len(A)):
for j in range(len(B)):
C[i+j] = (C[i+j] + A[i]*B[j]) % mod
return C
for j in range(min(N, 2*K)):
dp[0][j][2] = 1
if j + K <= N-1:
dp[1][j][0] = 1
if j - K >= 0:
dp[1][j][1] = 1
for i in range(-(-N//(2*K)) + 1):
for j in range(N):
if j + 2*K > N - 1:
break
r = dp[i][j][0]
l = dp[i][j][1]
n = dp[i][j][2]
if i == -(-N//(2*K)):
dp[i][j+2*K][2] = (dp[i][j+2*K][2] + r + l + n) % mod
continue
if j + 3*K <= N - 1:
dp[i+1][j+2*K][0] = (dp[i+1][j+2*K][0] + r + l + n) % mod
dp[i][j+2*K][2] = (dp[i][j+2*K][2] + r + l + n) % mod
dp[i+1][j+2*K][1] = (dp[i+1][j+2*K][1] + l + n) % mod
Ans = []
for j in range(min(2*K, N)):
j = - 1 - j
Ans.append([sum(dp[i][j]) for i in range(-(-N//(2*K)) + 1)])
A = reduce(merge, Ans)
A = [((-1)**i * frac[N - i] * a)%mod for i, a in enumerate(A)]
print(sum(A)%mod)
``` | output | 1 | 10,664 | 16 | 21,329 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083 | instruction | 0 | 10,665 | 16 | 21,330 |
"Correct Solution:
```
from collections import defaultdict
n,k = map(int,input().split())
mod = 924844033
rng = 2010
fctr = [1]
finv = [1]
for i in range(1,rng):
fctr.append(fctr[-1]*i%mod)
for i in range(1,rng):
finv.append(pow(fctr[i],mod-2,mod))
def cmb(n,k):
if n<0 or k<0:
return 0
else:
return fctr[n]*finv[n-k]*finv[k]%mod
if (n-k)*2 <= n:
x = (n-k)*2
ans = 0
for i in range(x+1):
if i%2 == 0:
ans += cmb(x,i)*fctr[n-i]
else:
ans -= cmb(x,i)*fctr[n-i]
ans %= mod
print(ans)
exit()
dc = defaultdict(int)
for j in range(1,k+1):
a = j
b = k+j
cnt = 0
while a<=n and b<=n:
if a>b:
b += 2*k
else:
a += 2*k
cnt += 1
dc[cnt] += 2
nn = (n-k)*2
cp = set()
cpp = 1
for i,x in dc.items():
for j in range(x):
cpp += i
cp.add(cpp)
cp.add(1)
dp = [[0 for j in range(n+1)] for i in range(nn+1)]
dp[0][0] = 1
for i in range(1,nn+1):
dp[i] = dp[i-1][:]
if i not in cp:
for j in range(1,min(i,n)+1):
dp[i][j] += dp[i-2][j-1]
dp[i][j] %= mod
else:
for j in range(1,min(i,n)+1):
dp[i][j] += dp[i-1][j-1]
dp[i][j] %= mod
ans = 0
for i in range(n+1):
if i%2 == 0:
ans += fctr[n-i]*dp[nn][i]
else:
ans -= fctr[n-i]*dp[nn][i]
ans %= mod
print(ans)
``` | output | 1 | 10,665 | 16 | 21,331 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083 | instruction | 0 | 10,666 | 16 | 21,332 |
"Correct Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
sys.setrecursionlimit(2147483647)
INF = 10 ** 13
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().rstrip().split()
def S(): return sys.stdin.readline().rstrip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod=924844033
n,k=LI()
fac = [1] * (n + 1)
for j in range(1, n + 1):
fac[j] = fac[j-1] * j % mod
dp=[[0]*2 for _ in range(n+1)]
dp[0][0]=1
last=0
for i in range(min(n,2*k)):
idx=i
while idx<n:
ndp = [[0] * 2 for _ in range(n+1)]
if idx==i:
for ll in range(n+1):
dp[ll][0]+=dp[ll][1]
dp[ll][1]=0
for l in range(1,n+1):
ndp[l][0]=sum(dp[l])
if idx-k>=0:
ndp[l][0]+=dp[l-1][0]
if idx+k<n:
ndp[l][1]=sum(dp[l-1])
ndp[l][0]%=mod
ndp[0][0]=1
dp=ndp
idx+=2*k
ans=fac[n]
for m in range(1,n+1):
if m%2:
ans-=sum(dp[m])*fac[n-m]%mod
else:
ans+=sum(dp[m])*fac[n-m]%mod
ans%=mod
print(ans)
``` | output | 1 | 10,666 | 16 | 21,333 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083
Submitted Solution:
```
from itertools import permutations
MAX = 924844033
n, k = [int(x) for x in input().split()]
k_perm = permutations(range(1, n+1))
ans = 0
# ans_list = []
for perm in k_perm:
like = True
for i in range(n):
if abs(perm[i] - (i+1)) == k:
like = False
if like:
# ans_list.append(perm)
ans +=1
print(ans % MAX)
# print(ans_list)
``` | instruction | 0 | 10,667 | 16 | 21,334 |
No | output | 1 | 10,667 | 16 | 21,335 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083
Submitted Solution:
```
from collections import defaultdict
n,k = map(int,input().split())
mod = 924844033
rng = 2010
fctr = [1]
finv = [1]
for i in range(1,rng):
fctr.append(fctr[-1]*i%mod)
for i in range(1,rng):
finv.append(pow(fctr[i],mod-2,mod))
def cmb(n,k):
if n<0 or k<0:
return 0
else:
return fctr[n]*finv[n-k]*finv[k]%mod
if (n-k)*2 <= n:
x = (n-k)*2
ans = 0
for i in range(x+1):
if i%2 == 0:
ans += cmb(x,i)*fctr[n-i]
else:
ans -= cmb(x,i)*fctr[n-i]
ans %= mod
print(ans)
exit()
dc = defaultdict(int)
for j in range(1,k+1):
a = j
b = k+j
cnt = 0
while a<=n and b<=n:
if a>b:
b += 2*k
else:
a += 2*k
cnt += 1
dc[cnt] += 2
nn = (n-k)*2
cp = set()
cpp = 1
for i,x in dc.items():
for j in range(x):
cpp += i
cp.add(cpp)
cp.add(1)
dp = [[0 for j in range(n+1)] for i in range(nn+1)]
dp[0][0] = 1
for i in range(1,nn+1):
dp[i] = dp[i-1][:]
if i not in cp:
for j in range(1,min(i,n)+1):
dp[i][j] += dp[i-2][j-1]
else:
for j in range(1,min(i,n)+1):
dp[i][j] += dp[i-1][j-1]
dp[i][j] %= mod
ans = 0
for i in range(n+1):
if i%2 == 0:
ans += fctr[n-i]*dp[nn][i]
else:
ans -= fctr[n-i]*dp[nn][i]
ans %= mod
print(ans)
``` | instruction | 0 | 10,668 | 16 | 21,336 |
No | output | 1 | 10,668 | 16 | 21,337 |
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