text stringlengths 198 433k | conversation_id int64 0 109k |
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array A, consisting of n positive integers a_1, a_2, ..., a_n, and an array B, consisting of m positive integers b_1, b_2, ..., b_m.
Choose some element a of A and some element b of B such that a+b doesn't belong to A and doesn't belong to B.
For example, if A = [2, 1, 7] and B = [1, 3, 4], we can choose 1 from A and 4 from B, as number 5 = 1 + 4 doesn't belong to A and doesn't belong to B. However, we can't choose 2 from A and 1 from B, as 3 = 2 + 1 belongs to B.
It can be shown that such a pair exists. If there are multiple answers, print any.
Choose and print any such two numbers.
Input
The first line contains one integer n (1β€ n β€ 100) β the number of elements of A.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 200) β the elements of A.
The third line contains one integer m (1β€ m β€ 100) β the number of elements of B.
The fourth line contains m different integers b_1, b_2, ..., b_m (1 β€ b_i β€ 200) β the elements of B.
It can be shown that the answer always exists.
Output
Output two numbers a and b such that a belongs to A, b belongs to B, but a+b doesn't belong to nor A neither B.
If there are multiple answers, print any.
Examples
Input
1
20
2
10 20
Output
20 20
Input
3
3 2 2
5
1 5 7 7 9
Output
3 1
Input
4
1 3 5 7
4
7 5 3 1
Output
1 1
Note
In the first example, we can choose 20 from array [20] and 20 from array [10, 20]. Number 40 = 20 + 20 doesn't belong to any of those arrays. However, it is possible to choose 10 from the second array too.
In the second example, we can choose 3 from array [3, 2, 2] and 1 from array [1, 5, 7, 7, 9]. Number 4 = 3 + 1 doesn't belong to any of those arrays.
In the third example, we can choose 1 from array [1, 3, 5, 7] and 1 from array [7, 5, 3, 1]. Number 2 = 1 + 1 doesn't belong to any of those arrays.
Submitted Solution:
```
n=int(input())
a = list(map(int, input().split()))
k=int(input())
b = list(map(int, input().split()))
d=a+b
i=0
j=0
while i<n:
while j<k:
if a[i]+b[j] not in d:
print(a[i],b[j])
j=k
i=n
```
No
| 102,100 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array A, consisting of n positive integers a_1, a_2, ..., a_n, and an array B, consisting of m positive integers b_1, b_2, ..., b_m.
Choose some element a of A and some element b of B such that a+b doesn't belong to A and doesn't belong to B.
For example, if A = [2, 1, 7] and B = [1, 3, 4], we can choose 1 from A and 4 from B, as number 5 = 1 + 4 doesn't belong to A and doesn't belong to B. However, we can't choose 2 from A and 1 from B, as 3 = 2 + 1 belongs to B.
It can be shown that such a pair exists. If there are multiple answers, print any.
Choose and print any such two numbers.
Input
The first line contains one integer n (1β€ n β€ 100) β the number of elements of A.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 200) β the elements of A.
The third line contains one integer m (1β€ m β€ 100) β the number of elements of B.
The fourth line contains m different integers b_1, b_2, ..., b_m (1 β€ b_i β€ 200) β the elements of B.
It can be shown that the answer always exists.
Output
Output two numbers a and b such that a belongs to A, b belongs to B, but a+b doesn't belong to nor A neither B.
If there are multiple answers, print any.
Examples
Input
1
20
2
10 20
Output
20 20
Input
3
3 2 2
5
1 5 7 7 9
Output
3 1
Input
4
1 3 5 7
4
7 5 3 1
Output
1 1
Note
In the first example, we can choose 20 from array [20] and 20 from array [10, 20]. Number 40 = 20 + 20 doesn't belong to any of those arrays. However, it is possible to choose 10 from the second array too.
In the second example, we can choose 3 from array [3, 2, 2] and 1 from array [1, 5, 7, 7, 9]. Number 4 = 3 + 1 doesn't belong to any of those arrays.
In the third example, we can choose 1 from array [1, 3, 5, 7] and 1 from array [7, 5, 3, 1]. Number 2 = 1 + 1 doesn't belong to any of those arrays.
Submitted Solution:
```
n = int(input())
ns = input().split()
m = int(input())
ms = input().split()
for i in range(n):
for x in range(m):
if int(ms[x]) + int(ns[i]) in ns:
pass
else:
if int(ms[x]) + int(ns[i]) in ns:
pass
else:
print(ns[i], ms[x])
exit()
```
No
| 102,101 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array A, consisting of n positive integers a_1, a_2, ..., a_n, and an array B, consisting of m positive integers b_1, b_2, ..., b_m.
Choose some element a of A and some element b of B such that a+b doesn't belong to A and doesn't belong to B.
For example, if A = [2, 1, 7] and B = [1, 3, 4], we can choose 1 from A and 4 from B, as number 5 = 1 + 4 doesn't belong to A and doesn't belong to B. However, we can't choose 2 from A and 1 from B, as 3 = 2 + 1 belongs to B.
It can be shown that such a pair exists. If there are multiple answers, print any.
Choose and print any such two numbers.
Input
The first line contains one integer n (1β€ n β€ 100) β the number of elements of A.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 200) β the elements of A.
The third line contains one integer m (1β€ m β€ 100) β the number of elements of B.
The fourth line contains m different integers b_1, b_2, ..., b_m (1 β€ b_i β€ 200) β the elements of B.
It can be shown that the answer always exists.
Output
Output two numbers a and b such that a belongs to A, b belongs to B, but a+b doesn't belong to nor A neither B.
If there are multiple answers, print any.
Examples
Input
1
20
2
10 20
Output
20 20
Input
3
3 2 2
5
1 5 7 7 9
Output
3 1
Input
4
1 3 5 7
4
7 5 3 1
Output
1 1
Note
In the first example, we can choose 20 from array [20] and 20 from array [10, 20]. Number 40 = 20 + 20 doesn't belong to any of those arrays. However, it is possible to choose 10 from the second array too.
In the second example, we can choose 3 from array [3, 2, 2] and 1 from array [1, 5, 7, 7, 9]. Number 4 = 3 + 1 doesn't belong to any of those arrays.
In the third example, we can choose 1 from array [1, 3, 5, 7] and 1 from array [7, 5, 3, 1]. Number 2 = 1 + 1 doesn't belong to any of those arrays.
Submitted Solution:
```
n=int(input())
a = list(map(int, input().split()))
k=int(input())
b = list(map(int, input().split()))
##n=5
##a=[1,2,3,4,5]
##k=1
##b=[1]
t=True
d=a+b
print(d)
for i in a:
for j in b:
if not i+j in d:
print(i,j)
t=False
break
elif i+j in d:
continue
if not t:
break
```
No
| 102,102 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array A, consisting of n positive integers a_1, a_2, ..., a_n, and an array B, consisting of m positive integers b_1, b_2, ..., b_m.
Choose some element a of A and some element b of B such that a+b doesn't belong to A and doesn't belong to B.
For example, if A = [2, 1, 7] and B = [1, 3, 4], we can choose 1 from A and 4 from B, as number 5 = 1 + 4 doesn't belong to A and doesn't belong to B. However, we can't choose 2 from A and 1 from B, as 3 = 2 + 1 belongs to B.
It can be shown that such a pair exists. If there are multiple answers, print any.
Choose and print any such two numbers.
Input
The first line contains one integer n (1β€ n β€ 100) β the number of elements of A.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 200) β the elements of A.
The third line contains one integer m (1β€ m β€ 100) β the number of elements of B.
The fourth line contains m different integers b_1, b_2, ..., b_m (1 β€ b_i β€ 200) β the elements of B.
It can be shown that the answer always exists.
Output
Output two numbers a and b such that a belongs to A, b belongs to B, but a+b doesn't belong to nor A neither B.
If there are multiple answers, print any.
Examples
Input
1
20
2
10 20
Output
20 20
Input
3
3 2 2
5
1 5 7 7 9
Output
3 1
Input
4
1 3 5 7
4
7 5 3 1
Output
1 1
Note
In the first example, we can choose 20 from array [20] and 20 from array [10, 20]. Number 40 = 20 + 20 doesn't belong to any of those arrays. However, it is possible to choose 10 from the second array too.
In the second example, we can choose 3 from array [3, 2, 2] and 1 from array [1, 5, 7, 7, 9]. Number 4 = 3 + 1 doesn't belong to any of those arrays.
In the third example, we can choose 1 from array [1, 3, 5, 7] and 1 from array [7, 5, 3, 1]. Number 2 = 1 + 1 doesn't belong to any of those arrays.
Submitted Solution:
```
a1=int(input())
a=list(map(int,input().split()))
b1=int(input())
b=list(map(int,input().split()))
z=0
x=0
l1=[]
l2=[]
for i in range(len(a)):
for j in range(len(b)):
x=(a[i]+b[j])
if x not in (b or a):
l1.append(a[i])
l2.append(b[j])
break
if z>0:
print("0")
else:
print(l1[0],l2[0])
```
No
| 102,103 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
import sys as _sys
def main():
q = int(input())
for i_q in range(q):
n, = _read_ints()
a = tuple(_read_ints())
result = find_min_sorting_cost(sequence=a)
print(result)
def _read_line():
result = _sys.stdin.readline()
assert result[-1] == "\n"
return result[:-1]
def _read_ints():
return map(int, _read_line().split(" "))
def find_min_sorting_cost(sequence):
sequence = tuple(sequence)
if not sequence:
return 0
indices_by_values = {x: [] for x in sequence}
for i, x in enumerate(sequence):
indices_by_values[x].append(i)
borders_by_values = {
x: (indices[0], indices[-1]) for x, indices in indices_by_values.items()
}
borders_sorted_by_values = [borders for x, borders in sorted(borders_by_values.items())]
max_cost_can_keep_n = curr_can_keep_n = 1
for prev_border, curr_border in zip(borders_sorted_by_values, borders_sorted_by_values[1:]):
if curr_border[0] > prev_border[1]:
curr_can_keep_n += 1
else:
if curr_can_keep_n > max_cost_can_keep_n:
max_cost_can_keep_n = curr_can_keep_n
curr_can_keep_n = 1
if curr_can_keep_n > max_cost_can_keep_n:
max_cost_can_keep_n = curr_can_keep_n
return len(set(sequence)) - max_cost_can_keep_n
if __name__ == '__main__':
main()
```
| 102,104 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
from collections import defaultdict
def main():
t=int(input())
allans=[]
for _ in range(t):
n=int(input())
a=readIntArr()
b=sorted(a)
if a==b:
allans.append(0)
continue
minIndexes=defaultdict(lambda:inf)
maxIndexes=defaultdict(lambda:-inf)
for i in range(n):
minIndexes[a[i]]=min(minIndexes[a[i]],i)
maxIndexes[a[i]]=max(maxIndexes[a[i]],i)
uniqueVals=list(minIndexes.keys())
uniqueVals.sort()
# iterating from left, if maxIdx[smaller]>minIdx[larger], then everything less than smaller must be shifted left
m=len(uniqueVals)
prefixMaxOverlapIndex=[0]*m
for i in range(1,m):
if maxIndexes[uniqueVals[i-1]]>minIndexes[uniqueVals[i]]:
prefixMaxOverlapIndex[i]=i
prefixMaxOverlapIndex[i]=max(prefixMaxOverlapIndex[i],prefixMaxOverlapIndex[i-1])
#similar logic when iterating from right
suffixMinOverlapIndex=[m-1]*m
for i in range(m-2,-1,-1):
if maxIndexes[uniqueVals[i]]>minIndexes[uniqueVals[i+1]]:
suffixMinOverlapIndex[i]=i
suffixMinOverlapIndex[i]=min(suffixMinOverlapIndex[i],suffixMinOverlapIndex[i+1])
preCnts=prefixMaxOverlapIndex
sufCnts=[m-1-x for x in suffixMinOverlapIndex]
ans=inf
for i in range(m): # find the min if I don't move uniqueVals[i]
ans=min(ans,preCnts[i]+sufCnts[i])
# print('minIndexes:{}'.format(minIndexes))
# print('maxIndexes:{}'.format(maxIndexes))
# print('uniqueVals:{}'.format(uniqueVals))
# print('pre:{}'.format(preCnts))
# print('suf:{}'.format(sufCnts))
allans.append(ans)
multiLineArrayPrint(allans)
return
import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
# input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
def oneLineArrayPrint(arr):
print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
def readIntArr():
return [int(x) for x in input().split()]
# def readFloatArr():
# return [float(x) for x in input().split()]
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
dv=defaultValFactory;da=dimensionArr
if len(da)==1:return [dv() for _ in range(da[0])]
else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
def queryInteractive(i,j):
print('? {} {}'.format(i,j))
sys.stdout.flush()
return int(input())
def answerInteractive(ans):
print('! {}'.format(' '.join([str(x) for x in ans])))
sys.stdout.flush()
inf=float('inf')
MOD=10**9+7
# MOD=998244353
for _abc in range(1):
main()
```
| 102,105 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
import sys
input = sys.stdin.readline
def solve():
n = int(input())
a = list(map(int,input().split()))
s = set(a)
s = sorted(list(s))
ref = {x:i for i,x in enumerate(list(s))}
sz = len(s)
L = [1<<32]*sz
R = [-1<<32]*sz
for i in range(n):
k = ref[a[i]]
L[k] = min(L[k], i)
R[k] = max(R[k], i)
dp = [0]*sz
for k in range(sz):
if k == 0 or L[k] < R[k-1]:
dp[k] = 1
else:
dp[k] = 1 + dp[k-1]
ans = 1<<32
for k in range(sz):
ans = min(ans, sz - dp[k])
print(ans)
return 0
for nt in range(int(input())):
solve()
```
| 102,106 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
# |
# _` | __ \ _` | __| _ \ __ \ _` | _` |
# ( | | | ( | ( ( | | | ( | ( |
# \__,_| _| _| \__,_| \___| \___/ _| _| \__,_| \__,_|
import sys
import math
def read_line():
return sys.stdin.readline()[:-1]
def read_int():
return int(sys.stdin.readline())
def read_int_line():
return [int(v) for v in sys.stdin.readline().split()]
def read_float_line():
return [float(v) for v in sys.stdin.readline().split()]
t = read_int()
for i in range(t):
n = read_int()
a = read_int_line()
d = {}
for i in range(n):
if a[i] in d:
d[a[i]].append(i)
else:
d[a[i]] = [i]
dp = [1]*len(list(d.keys()))
s = list(d.keys())
s.sort()
for i in range(len(s)-2,-1,-1):
if d[s[i]][-1] < d[s[i+1]][0]:
dp[i] = dp[i+1]+1
else:
dp[i] = 1
ans = len(s)-max(dp)
print(ans)
```
| 102,107 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
# SHRi GANESHA author: Kunal Verma #
import os
import sys
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict
from io import BytesIO, IOBase
from math import gcd, inf, sqrt, ceil, floor
#sys.setrecursionlimit(2*10**5)
def lcm(a, b):
return (a * b) // gcd(a, b)
'''
mod = 10 ** 9 + 7
fac = [1]
for i in range(1, 2 * 10 ** 5 + 1):
fac.append((fac[-1] * i) % mod)
fac_in = [pow(fac[-1], mod - 2, mod)]
for i in range(2 * 10 ** 5, 0, -1):
fac_in.append((fac_in[-1] * i) % mod)
fac_in.reverse()
def comb(a, b):
if a < b:
return 0
return (fac[a] * fac_in[b] * fac_in[a - b]) % mod
'''
MAXN = 1000004
spf = [0 for i in range(MAXN)]
def sieve():
spf[1] = 1
for i in range(2, MAXN):
spf[i] = i
for i in range(4, MAXN, 2):
spf[i] = 2
for i in range(3, ceil(sqrt(MAXN))):
if (spf[i] == i):
for j in range(i * i, MAXN, i):
if (spf[j] == j):
spf[j] = i
def getFactorization(x):
ret = Counter()
while (x != 1):
ret[spf[x]] += 1
x = x // spf[x]
return ret
def printDivisors(n):
i = 2
z = [1, n]
while i <= sqrt(n):
if (n % i == 0):
if (n / i == i):
z.append(i)
else:
z.append(i)
z.append(n // i)
i = i + 1
return z
def create(n, x, f):
pq = len(bin(n)[2:])
if f == 0:
tt = min
else:
tt = max
dp = [[inf] * n for _ in range(pq)]
dp[0] = x
for i in range(1, pq):
for j in range(n - (1 << i) + 1):
dp[i][j] = tt(dp[i - 1][j], dp[i - 1][j + (1 << (i - 1))])
return dp
def enquiry(l, r, dp, f):
if l > r:
return inf if not f else -inf
if f == 1:
tt = max
else:
tt = min
pq1 = len(bin(r - l + 1)[2:]) - 1
return tt(dp[pq1][l], dp[pq1][r - (1 << pq1) + 1])
def SieveOfEratosthenes(n):
prime = [True for i in range(n + 1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n + 1, p):
prime[i] = False
p += 1
x = []
for i in range(2, n + 1):
if prime[i]:
x.append(i)
return x
def main():
for _ in range(int(input())):
n = int(input())
a = [int(X) for X in input().split()]
x = sorted(list(set(a)))
y = [-1] * n
mi, ma = [-1] * len(x), [0] * len(x)
dp = [1] * len(x)
for i in range(len(x)):
y[x[i] - 1] = i
for i in range(n):
if mi[y[a[i] - 1]] == -1:
mi[y[a[i] - 1]] = i
ma[y[a[i] - 1]] = i
# print(mi,ma)
for i in range(1, len(x)):
if mi[i] > ma[i - 1]:
dp[i] += dp[i - 1]
# print(dp)
print(len(x) - max(dp))
# Fast IO Region
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == '__main__':
main()
```
| 102,108 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
def main():
from sys import stdin, stdout
for _ in range(int(stdin.readline())):
n = int(stdin.readline())
inp1 = [-1] * (n + 1)
inp2 = [-1] * (n + 1)
for i, ai in enumerate(map(int, stdin.readline().split())):
if inp1[ai] < 0:
inp1[ai] = i
inp2[ai] = i
inp1 = tuple((inp1i for inp1i in inp1 if inp1i >= 0))
inp2 = tuple((inp2i for inp2i in inp2 if inp2i >= 0))
n = len(inp1)
ans = 0
cur = 0
for i in range(n):
if i and inp1[i] < inp2[i - 1]:
cur = 1
else:
cur += 1
ans = max(ans, cur)
stdout.write(f'{n - ans}\n')
main()
```
| 102,109 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
from sys import stdin, stdout, setrecursionlimit
input = stdin.readline
# import string
# characters = string.ascii_lowercase
# digits = string.digits
# setrecursionlimit(int(1e5))
# dir = [-1,0,1,0,-1]
# moves = 'NESW'
inf = float('inf')
from functools import cmp_to_key
from collections import defaultdict as dd
from collections import Counter, deque
from heapq import *
import math
from math import floor, ceil, sqrt
def geti(): return map(int, input().strip().split())
def getl(): return list(map(int, input().strip().split()))
def getis(): return map(str, input().strip().split())
def getls(): return list(map(str, input().strip().split()))
def gets(): return input().strip()
def geta(): return int(input())
def print_s(s): stdout.write(s+'\n')
def solve():
for _ in range(geta()):
n = geta()
a = getl()
mini = dd(int)
maxi = dd(int)
for i in range(n):
if a[i] not in mini:
mini[a[i]] = i
maxi[a[i]] = i
order = sorted(set(a))
good = 0
count = 1
for i in range(1, len(order)):
if mini[order[i]] > maxi[order[i-1]]:
count += 1
else:
good = max(good, count)
count = 1
good = max(good, count)
print(len(order) - good)
if __name__=='__main__':
solve()
```
| 102,110 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Tags: dp, greedy, two pointers
Correct Solution:
```
from sys import stdin
input = stdin.readline
def main():
anses = []
for _ in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
f = [0]*(n+1)
d = sorted(list(set(a)))
for q in range(1, len(d)+1):
f[d[q-1]] = q
for q in range(len(a)):
a[q] = f[a[q]]
n = len(d)
starts, ends = [-1]*(n+1), [n+1]*(n+1)
for q in range(len(a)):
if starts[a[q]] == -1:
starts[a[q]] = q
ends[a[q]] = q
s = [0]*(n+1)
max1 = -float('inf')
for q in range(1, n+1):
s[q] = s[q-1]*(ends[q-1] < starts[q])+1
max1 = max(max1, s[q])
anses.append(str(len(d)-max1))
print('\n'.join(anses))
main()
```
| 102,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
from math import factorial
from collections import Counter, defaultdict, deque
from heapq import heapify, heappop, heappush
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0
def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0
def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2)
def ctd(chr): return ord(chr)-ord("a")
mod = 998244353
INF = float('inf')
from bisect import bisect_left
# ------------------------------
def main():
for _ in range(N()):
n = N()
arr = RLL()
dic = defaultdict(list)
for i in range(n): dic[arr[i]].append(i)
nl = list(dic.keys())
nl.sort(reverse=1)
le = len(nl)
dp = [1]*le
for i in range(1, le):
if dic[nl[i]][-1]<dic[nl[i-1]][0]:
dp[i] = dp[i-1]+1
print(le-max(dp))
if __name__ == "__main__":
main()
```
Yes
| 102,112 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
from sys import stdin
input = stdin.readline
def Input():
global A, n, D ,F
n = int(input())
A = list(map(int, input().split()))
D = sorted(list(set(A)))
F = [0] * (n + 1)
def Ans():
for i in range(1, len(D) + 1):
F[D[i - 1]] = i
for i in range(n):
A[i] = F[A[i]]
m = len(D)
Start = [-1] * (m + 1)
End = [n + 1] * (m + 1)
for i in range(n):
if Start[A[i]] == -1:
Start[A[i]] = i
End[A[i]] = i
S = [0] * (m + 1)
Max = -float('inf')
for i in range(1, m + 1):
S[i] = S[i - 1] * (End[i - 1] < Start[i]) + 1
Max = max(Max, S[i])
Result.append(str(m-Max))
def main():
global Result
Result=[]
for _ in range(int(input())):
Input()
Ans()
print('\n'.join(Result))
if __name__ == '__main__':
main()
```
Yes
| 102,113 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
import copy
def DeleteRepetitionsIn(Array):
AlreadyRead = {}
index = 0
ConstantArray = copy.deepcopy(Array)
for a in range(len(ConstantArray)):
if Array[index] not in AlreadyRead:
AlreadyRead[Array[index]] = ""
index += 1
continue
Array = Array[0:index] + Array[index + 1:len(Array)]
return Array
def DeleteRepetitionsIn2(Array):
AlreadyRead = {}
for elem in Array:
if elem in AlreadyRead:
continue
AlreadyRead[elem] = ""
return list(AlreadyRead)
Results = []
ArraysNumber = int(input())
for e in range(ArraysNumber):
AbsolutelyUselessNumber = int(input())
Array = list(map(int, input().split()))
if len(Array) == 1:
Results.append(0)
continue
#print(Array)
TheRightOrder = DeleteRepetitionsIn2(Array)
TheRightOrder.sort()
TheCurrentOrder = {}
for i in range(len(Array)):
if Array[i] not in TheCurrentOrder:
TheCurrentOrder[Array[i]] = [i, i]
continue
TheCurrentOrder[Array[i]][1] = i
#print(TheRightOrder)
#print(TheCurrentOrder)
#print(Array)
TheCurrentResult = 1
TheMaxResult = 1
for i in range(len(TheRightOrder)):
#print("a =", TheCurrentResult)
#print("b =", TheMaxResult)
if i == len(TheRightOrder) - 1:
if TheCurrentResult >= TheMaxResult:
TheMaxResult = TheCurrentResult
continue
if TheCurrentOrder[TheRightOrder[i]][1] > TheCurrentOrder[TheRightOrder[i + 1]][0]:
if TheCurrentResult >= TheMaxResult:
TheMaxResult = TheCurrentResult
TheCurrentResult = 1
continue
TheCurrentResult += 1
Results.append(len(TheRightOrder) - TheMaxResult)
for i in Results:
print(i)
```
Yes
| 102,114 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
import os
import sys
def solve(arr):
items = sorted(set(arr))
min_max = [(float("inf"), float("-inf"))] * len(items)
item_to_idx = {k: idx for idx, k in enumerate(items)}
for idx, a in enumerate(arr):
m, M = min_max[item_to_idx[a]]
min_max[item_to_idx[a]] = (min(idx, m), max(idx, M))
best = 1
current = 1
for i in range(1, len(items)):
_, prev_M = min_max[i - 1]
m, _ = min_max[i]
if prev_M <= m:
current += 1
else:
current = 1
best = max(best, current)
return len(items) - best
def pp(input):
T = int(input())
for t in range(T):
input()
arr = list(map(int, input().strip().split()))
print(solve(arr))
if "paalto" in os.getcwd():
from string_source import string_source, codeforces_parse
pp(
string_source(
"""3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7"""
)
)
else:
pp(sys.stdin.readline)
```
Yes
| 102,115 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
import copy
def DeleteRepetitionsIn(Array):
AlreadyRead = {}
index = 0
ConstantArray = copy.deepcopy(Array)
for a in range(len(ConstantArray)):
if Array[index] not in AlreadyRead:
AlreadyRead[Array[index]] = ""
index += 1
continue
Array = Array[0:index] + Array[index + 1:len(Array)]
return Array
def DeleteRepetitionsIn2(Array):
AlreadyRead = {}
for elem in Array:
if elem in AlreadyRead:
continue
AlreadyRead[elem] = ""
return list(AlreadyRead)
Results = []
ArraysNumber = int(input())
for e in range(ArraysNumber):
AbsolutelyUselessNumber = int(input())
Array = list(map(int, input().split()))
if len(Array) == 1:
Results.append(0)
continue
if len(Array) == 300000:
Results.append(0)
continue
#print(Array)
TheRightOrder = DeleteRepetitionsIn2(Array)
TheRightOrder.sort()
TheCurrentOrder = {}
for i in range(len(Array)):
if Array[i] not in TheCurrentOrder:
TheCurrentOrder[Array[i]] = [i, i]
continue
TheCurrentOrder[Array[i]][1] = i
#print(TheRightOrder)
#print(TheCurrentOrder)
#print(Array)
TheCurrentResult = 1
TheMaxResult = 1
for i in range(len(TheRightOrder)):
#print("a =", TheCurrentResult)
#print("b =", TheMaxResult)
if i == len(TheRightOrder) - 1:
if TheCurrentResult >= TheMaxResult:
TheMaxResult = TheCurrentResult
continue
if TheCurrentOrder[TheRightOrder[i]][1] > TheCurrentOrder[TheRightOrder[i + 1]][0]:
if TheCurrentResult >= TheMaxResult:
TheMaxResult = TheCurrentResult
TheCurrentResult = 1
continue
TheCurrentResult += 1
Results.append(len(TheRightOrder) - TheMaxResult)
for i in Results:
print(i)
```
No
| 102,116 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
import sys as _sys
def main():
q = int(input())
for i_q in range(q):
n, = _read_ints()
a = tuple(_read_ints())
result = find_min_sorting_cost(sequence=a)
print(result)
def _read_line():
result = _sys.stdin.readline()
assert result[-1] == "\n"
return result[:-1]
def _read_ints():
return map(int, _read_line().split(" "))
def find_min_sorting_cost(sequence):
sequence = tuple(sequence)
if not sequence:
return 0
indices_by_values = {x: [] for x in sequence}
for i, x in enumerate(sequence):
indices_by_values[x].append(i)
borders_by_values = {
x: (indices[0], indices[-1]) for x, indices in indices_by_values.items()
}
max_lengths_by_right_borders_tree = [0] * (len(sequence) + 1)
for x in sorted(borders_by_values.keys()):
left_border, right_border = borders_by_values[x]
# max_prev_length = max(max_lengths_by_right_borders[:left_border+1])
max_prev_length = _prefix_max_fenwick_tree(max_lengths_by_right_borders_tree, left_border)
max_new_length = max_prev_length + 1
_set_new_max_fenwick_tree(max_lengths_by_right_borders_tree, right_border, max_new_length)
max_cost_can_keep_n = _prefix_max_fenwick_tree(
max_lengths_by_right_borders_tree, len(sequence) - 1
)
return len(set(sequence)) - max_cost_can_keep_n
def _prefix_max_fenwick_tree(tree, i):
i += 1
result = tree[1]
while i:
if tree[i] > result:
result = tree[i]
i -= i & (-i)
return result
def _set_new_max_fenwick_tree(tree, i, x):
i += 1
if x < tree[i]:
return
while i < len(tree):
if x > tree[i]:
tree[i] = x
i += i & (-i)
if __name__ == '__main__':
main()
```
No
| 102,117 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
def solveForMovingItemsRight(a,n):
# Preserve the Longest Increasing Subsequence containing min. Everything else must shift
latestIdx=dict()
for i in range(n):
latestIdx[a[i]]=i
numIdx=[] # [number, latest idx]
for k,v in latestIdx.items():
numIdx.append([k,v])
numIdx.sort() # sort by number asc
removedNumbers=set()
j=0
for i in range(n):
if a[i]!=numIdx[j][0]:
removedNumbers.add(a[i])
else:
if i==numIdx[j][1]: # last idx for this number
j+=1
# print('a:{} latestIdx:{} numIdx:{} removedNumbers:{}'.format(a,latestIdx,numIdx,removedNumbers))
return len(removedNumbers)
def solveForMovingItemsLeft(a,n): # equivalent to move right, with negated and reversed array
b=a.copy()
b.reverse()
for i in range(n):
b[i]*=-1
return solveForMovingItemsRight(b,n)
def main():
t=int(input())
allans=[]
for _ in range(t):
n=int(input())
a=readIntArr()
b=sorted(a)
if b==a:
allans.append(0)
continue
ans=min(solveForMovingItemsLeft(a,n),solveForMovingItemsRight(a,n))
allans.append(ans)
multiLineArrayPrint(allans)
return
import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
# input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
def oneLineArrayPrint(arr):
print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
def readIntArr():
return [int(x) for x in input().split()]
# def readFloatArr():
# return [float(x) for x in input().split()]
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
dv=defaultValFactory;da=dimensionArr
if len(da)==1:return [dv() for _ in range(da[0])]
else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
def queryInteractive(i,j):
print('? {} {}'.format(i,j))
sys.stdout.flush()
return int(input())
def answerInteractive(ans):
print('! {}'.format(' '.join([str(x) for x in ans])))
sys.stdout.flush()
inf=float('inf')
MOD=10**9+7
# MOD=998244353
for _abc in range(1):
main()
```
No
| 102,118 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, ..., a_n, consisting of integers.
You can apply the following operation to this sequence: choose some integer x and move all elements equal to x either to the beginning, or to the end of a. Note that you have to move all these elements in one direction in one operation.
For example, if a = [2, 1, 3, 1, 1, 3, 2], you can get the following sequences in one operation (for convenience, denote elements equal to x as x-elements):
* [1, 1, 1, 2, 3, 3, 2] if you move all 1-elements to the beginning;
* [2, 3, 3, 2, 1, 1, 1] if you move all 1-elements to the end;
* [2, 2, 1, 3, 1, 1, 3] if you move all 2-elements to the beginning;
* [1, 3, 1, 1, 3, 2, 2] if you move all 2-elements to the end;
* [3, 3, 2, 1, 1, 1, 2] if you move all 3-elements to the beginning;
* [2, 1, 1, 1, 2, 3, 3] if you move all 3-elements to the end;
You have to determine the minimum number of such operations so that the sequence a becomes sorted in non-descending order. Non-descending order means that for all i from 2 to n, the condition a_{i-1} β€ a_i is satisfied.
Note that you have to answer q independent queries.
Input
The first line contains one integer q (1 β€ q β€ 3 β
10^5) β the number of the queries. Each query is represented by two consecutive lines.
The first line of each query contains one integer n (1 β€ n β€ 3 β
10^5) β the number of elements.
The second line of each query contains n integers a_1, a_2, ... , a_n (1 β€ a_i β€ n) β the elements.
It is guaranteed that the sum of all n does not exceed 3 β
10^5.
Output
For each query print one integer β the minimum number of operation for sorting sequence a in non-descending order.
Example
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7
Output
2
0
1
Note
In the first query, you can move all 1-elements to the beginning (after that sequence turn into [1, 1, 1, 3, 6, 6, 3]) and then move all 6-elements to the end.
In the second query, the sequence is sorted initially, so the answer is zero.
In the third query, you have to move all 2-elements to the beginning.
Submitted Solution:
```
import sys as _sys
ZERO = '0'
ONE = '1'
def main():
t = int(input())
for i_t in range(t):
n, = _read_ints()
s = _read_line()
result = find_max_operations_n_can_make(s)
print(result)
def _read_line():
result = _sys.stdin.readline()
assert result[-1] == "\n"
return result[:-1]
def _read_ints():
return map(int, _read_line().split())
def find_max_operations_n_can_make(s):
assert isinstance(s, str)
islands_lengths = []
curr_length = 1
for prev_x, curr_x in zip(s, s[1:]):
if curr_x == prev_x:
curr_length += 1
else:
islands_lengths.append(curr_length)
curr_length = 1
islands_lengths.append(curr_length)
islands_n = len(islands_lengths)
islands_powers = [length - 1 for length in islands_lengths]
indexed_nonzero_islands_powers_rev = [
[i, power] for i, power in enumerate(islands_powers) if power != 0
][::-1]
i_next_island_to_eat = 0
while indexed_nonzero_islands_powers_rev:
indexed_nonzero_islands_powers_rev[-1][1] -= 1
if indexed_nonzero_islands_powers_rev[-1][1] == 0:
indexed_nonzero_islands_powers_rev.pop()
while indexed_nonzero_islands_powers_rev \
and indexed_nonzero_islands_powers_rev[-1][0] <= i_next_island_to_eat:
indexed_nonzero_islands_powers_rev.pop()
i_next_island_to_eat += 1
islands_eaten = i_next_island_to_eat
assert islands_eaten <= islands_n
one_elem_islands_remain = islands_n - islands_eaten
moves_used = islands_eaten
moves_used += one_elem_islands_remain // 2 + one_elem_islands_remain % 2
return moves_used
if __name__ == '__main__':
main()
```
No
| 102,119 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
q = int(input())
for queries in range(q):
n = int(input())
skill = list(map(int, input().split()))
skill.sort()
times = 1
for i in range(len(skill) - 1):
if skill[i + 1] - skill[i] == 1:
times = 2
print(times)
```
| 102,120 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
q=int(input())
for i in range(q):
n=int(input())
a=list(map(int,input().split()))
grp=1
for j in range(n):
if a[j]-1 in a or a[j]+1 in a:
grp=2
break
print(grp)
```
| 102,121 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input());c=0;y=[]
x=list(map(int,input().split()))
y=sorted(x)
#print(y)
for j in range(len(y)-1):
#print(j+1," hj ",j)
#print(y[j+1]," hj ",y[j])
if ((abs(y[j+1]-y[j]))==1):
c+=1
y[j+1]=0
#del y[j+1]
#del y[j]
if c==0:
print(1)
else:
print(2)
y.clear()
```
| 102,122 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
t = int(input())
for _ in range(t):
n, ok = int(input()), 0
a = list(map(int, input().split()))
a.sort()
for i in range(0, n-1):
if a[i+1] - a[i] == 1:
ok = 1
print([1, 2][ok])
```
| 102,123 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
f = 0
for i in a:
if i+1 in a:
f = 1
break
if f:
print(2)
else:
print(1)
```
| 102,124 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
q = int(input())
n=[0]*q
answer=[1]*q
for i in range(q):
n[i]=int(input())
a= [int(x) for x in input().split()]
# ΡΠ΅ΡΠ°Π΅ΠΌ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΎΠ΄Π½Π° ΠΊΠΎΠΌΠ°Π½Π΄Π° ΠΈΠ»ΠΈ 2. ΠΏΡΠΈ ΠΊΠ°ΠΊΠΎΠΌ ΡΡΠ»ΠΎΠ²ΠΈΠΈ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ 3 ΠΊΠΎΠΌΠ°Π½Π΄Ρ? Π² ΠΎΠ΄Π½Ρ Π²ΡΠ΅ ΡΠ΅ΡΠ½ΡΠ΅, Π² Π΄ΡΡΠ³ΡΡ Π½Π΅ΡΠ΅ΡΠ½ΡΠ΅.
for j in range(n[i]):
for k in range(j+1,n[i]):
if (abs(a[j]-a[k])==1):
answer[i]=2
break
else:
continue
break
for i in answer:
print(i)
```
| 102,125 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
t=int(input());
for i in range(t):
m=int(input());
n=input();
n=n.split();
for j in range(m):
n[j]=int(n[j]);
n.sort();
counter=0;
for j in range(1,m):
if(n[j]-n[j-1]<=1):
counter+=1;
if(counter==0):
print(1);
else:
print(2);
```
| 102,126 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Tags: math
Correct Solution:
```
q = int(input())
for test in range(q):
n = int(input())
a = [int(i) for i in input().split()]
a.sort()
ans = False
for i in range(n - 1):
if a[i + 1] - a[i] == 1:
ans = True
if ans == True:
print(2)
else:
print(1)
```
| 102,127 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
for _ in range(int(input())):
x=int(input())
s=sorted(list(map(int,input().split())))
even=[]
odd=[]
indicator=0
for n in range(x):
if s[n]%2==0:
even.append(s[n])
else:
odd.append(s[n])
for n in even:
if (n+1) in odd:
indicator=1
break
elif (n-1) in odd:
indicator=1
break
else:
indicator=0
if indicator==1:
print(2)
else:
print(1)
```
Yes
| 102,128 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
T= int(input())
while(T>0):
N=int(input())
a=[int(x) for x in input().split()]
a.sort()
f=a[0]
c=0
for i in range(1,len(a)):
if abs(a[i]-f)==1:
c+=1
f=a[i]
if c>0:
print(2)
else:
print(1)
T=T-1
```
Yes
| 102,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
q=int(input())
for j in range(q):
n=int(input())
ch=input()
L=ch.split()
for i in range(n):
L[i] = int(L[i])
L.sort()
nb=1
for i in range(n-1):
if L[i+1]-L[i]==1:
nb=2
break
print(nb)
```
Yes
| 102,130 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
t=int(input())
for i in range(t):
n=int(input())
c=1
a=list(map(int,input().split()))[:n]
for i in range(len(a)):
for j in range(i,len(a)):
if abs(a[i]-a[j])==1:
c=c+1
if c>2:
print(2)
else:
print(c)
```
Yes
| 102,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
a=list(map(int,input().split()))
a.sort()
c=0
for i in range(n-1):
if abs(a[i]-a[i+1])==1:
c=-1
if c==0:
print(2)
else:
print(1)
```
No
| 102,132 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
#!/usr/bin/env python
# coding: utf-8
# In[6]:
q=int(input())
ans=[]
for i in range(0,q):
n=int(input())
s=input().split()
if len(s)==1:
ans.append(1)
else:
a=int(s[0])
for i in s:
c=0
x=abs(a-int(i))
if x==1:
break
else :
c+=1;
if c==0:
ans.append(2)
else:
ans.append(1)
for i in ans:
print(i)
# In[ ]:
```
No
| 102,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
q=int(input())
ans=[]
for i in range(0,q):
n=int(input())
s=input().split()
a=int(s[0])
for i in s:
c=0
x=abs(a-int(i))
if x==1:
break
else :
c+=1;
if c==0:
ans.append(2)
else:
ans.append(1)
for i in ans:
print(i)
ans.clear()
```
No
| 102,134 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a coach of a group consisting of n students. The i-th student has programming skill a_i. All students have distinct programming skills. You want to divide them into teams in such a way that:
* No two students i and j such that |a_i - a_j| = 1 belong to the same team (i.e. skills of each pair of students in the same team have the difference strictly greater than 1);
* the number of teams is the minimum possible.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 100) β the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 β€ n β€ 100) β the number of students in the query. The second line of the query contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100, all a_i are distinct), where a_i is the programming skill of the i-th student.
Output
For each query, print the answer on it β the minimum number of teams you can form if no two students i and j such that |a_i - a_j| = 1 may belong to the same team (i.e. skills of each pair of students in the same team has the difference strictly greater than 1)
Example
Input
4
4
2 10 1 20
2
3 6
5
2 3 4 99 100
1
42
Output
2
1
2
1
Note
In the first query of the example, there are n=4 students with the skills a=[2, 10, 1, 20]. There is only one restriction here: the 1-st and the 3-th students can't be in the same team (because of |a_1 - a_3|=|2-1|=1). It is possible to divide them into 2 teams: for example, students 1, 2 and 4 are in the first team and the student 3 in the second team.
In the second query of the example, there are n=2 students with the skills a=[3, 6]. It is possible to compose just a single team containing both students.
Submitted Solution:
```
def main():
q = int(input())
for i in range(q):
n = int(input())
l = input().split()
count = 0
while (len(l) > 0):
tmp = 1
while tmp < len(l):
#print(l[0], l[tmp])
if (abs(int(l[0]) - int(l[tmp])) > 1):
l.pop(tmp)
else:
tmp += 1
l.pop(0)
count += 1
#print(l)
print(count)
if __name__ == '__main__':
main()
```
No
| 102,135 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price β c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 β€ n β€ 100; 1 β€ x β€ 10 000) β the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, β¦, c_n (x β€ c_i β€ 10 000; β{c_i} β€ 10 000) β the prices of n relics.
Output
Print a single real number β the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
n,x = [int(i) for i in input().split()]
c = [int(i) for i in input().split()]
res = 0
for i in range(n):
for j in range(n):
res += min(c[j],(2*n-i)/(2*n-2*i) * x)
res /= n
print(res)
```
No
| 102,136 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price β c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 β€ n β€ 100; 1 β€ x β€ 10 000) β the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, β¦, c_n (x β€ c_i β€ 10 000; β{c_i} β€ 10 000) β the prices of n relics.
Output
Print a single real number β the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
from decimal import *
line = input()
content = line.split(" ")
n = int(content[0])
x = int(content[1])
c = [0 for _ in range(n)]
line = input()
content = line.split(" ")
for i in range(n):
c[i] = int(content[i])
getcontext().prec = 50
ans = Decimal(0)
for i in range(n):
for j in range(n):
k = j
tmp = Decimal(x) + Decimal(k) * Decimal(x) / Decimal(2 * n - 2 * k)
if (2 * n - k) * x > c[i] * (2 * n - 2 * k):
ans += Decimal(c[i])
else:
ans += tmp
ans = ans / Decimal(n)
print(ans)
```
No
| 102,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price β c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 β€ n β€ 100; 1 β€ x β€ 10 000) β the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, β¦, c_n (x β€ c_i β€ 10 000; β{c_i} β€ 10 000) β the prices of n relics.
Output
Print a single real number β the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
from decimal import *
line = input()
content = line.split(" ")
n = int(content[0])
x = int(content[1])
c = [0 for _ in range(n)]
line = input()
content = line.split(" ")
for i in range(n):
c[i] = int(content[i])
getcontext().prec = 100
ans = Decimal(0)
for i in range(n):
for j in range(n):
k = j
tmp = Decimal(x) + Decimal(k) * Decimal(x) / Decimal(2 * n - 2 * k)
if (2 * n - k) * x > c[i] * (2 * n - 2 * k):
ans += Decimal(c[i])
else:
ans += tmp
ans = ans / Decimal(n)
print('%.100f'%ans)
```
No
| 102,138 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price β c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 β€ n β€ 100; 1 β€ x β€ 10 000) β the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, β¦, c_n (x β€ c_i β€ 10 000; β{c_i} β€ 10 000) β the prices of n relics.
Output
Print a single real number β the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
from decimal import *
line = input()
content = line.split(" ")
n = int(content[0])
x = int(content[1])
c = [0 for _ in range(n)]
line = input()
content = line.split(" ")
for i in range(n):
c[i] = int(content[i])
getcontext().prec = 10000
ans = Decimal(0)
for i in range(n):
for j in range(n):
k = j
tmp = Decimal(x) + Decimal(k) * Decimal(x) / Decimal(2 * n - 2 * k)
if (2 * n - k) * x > c[i] * (2 * n - 2 * k):
ans += Decimal(c[i])
else:
ans += tmp
ans = ans / Decimal(n)
print('%.100f'%ans)
```
No
| 102,139 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
a=list(input() for i in range(8))
ok1=list()
ok2=set()
ok1.append((7,0))
w=[(1,0),(-1,0),(0,1),(0,-1),(1,-1),(1,1),(-1,-1),(-1,1),(0,0)]
for i in range(8) :
for pos in ok1 :
if pos[0]>=i and a[pos[0]-i][pos[1]] == 'S' :
continue
for j in w:
to=(pos[0]+j[0],pos[1]+j[1])
if to[0]<8 and to[1]<8 and to[0]>-1 and to[1]>-1:
if to[0]<i or a[to[0]-i][to[1]] != 'S' :
ok2.add(to)
ok1.clear()
ok1=list(ok2.copy())
ok2.clear()
print("WIN" if len(ok1)>0 else "LOSE")
```
| 102,140 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
f = []
for i in range(8):
f.append(input())
d = [[[0 for i in range(8)] for j in range(8)] for k in range(100)]
d[0][7][0] = 1
dx = [1, 1, 1, 0, 0, -1, -1, -1, 0]
dy = [1, 0, -1, 1, -1, 1, 0, -1, 0]
ans = 'LOSE'
for i in range(99):
for x in range(8):
for y in range(8):
if not d[i][x][y]:
continue
for j in range(9):
nx = x + dx[j]
ny = y + dy[j]
if not(0 <= nx < 8 and 0 <= ny < 8):
continue
valid = True
if 0 <= nx - i < 8 and f[nx - i][ny] == 'S':
valid = False
if 0 <= nx - i - 1 < 8 and f[nx - i - 1][ny] == 'S':
valid = False
if not valid:
continue
d[i + 1][nx][ny] = 1
if nx == 0 and ny == 7:
ans = 'WIN'
print(ans)
```
| 102,141 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
grid=None
gridsovertime=None
visited=None
def readInput():
global grid
grid = []
for _ in range(8):
grid.append(input())
grid = [[(False if char=='S' else True) for char in row] for row in grid]
return grid
def getNeighbours(pos):
x,y,t = pos
newposes = []
for i in range(-1,2):
for j in range(-1,2):
newposes.append((x+i,y+j,t+1))
# print(newposes, len(gridsovertime), len(gridsovertime[0]), len(gridsovertime[0][0]))
newposes = [(x,y,t) for x,y,t in newposes if (x>=0 and y>=0 and x<8 and y<8 and gridsovertime[t][x][y] and gridsovertime[t-1][x][y])]
return newposes
def dfs(pos):
x,y,t = pos
visited[t][x][y]=True
if t==10:
return True
out = []
for x,y,t in getNeighbours(pos):
# print(x,y,t)
if visited[t][x][y]:
continue
out.append(dfs((x,y,t)))
return any(out)
def solve():
global gridsovertime,visited
gridsovertime = [grid]
for _ in range(12):
currgrid = gridsovertime[-1]
newgrid = [[True]*8] + currgrid[:-1]
gridsovertime.append(newgrid)
visited = [[[False for _ in range(8)] for _ in range(8)] for _ in range(13)]
start = (7,0,0)
# visited[7][0][0] = True
return dfs(start)
def main():
readInput()
out = solve()
if out:
print("WIN")
else:
print("LOSE")
pass
if __name__ == '__main__':
main()
```
| 102,142 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
start=[]
for i in range(8): start.append(input())
a=[start]
#start=[".......A","........","........","........","........",".SSSSSSS","S.......","M......."]
#a=[start]
for i in range(10):
tmp=a[-1]
tmp=[".......A"]+tmp
tmp[1]=tmp[1][:-1]+"."
a.append(tmp[:-1])
dx=[-1,1,0,0,0,1,1,-1,-1]
dy=[0,0,-1,1,0,-1,1,-1,1]
def chk(x,y,step):
if a[step][y][x]=="S": return False
if step==9:return True
for i in range(8):
x_,y_=x+dx[i],y+dy[i]
if min(x_,y_)<0 or max(x_,y_)>7:continue
if a[step][y_][x_]!='S' and chk(x_,y_,step+1): return True
return False
if chk(0,7,0):
print("WIN")
else:
print("LOSE")
```
| 102,143 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
from sys import stdin
from collections import *
from copy import deepcopy
def valid(i, j):
n, m = [8] * 2
return i > -1 and i < n and j > -1 and j < m
def str_inp(n):
return list(reversed(list((list(stdin.readline()[:-1]) for x in range(n)))))
def check(x, y, step):
if step + 1 < 8 and all[step + 1][x][y] == 'S' or step < 8 and all[step][x][y] == 'S':
# print(all[step][x][y], x, y)
return False
return True
def print_maze(x):
for i in range(8):
print(*all[x][i], sep='')
print(end='\n')
def dfs(x, y):
stack, visit, step = [[x, y, -1]], defaultdict(int), -1
while (stack):
x, y, step = stack.pop()
step += 1
if chess[x][y] == 'A':
exit(print('WIN'))
st = 0
for i in range(9):
nx, ny = [x + dx[i], y + dy[i]]
if i == 0:
if step >= 8:
continue
else:
visit[nx, ny] = 0
if valid(nx, ny) and check(nx, ny, step) and not visit[nx, ny]:
stack.append([nx, ny, step])
# print(nx, ny, step, check(nx, ny, step))
# print_maze(min(step, 7))
visit[nx, ny] = 1
else:
st += 1
# print(stack, step)
if st == 9:
step -= 1
visit[x, y] = 0
dx, dy, chess = [0, -1, 0, 1, 0, 1, -1, 1, -1], [0, 0, 1, 0, -1, 1, -1, -1, 1], str_inp(8)
all, ini = [chess], [['.' for i in range(8)] for j in range(8)]
for k in range(1, 9):
tem = deepcopy(ini)
for i in range(8):
for j in range(8):
if chess[i][j] == 'S' and i - k > -1:
tem[i - k][j] = 'S'
all.append(tem)
dfs(0, 0)
print('LOSE')
```
| 102,144 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
r, s = [63], ''.join(input() + 'T' for i in range(8)) + 'T' * 9
for i in range(0, 72, 9):
t = set()
for x in r:
for y in (x, x - 1, x + 1, x - 9, x + 9, x - 10, x - 8, x + 10, x + 8):
if s[y] == 'T': continue
if (y < i or s[y - i] != 'S') and (y < i + 9 or s[y - i - 9] != 'S'): t.add(y)
r = t
print('WIN' if r else 'LOSE')
# Made By Mostafa_Khaled
```
| 102,145 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
r, s = [63], ''.join(input() + 'T' for i in range(8)) + 'T' * 9
for i in range(0, 72, 9):
t = set()
for x in r:
for y in (x, x - 1, x + 1, x - 9, x + 9, x - 10, x - 8, x + 10, x + 8):
if s[y] == 'T': continue
if (y < i or s[y - i] != 'S') and (y < i + 9 or s[y - i - 9] != 'S'): t.add(y)
r = t
print('WIN' if r else 'LOSE')
```
| 102,146 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Tags: dfs and similar
Correct Solution:
```
def play(b, x, y, c):
if c == 9:
return True
if b[c][y][x] == 'S':
return False
dx = [-1, 1, 0, 0, 0, 1, 1, -1, -1]
dy = [0, 0, -1, 1, 0, -1, 1, -1, 1]
for i in range(len(dx)):
nx = x + dx[i]
ny = y + dy[i]
if min(nx, ny) < 0 or max(nx, ny) >= 8: continue
if b[c][ny][nx] != 'S' and play(b, nx, ny, c+1):
return True
return False
board = []
for x in range(8):
board.append(input().strip())
B = [board]
for x in range(10):
b = B[-1]
b_ = b[:]
b_[0] = b_[0][:-1] + '.'
b_.insert(0, ".......A")
B.append(b_[:-1])
if play(B, 0, 7, 0):
print("WIN")
else:
print("LOSE")
```
| 102,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
def bad(x, y, t):
x1, y1 = x, y + t
return 0 <= 8 - y1 < 8 and 0 <= x1 < 8 and a[8 - y1][x1] == "S" or 0 <= 7 - y1 < 8 and 0 <= x1 < 8 and a[7 - y1][x1] == "S"
dp = [[[False] * 30 for i in range(8)] for j in range(8)]
a = []
for i in range(8):
a.append(input().rstrip())
dp[0][0][0] = True
for t1 in range(29):
for x in range(8):
for y in range(8):
if dp[x][y][t1]:
for i in [(x + 1, y), (x - 1, y), (x + 1, y + 1), (x - 1, y + 1), (x + 1, y - 1), (x - 1, y - 1), (x, y + 1), (x, y - 1), (x, y)]:
if 0 <= i[0] < 8 and 0 <= i[1] < 8:
if not bad(i[0], i[1], t1 + 1):
dp[i[0]][i[1]][t1 + 1] = True
for i in range(30):
if dp[7][7][i]:
print("WIN")
exit()
print("LOSE")
```
Yes
| 102,148 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
grid = [ list(input().strip()) for r in range(8) ]
grid[0][7] = '.'
grid[7][0] = '.'
mark = [ [ False for c in range(8) ] for r in range(8) ]
mark[7][0] = True
def display_grid():
print('\n'.join(map(lambda row: ''.join(row), grid)))
print()
def display_mark():
for row in mark:
row = map(lambda a: 'X' if a else '_', row)
print(''.join(row))
print()
for i in range(8):
moved = False
new_mark = [ [ False for c in range(8) ] for r in range(8) ]
for r in range(8):
for c in range(8):
if not mark[r][c]:
continue
for R in range(max(0, r - 1), min(r + 2, 8)):
for C in range(max(0, c - 1), min(c + 2, 8)):
if grid[R][C] == 'S':
continue
if R - 1 >= 0 and grid[R - 1][C] == 'S':
continue
new_mark[R][C] = True
moved = True
mark = new_mark
grid.insert(0, 8 * [ '.' ])
grid.pop()
if not moved:
break
if moved:
print('WIN')
else:
print('LOSE')
```
Yes
| 102,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
d=[[1,0],[-1,0],[0,1],[0,-1],[1,1],[1,-1],[-1,1],[-1,-1],[0,0]]
l=[]
for i in range(8):
l.append(input())
#print("l is",l)
statues=[]
statues.append([])
for i in range(8):
for j in range(8):
#print(l[i][j],l[i][j]=='S')
if l[i][j]=="S":
statues[0].append(tuple([i,j]))
for i in range(1,8):
statues.append([])
for statue in statues[0]:
statues[i].append(tuple([statue[0]+i,statue[1]]))
#print(statues[0])
def possible(move_no,pos):
global d
global statues
if move_no>7 or (pos[0]==0 and pos[1]==7):
#print(move_no, pos[0],pos[1])
return(True)
b=False
for di in d:
pos[0]+=di[0]
pos[1]+=di[1]
if pos[0]>-1 and pos[0]<8 and pos[1]>-1 and pos[1]<8 and tuple(pos) not in statues[move_no] and tuple([pos[0]-1,pos[1]]) not in statues[move_no]:
#print(pos)
if(possible(move_no+1,pos)):
b=True
break
pos[0]-=di[0]
pos[1]-=di[1]
return(b)
if(possible(0,[7,0])):
print("WIN")
else:
print("LOSE")
```
Yes
| 102,150 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
from typing import List, Tuple
def is_row_clear(board: List[str], time: int, x: int, y: int) -> bool:
if all(row[y] != 'S' for row in board):
return True
first_statue_index = [row[y] for row in board].index('S')
if first_statue_index + time > x:
return True
else:
return False
def moves(x: int, y: int) -> List[Tuple[int, int]]:
adj = [(x - 1, y - 1), (x - 1, y), (x - 1, y + 1), (x, y - 1), (x, y + 1),
(x + 1, y - 1), (x + 1, y), (x + 1, y + 1), (x, y)]
return [(xo, yo) for xo, yo in adj if 0 <= xo < 8 and 0 <= yo < 8]
def solve(board: List[str]) -> str:
stack = [(0, idx, idy) for idx, line in enumerate(board)
for idy, sq in enumerate(line) if board[idx][idy] == 'M']
while stack:
time, idx, idy = stack.pop()
if is_row_clear(board, time, idx, idy) or idx == 0:
return 'WIN'
for xo, yo in moves(idx, idy):
if (
board[xo - time][yo] != 'S' and
board[xo - 1 - time][yo] != 'S'
):
stack.append((time + 1, xo, yo))
return 'LOSE'
board = [input() for _ in range(8)]
print(solve(board))
```
Yes
| 102,151 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
a=[]
for i in range(8):
s=input()
if s.count('S')>0:
a.append(1)
else:
a.append(0)
a=str(a)
if a.count('1')>0:
if a.find('1')>5:
print('LOSE')
else:
print('WIN')
else:
print('Win')
```
No
| 102,152 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
grid = []
for _ in range(8):
grid.append(list(input()))
row = -1
for i in range(8):
if grid[i][0] == 'S':row = i
if row == -1:
print('WIN')
elif row == 0:
if grid[6][1] != 'S' and grid[4][2] != 'S' and grid[2][3] != 'S' and grid[0][4]:
print('WIN')
else: print('LOSE')
else:
print('LOSE')
```
No
| 102,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
r, s = [63], ''.join(input() + 'S' for i in range(8)) + 'S' * 9
for i in range(0, 72, 9):
t = set()
for x in r:
for y in (x - 1, x + 1, x - 9, x + 9, x - 10, x - 8, x + 10, x + 8):
if s[y] == 'S': continue
if (y < i or s[y - i] != 'S') and (y < i + 9 or s[y - i - 9] != 'S'): t.add(y)
r = t
print('WIN' if r else 'LOSE')
```
No
| 102,154 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 Γ 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone β neither any other statues, nor Anna, nor Maria.
Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is β to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.
At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.
Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.
Input
You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one β for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S".
It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".
Output
If Maria wins, print string "WIN". If the statues win, print string "LOSE".
Examples
Input
.......A
........
........
........
........
........
........
M.......
Output
WIN
Input
.......A
........
........
........
........
........
SS......
M.......
Output
LOSE
Input
.......A
........
........
........
........
.S......
S.......
MS......
Output
LOSE
Submitted Solution:
```
from itertools import product
from queue import Queue
BOARD_SIZE = 10
OCC_OR_VISITED, EMPTY = 1, 0
board = [input() for _ in range(8)]
graph = []
for _ in range(BOARD_SIZE):
graph += [[[EMPTY for _ in range(BOARD_SIZE)] for _ in range(BOARD_SIZE)]]
for i, j in product(range(8), repeat = 2):
if board[i][j] == 'S':
graph[0][i + 1][j + 1] = OCC_OR_VISITED
for i in range(BOARD_SIZE):
graph[0][i][0] = OCC_OR_VISITED
graph[0][i][BOARD_SIZE - 1] = OCC_OR_VISITED
graph[0][0][i] = OCC_OR_VISITED
graph[0][BOARD_SIZE - 1][i] = OCC_OR_VISITED
for time in range(1, BOARD_SIZE):
for i, j in product(range(2, 9), range(1, 9)):
graph[time][i][j] = graph[time - 1][i - 1][j]
for i in range(BOARD_SIZE):
graph[time][i][0] = OCC_OR_VISITED
graph[time][i][BOARD_SIZE - 1] = OCC_OR_VISITED
graph[time][0][i] = OCC_OR_VISITED
graph[time][BOARD_SIZE - 1][i] = OCC_OR_VISITED
Q = Queue()
Q.put((0, 8, 1))
pos_moves = [
[-1, -1],
[-1, 0],
[-1, 1],
[0, -1],
[0, 0],
[0, 1],
[1, -1],
[1, 0],
[1, 1]
]
while not Q.empty():
time, i, j = Q.get()
if time < BOARD_SIZE - 1:
for d in pos_moves:
if graph[time][i + d[0]][j + d[1]] == EMPTY and \
graph[time + 1][i + d[0]][j + d[1]] == EMPTY:
graph[time + 1][i + d[0]][j + d[1]] = OCC_OR_VISITED
Q.put((time + 1, i + d[0], j + d[1]))
any_pos = False
for i, j in product(range(1, 9), repeat = 2):
if graph[BOARD_SIZE - 1][i][j] == OCC_OR_VISITED:
any_pos = True
if any_pos:
print("WIN")
else:
print("LOSE")
```
No
| 102,155 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
colors = ''
used = [0]*11
count = 0
for ai in a:
for i in range(11):
if ai%primes[i] is 0:
if used[i] is 0:
count += 1
used[i] = count
colors += str(used[i]) + ' '
break
print("{0}\n{1}".format(count, colors))
```
| 102,156 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
import math
t = int(input())
def check(c, a, n):
for i in range(n):
for j in range(n):
if (c[i] == c[j] and math.gcd(a[i], a[j]) == 1):
return False
return True
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
c = [0 for i in range(n)]
freq = [[0, i] for i in range(101)]
need = max(0, n-11)
for j in range(2, 101):
for i in range(n):
if a[i] % j == 0:
freq[j][0] += 1
cur = 1
if need > 0:
for frequency, num in freq:
if num <= 1:
continue
did = False
for i in range(n):
if a[i] % num == 0 and c[i] == 0:
c[i] = cur
did = True
if did:
cur += 1
if all([i != 0 for i in c]):
break
for i in range(n):
if c[i] == 0:
c[i] = cur
cur += 1
print(max(c))
print(*c)
```
| 102,157 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
testcases=int(input())
for j in range(testcases):
n=int(input())
comps=list(map(int,input().split()))
primes=[2,3,5,7,11,13,17,19,23,29,31]
dict1={}
for s in range(len(comps)):
for k in primes:
if comps[s]%k==0:
if k in dict1:
dict1[k].append(s)
else:
dict1[k]=[s]
break
#
counter=1
for b in dict1:
for l in dict1[b]:
comps[l]=str(counter)
counter+=1
print(counter-1)
print(" ".join(comps))
```
| 102,158 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
from math import sqrt
for _ in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
dd = dict()
for j in range(n):
i = a[j]
# firstfactor = 2
for firstfactor in range(2, int(sqrt(i)) + 1):
if i % firstfactor == 0:
if firstfactor in dd:
dd[firstfactor].append(j)
else:
dd[firstfactor] = [j]
break
# print(dd)
ks = sorted(dd.keys())
ans = [0] * n
print(len(ks))
for i in range(len(ks)):
for x in dd[ks[i]]:
ans[x] = i+1
print(*ans)
```
| 102,159 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
import math
for h in range(int(input())):
n = int(input())
arr = list(map(int, input().strip().split()))
primes = [2,3,5,7,11,13,17,19,23,29,31,37]
ans = [0 for i in range(n)]
col = 1
dicti = {}
for i in range(n):
for j in primes:
if arr[i]%j == 0:
if j in dicti:
ans[i] = dicti[j]
else:
ans[i] = col
dicti[j] = col
col += 1
break
print(max(ans))
print(*ans)
```
| 102,160 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
primes=[2,3,5,7,11,13,17,19,23,29,31]
t=int(input())
for i in range(t):
n=int(input())
ls=[int(a) for a in input().split()]
an=[]
for j in range(n):
an.append(0)
ctr=1
for p in range(len(primes)):
nx=False
for j in range(n):
if ls[j]%primes[p]==0 and an[j]==0:
an[j]=ctr
nx=True
if nx==True:
ctr+=1
s=''
for a in an:
s+=str(a)+' '
print(ctr-1)
print(s)
```
| 102,161 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
for _ in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
k=1
ans=[0]*n
for i in range(2,1001):
f=0
for j in range(n):
if l[j]%i==0 and ans[j]==0:
ans[j]=k
f=1
if f==1:
k+=1
print(k-1)
print(*ans)
```
| 102,162 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Tags: brute force, constructive algorithms, greedy, math, number theory
Correct Solution:
```
c = [0] * 1001
col = 1
for i in range(2, 1001):
if c[i] == 0:
for j in range(i * 2, 1001, i):
if c[j] == 0:
c[j] = col
col += 1
def tc():
n = int(input())
a = [int(x) for x in input().split()]
if n <= 11:
print(n)
print(' '.join(map(str, range(1, n + 1))))
return
ans = [c[x] for x in a]
key = {k: v for k, v in zip(set(ans), range(1, 12))}
ans = [key[x] for x in ans]
print(len(key))
print(' '.join(map(str, ans)))
################################
T = int(input())
for _ in range(T):
tc()
```
| 102,163 |
Evaluate the correctness of the submitted Python 2 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
from fractions import gcd
raw_input = stdin.readline
pr = stdout.write
def in_arr():
return map(int,raw_input().split())
def pr_num(n):
stdout.write(str(n)+'\n')
def pr_arr(arr):
for i in arr:
stdout.write(str(i)+' ')
stdout.write('\n')
range = xrange # not for python 3.0+
arr=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
for t in range(input()):
n=input()
l=map(int,raw_input().split())
ans=[0]*n
d=Counter()
for i in range(n):
for j in range(11):
if l[i]%arr[j]==0:
d[j]=1
ans[i]=j+1
break
d1=Counter()
c=0
for i in range(11):
d1[i]=c
if not d[i]:
c+=1
for i in range(n):
ans[i]-=d1[ans[i]-1]
pr_num(max(ans))
pr_arr(ans)
```
Yes
| 102,164 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
def answer(n,A):
dp=[1]*32
dp[0]=dp[1]=0
for i in range(2,32):
if dp[i]==1:
p=2*i
while p<=31:
if dp[p]==1:
dp[p]=0
p+=i
count=1
res=[0]*n
for i in range(2,32):
if dp[i]==1:
flag=0
for j in range(n):
if res[j]==0 and A[j]%i==0:
flag=1
res[j]=count
if flag==1:
count+=1
return count,res
t=int(input())
for i in range(t):
n=int(input())
arr=list(map(int,input().split()))
a,b=answer(n,arr)
print(a-1)
print(*b)
```
Yes
| 102,165 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
t=int(input())
sosu=[2,3,5,7,11,13,17,19,23,29,31]
for _ in range(t):
n=int(input())
a=list(map(int,input().split()))
ans=[]
ans2=0
for i in range(n):
for j in range(11):
if a[i]%sosu[j]==0:
ans.append(j+1)
ans2=max(j+1,ans2)
break
used=[1]*ans2
for x in ans:
used[x-1]=0
for i in range(ans2-1):
used[i+1]+=used[i]
for i in range(n):
ans[i]-=used[ans[i]-1]
print(ans2-used[-1])
print(*ans)
```
Yes
| 102,166 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
import sys
input=sys.stdin.buffer.readline
first11Primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
def getSmallestPrimeFactor(x):
for p in first11Primes:
if x%p==0:
return p
t=int(input())
for _ in range(t):
n=int(input())
a=[int(x) for x in input().split()]
ans=[-1 for __ in range(n)]
mapp=dict() #{prime:colour}
j=1
for i in range(n):
p=getSmallestPrimeFactor(a[i])
if p not in mapp.keys():
mapp[p]=j
j+=1
ans[i]=mapp[p]
print(j-1)
print(' '.join([str(x) for x in ans]))
```
Yes
| 102,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
stat=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547]
from collections import defaultdict
for _ in range(int(input())):
index=defaultdict(lambda:0)
N=int(input())
L=list(map(int,input().split()))
Color=1
for i in stat:
FLAG=0
for j in range(N):
if index[j]==0 and L[j]%i==0:
index[j]=Color
FLAG=1
if FLAG==1:
Color+=1
print(Color-1)
for i in range(N):
print(index[i],end=" ")
# print(index[i],end=" ")
print()
```
Yes
| 102,168 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
from math import ceil
def is_prime(x):
if x==2:
return True
for i in range(2,ceil(x**0.5)+1):
if x%i==0:
return False
return True
for t in range(int(input())):
n = int(input())
factors = {}
ans = [0]*n
arr = list(map(int,input().split()))
for i in range(n):
for j in range(2,ceil(arr[i]**0.5)+1):
if is_prime(j):
if arr[i]%j == 0:
try:
if type(factors[j])==list:
factors[j].append(i)
except:
factors[j] = [i]
# print(factors)
m = 1
done = {}
for i in range(n):
done[i] = False
for i in factors.keys():
for j in factors[i]:
if not done[j]:
ans[j] = m
done[j] = True
m+=1
print(m-1)
print(*ans)
```
No
| 102,169 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
t=int(input())
r=[3,5,7,11,13,17,19,23,29,31]
while(t):
t-=1
n=int(input())
a=list(map(int,input().split()))
ind={2:1}
cc=1
r1=[1]*n
for i in range(n):
if(a[i]%2==0):
continue
for j in range(10):
if(a[i]%r[j]==0):
if(r[j] not in ind):
ind[r[j]]=cc+1
cc+=1
r1[i]=cc
break
c=set()
for i in r1:
c.add(i)
print(max(r1))
print(*r1)
```
No
| 102,170 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
t = input() #Number of tests
for i in range(int(t)):
n = input() #Number of numbers in this test
n = int(n)
a_list_string = input()
a_list = a_list_string.split(" ")
a_list = [int(j) for j in a_list]
prime_list = [prime_factors(k) for k in a_list]
#print(prime_list)
color_dict = dict()
for i in range(1,12):
color_dict[i] = set()
color_map = []
for i in range(len(prime_list)):
c = 0
for color in range(1, 12):
if len(color_dict[color]) == 0:
c = color
else:
for prime in prime_list[i]:
if prime in color_dict[color]:
c = color
break
if c != 0: #color found
color_map.append(c)
color_dict[color].update(prime_list[i])
break
tot = 0
for entry in color_dict:
if len(color_dict[entry]) != 0:
tot += 1
s = " ".join(str(x) for x in color_map)
print(tot)
print(s)
#print(color_dict)
```
No
| 102,171 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.
Alice is given a sequence of n composite numbers a_1,a_2,β¦,a_n.
She wants to choose an integer m β€ 11 and color each element one of m colors from 1 to m so that:
* for each color from 1 to m there is at least one element of this color;
* each element is colored and colored exactly one color;
* the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color.
Note that equal elements can be colored different colors β you just have to choose one of m colors for each of the indices from 1 to n.
Alice showed already that if all a_i β€ 1000 then she can always solve the task by choosing some m β€ 11.
Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Input
The first line contains a single integer t (1 β€ t β€ 1000) β the number of test cases. Then the descriptions of the test cases follow.
The first line of the test case contains a single integer n (1 β€ n β€ 1000) β the amount of numbers in a sequence a.
The second line of the test case contains n composite integers a_1,a_2,β¦,a_n (4 β€ a_i β€ 1000).
It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.
Output
For each test case print 2 lines. The first line should contain a single integer m (1 β€ m β€ 11) β the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 β€ c_i β€ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.
Remember that each color from 1 to m should be used at least once. Any two elements of the same color should not be coprime (i.e. their GCD should be greater than 1).
Example
Input
3
3
6 10 15
2
4 9
23
437 519 865 808 909 391 194 291 237 395 323 365 511 497 781 737 871 559 731 697 779 841 961
Output
1
1 1 1
2
2 1
11
4 7 8 10 7 3 10 7 7 8 3 1 1 5 5 9 2 2 3 3 4 11 6
Note
In the first test case, \gcd(6,10)=2, \gcd(6,15)=3 and \gcd(10,15)=5. Therefore, it's valid to color all elements the same color. Note that there are other colorings which satisfy Alice's requirement in this test case.
In the second test case there is only one element of each color, so the coloring definitely satisfies Alice's requirement.
Submitted Solution:
```
import math,sys
from sys import stdin, stdout
from collections import Counter, defaultdict, deque
input = stdin.readline
I = lambda:int(input())
li = lambda:list(map(int,input().split()))
def case():
n=I()
a=li()
primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 29, 31]
pri=[]
for i in a:
for j in primes:
if i%j==0 :
pri.append(j)
break
print(len(set(pri)))
print(*pri)
for _ in range(int(input())):
case()
```
No
| 102,172 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
import sys,math
#sys.setrecursionlimit(100000000)
input = sys.stdin.readline
############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
return(int(input()))
def inara():
return(list(map(int,input().split())))
def insr():
s = input()
return(list(s[:len(s) - 1]))
def invr():
return(map(int,input().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############
t=inp()
for _ in range(t):
n=inp()
ara=inara()
fre=[0]*(n+2)
special=set()
for i in range(n):
tot=ara[i]
fre[ara[i]]+=1
for j in range(i+1,n):
tot+=ara[j]
if tot<=n:
special.add(tot)
ans=0
for element in special:
ans+=fre[element]
print(ans)
```
| 102,173 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
t = int(input())
for i in range(t):
n = int(input())
ai = list(map(int,input().split()))
ai3 = [0] * (n+1)
ai3[1] = ai[0]
for i in range(1,n):
ai3[i+1] = ai[i] + ai3[i]
ai2 = [0] * (n*2+1)
i = 0
j = 1
while j <= n:
for z in range(i+2,j+1):
ai2[ai3[z] - ai3[i]] += 1
if ai3[j] - ai3[i] > n:
i += 1
else:
j += 1
while i < n:
for z in range(i+2,n+1):
ai2[ai3[z] - ai3[i]] += 1
i += 1
ans = 0
for i in range(n):
ans += int(ai2[ai[i]] != 0)
print(ans)
```
| 102,174 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
def main():
LMIIS = lambda: list(map(int,input().split()))
II = lambda: int(input())
MOD = 10**9+7
from collections import defaultdict
for _ in range(II()):
n = II()
A = LMIIS()
d = [0]*(n+1)
u = max(A)
numcounts = [0]*(u+1)
for i in range(n):
numcounts[A[i]] += 1
d[i+1] = d[i] + A[i]
ans = 0
for i in range(n-1):
for j in range(i+2,n+1):
if d[j] - d[i] <= u:
ans += numcounts[d[j] - d[i]]
numcounts[d[j] - d[i]] = 0
print(ans)
if __name__ == '__main__':
main()
```
| 102,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
t=int(input())
for w in range(t):
n=int(input())
l=[int(i) for i in input().split()]
l1=[0]*8001
for i in range(n):
k=l[i]
for j in range(i+1,n):
k+=l[j]
if(k<=n):
l1[k]+=1
c=0
for i in range(n):
if(l1[l[i]]!=0):
c+=1
print(c)
```
| 102,176 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
from collections import Counter
for _ in " "*int(input()):
n=int(input())
a=list(map(int,input().split()))
d=Counter(a)
cnt=0
for i in range(n):
s=a[i]
for j in range(i+1,n):
s+=a[j]
if s in d:
cnt+=d[s]
d[s]=0
print(cnt)
```
| 102,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
from collections import defaultdict
import sys
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip()
for _ in range(int(input())):
n = int(input())
a = get_array()
d = defaultdict(int)
for i in range(len(a)):
d[a[i]] += 1
sum1 = 0
for i in range(n):
sum = a[i]
for j in range(i + 1, n):
sum += a[j]
if sum > n:
break
sum1 += d[sum]
d[sum]=0
print(sum1)
```
| 102,178 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
# Why do we fall ? So we can learn to pick ourselves up.
t = int(input())
for _ in range(0,t):
n = int(input())
aa = [int(i) for i in input().split()]
dic = dict()
ss = 0
for i in aa:
if i not in dic:
dic[i] = 1
else:
dic[i] += 1
for i in range(0,n):
temp = aa[i]
for j in range(i+1,n):
temp += aa[j]
if temp in dic:
# print(temp,"temp")
ss += dic[temp]
dic[temp] = 0
print(ss)
"""
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
"""
```
| 102,179 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Tags: brute force, implementation, two pointers
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
b=list(map(int,input().split()))
d=dict()
e=dict()
for j in range(n):
if b[j] in d.keys():
d[b[j]]+=1
else:
d[b[j]]=1
for i in range(0,n):
temp = b[i]
for j in range(i+1, n):
temp += b[j]
if temp>n:
break
e[temp]=1
c=list(set(b))
p=0
for j in c:
if j in e.keys():
p+=d[j]
print(p)
```
| 102,180 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
tc=int(input())
while tc!=0:
tc=tc-1
n=int(input())
a=list(map(int,input().split(' ')))
c=0
b=[]
m={}
mx=0
for i in range(len(a)):
c=c+a[i]
b.append(c)
mx=max(mx,a[i])
if a[i] in m:
m[a[i]]=m[a[i]]+1
else:
m[a[i]]=1
c=0
for i in range(len(a)):
s=0
for j in range(i,len(a)):
s=s+a[j]
if s>mx:
break
if s in m and i!=j:
if m[s]!=0:
c=c+m[s]
m[s]=0
print(c)
```
Yes
| 102,181 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
# Don't ask for what the world needs. Ask what makes you come alive, and go do it. BrenοΏ½ Brown
# by : Blue Edge - Create some chaos
for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split()))
b=[0]*(n+1)
i=0
for i in range(n):
s=a[i]
for j in range(i+1,n):
s+=a[j]
if s<=n:
b[s]=1
else:
break
# print(b)
print(sum([b[x] for x in a]))
```
Yes
| 102,182 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
from collections import Counter,defaultdict,deque
#import heapq as hq
#import itertools
#from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
#import math
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)
def solve():
n = int(input())
arr = [int(x) for x in input().split()]
c = defaultdict(int)
mx = 0
for el in arr:
if el>mx:
mx=el
c[el]+=1
res = 0
for i in range(n):
su = arr[i]
p = i+1
while su<=mx and p<n:
su+=arr[p]
if c[su]:
res+=c[su]
c[su]=0
p+=1
print(res)
tt = int(input())
for test in range(tt):
solve()
#
```
Yes
| 102,183 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
tc=int(input())
for _ in range(tc):
n=int(input())
a=list(map(int,input().split()))
present=[0 for _ in range(n+1)]
is_seg_sum=[0 for _ in range(n+1)]
for i in range(n):
present[a[i]]+=1
for i in range(n):
seg_sum=a[i]
for j in range(i+1,n):
seg_sum+=a[j]
if seg_sum>n: break
is_seg_sum[seg_sum]=1
ans=0
for i in range(1,n+1):
if is_seg_sum[i]==1:
ans+=present[i]
print(ans)
```
Yes
| 102,184 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
from collections import Counter
for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split()))
b=Counter(a)
c=list(a)
for i in range(1,n):
c[i]+=c[i-1]
ans=0
for i in range(n):
for j in range(i+1,n):
v=c[j]-c[i]+a[i]
if v in b:
ans+=1
b[v]-=1
if b[v]==0:
b.pop(v)
print(ans)
```
No
| 102,185 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
n=int(input())
for i in range(n):
a=int(input())
x=list(map(int,input().split()))
count=0
for j in range(a):
abc=0
aa=0
k=0
for k in range(a):
# while k!=a:
abc+=x[k]
if abc>x[j]:
abc-=x[aa]
aa+=1
if x[j]==abc and (k-aa)>0:
# print(x[j])
# print(aa,k)
count+=1
break
abc=0
aa=k+1
# k+=1
print(count)
```
No
| 102,186 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
from collections import deque
from collections import OrderedDict
import math
#data = sys.stdin.readlines()
import sys
import os
from io import BytesIO
import threading
import bisect
#input = sys.stdin.readline
for t in range(int(input())):
n = int(input())
array = input().split()
prefixSum = [0]*n
hashS = set()
prefS = set()
for i in range(n):
array[i] = int(array[i])
hashS.add(array[i])
prefixSum[0]=array[0]
prefS.add(0)
prefS.add(array[0])
for i in range(1,n):
prefixSum[i]=array[i]+prefixSum[i-1]
answer = 0
for i in range(1,n):
for j in hashS:
value = prefixSum[i]-j
print(i, "++", value, j)
if value in prefS and j!=array[i]:
print("YES", prefS)
answer+=1
prefS.add(prefixSum[i])
print(answer)
```
No
| 102,187 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pay attention to the non-standard memory limit in this problem.
In order to cut off efficient solutions from inefficient ones in this problem, the time limit is rather strict. Prefer to use compiled statically typed languages (e.g. C++). If you use Python, then submit solutions on PyPy. Try to write an efficient solution.
The array a=[a_1, a_2, β¦, a_n] (1 β€ a_i β€ n) is given. Its element a_i is called special if there exists a pair of indices l and r (1 β€ l < r β€ n) such that a_i = a_l + a_{l+1} + β¦ + a_r. In other words, an element is called special if it can be represented as the sum of two or more consecutive elements of an array (no matter if they are special or not).
Print the number of special elements of the given array a.
For example, if n=9 and a=[3,1,4,1,5,9,2,6,5], then the answer is 5:
* a_3=4 is a special element, since a_3=4=a_1+a_2=3+1;
* a_5=5 is a special element, since a_5=5=a_2+a_3=1+4;
* a_6=9 is a special element, since a_6=9=a_1+a_2+a_3+a_4=3+1+4+1;
* a_8=6 is a special element, since a_8=6=a_2+a_3+a_4=1+4+1;
* a_9=5 is a special element, since a_9=5=a_2+a_3=1+4.
Please note that some of the elements of the array a may be equal β if several elements are equal and special, then all of them should be counted in the answer.
Input
The first line contains an integer t (1 β€ t β€ 1000) β the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines. The first line contains an integer n (1 β€ n β€ 8000) β the length of the array a. The second line contains integers a_1, a_2, ..., a_n (1 β€ a_i β€ n).
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 8000.
Output
Print t numbers β the number of special elements for each of the given arrays.
Example
Input
5
9
3 1 4 1 5 9 2 6 5
3
1 1 2
5
1 1 1 1 1
8
8 7 6 5 4 3 2 1
1
1
Output
5
1
0
4
0
Submitted Solution:
```
def solution(t):
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
o = set()
c = 0
dic = {}
if n == 7999:
print(7999)
else:
for d in range(2, len(a) + 1):
for i in range(len(a) - d + 1):
temp = 0
for k in range(d):
temp += a[i+k]
o.add(temp)
for i in a:
if i in o:
c += 1
print(c)
solution(int(input()))
```
No
| 102,188 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
arr=[int(x) for x in input().split()]
a=-1
b=n
for i in range(n):
if arr[i]!=i+1:
break
a=i
for i in range(n-1,-1,-1):
if arr[i]!=i+1:
break
b=i
if a==n-1:
print(0)
continue
ans=1
for i in range(a+1,b):
if arr[i]==i+1:
ans+=1
break
print(ans)
```
| 102,189 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
# list(map(int, input().split()))
rw = int(input())
for ewq in range(rw):
n = int(input())
a = list(map(int, input().split()))
asorted = sorted(a)
b = []
s = 0
t = True
for i in range(n):
if a[i] == i + 1:
b.append(1)
else:
b.append(0)
i = 0
if b.count(1) == n:
print(0)
continue
while i < n:
if b[i] == 0:
s += 1
while i < n and b[i] == 0:
i += 1
i += 1
t = False
if s == 1:
b0 = b.index(0)
for i in range(b0, n):
bk = i
if b[i] == 1:
break
else:
bk = n
c = {i + 1 for i in range(b0, bk)}
d = set()
for i in range(b0, bk):
d.add(a[i])
t = False
if c == d:
t = True
if t:
print(1)
else:
print(2)
```
| 102,190 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
li = list(map(int, input().split()))
if(li == sorted(li)):
print(0)
continue
else:
x = sorted(li)
xs = list(range(1, n+1))
li = li[::-1]; x = x[::-1]; xs = xs[::-1]
while(li[-1] == x[-1]):
li.pop(); x.pop(); xs.pop()
li = li[::-1]; x = x[::-1]; xs = xs[::-1]
while(li[-1] == x[-1]):
li.pop(); x.pop(); xs.pop()
fnd = 0
for i in range(len(li)):
if(li[i] == xs[i]):
fnd = 1
break
if(fnd):
print(2)
continue
else:
print(1)
continue
```
| 102,191 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
from collections import Counter,defaultdict,deque
#from heapq import *
#from itertools import *
#from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#dirs = [[1,0],[0,1],[-1,0],[0,-1]]
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
#import math
#from math import *
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)
#MOD = 10**9+7
def primes(n):
arr = []
nn = n
d = 2
while d*d<=nn and n!=1:
if n%d==0:
arr.append(d)
while n%d==0:
n//=d
d+=1
if n>1:
arr.append(n)
return arr
def solve():
n = int(input())
arr = [int(x) for x in input().split()]
if arr == sorted(arr):
print(0)
else:
flag = False
i = 0
while arr[i] == i+1:
i+=1
while i<n:
if flag and arr[i]!=i+1:
print(2)
return
if arr[i] == i+1:
flag = True
i+=1
print(1)
tt = int(input())
for test in range(tt):
solve()
#
```
| 102,192 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
'''
bug is : the 2134 case -> printed 2 it should be 1
'''
t = int(input())
for _ in range(t):
n = int(input())
c, m = 0, 0
c_arr = [0 for _ in range(n)]
a = [int(e) - 1 for e in input().split()]
for i in range(n):
if a[i] == i:
c_arr[i] = 1
c = c + 1
if c != n:
left, right = 0, 0
while a[left] == left:
left = left + 1
while a[n - right - 1] == n - right - 1:
right = right + 1
if c == n:
ans = 0
elif (c == 0) or (c == left + right):
ans = 1
else:
ans = 2
print(ans)
```
| 102,193 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
from sys import stdin
input=stdin.readline
for _ in range(int(input())):
n=int(input())
lis=list(map(int,input().split()))
lis.insert(0,0)
if lis==sorted(lis):
print(0)
else:
for i in range(1,n+1):
if i!=lis[i]:
break
for j in range(n,0,-1):
if j!=lis[j]:
break
for k in range(i,j+1):
if lis[k]==k:
print(2)
break
else:
print(1)
```
| 102,194 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
arr=list(map(int,input().split()))
count=0
f=1
for i in range(n):
if(arr[i]!=i+1):
if(f==1):
count+=1
f=0
else:
f=1
print(min(2,count))
```
| 102,195 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Tags: constructive algorithms, math
Correct Solution:
```
#!/usr/bin/env python3
import sys
input=sys.stdin.readline
t=int(input())
for _ in range(t):
n=int(input())
arr=list(map(int,input().split()))
persuit=sorted(arr)
l=0
for i in range(n):
if arr[i]!=persuit[i]:
l=i
break
else:
print(0)
continue
r=0
for i in range(n-1,-1,-1):
if arr[i]!=persuit[i]:
r=i
break
for i in range(l,r+1):
if arr[i]==persuit[i]:
print(2)
break
else:
print(1)
```
| 102,196 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
#!/usr/bin/env python3
from sys import stdin as cin
from itertools import groupby
from operator import eq
lmap = lambda f, v: list(map(f, v))
def main():
t = int(next(cin).strip())
for i in range(t):
n = int(next(cin).strip())
a = lmap(int, next(cin).strip().split())
inplace = [inplace for (inplace, _) in groupby(i == ai for (i, ai) in enumerate(a, 1))]
if inplace == [True]:
print(0)
elif len(inplace) < 3 or inplace == [True, False, True]:
print(1)
else:
print(2)
main()
```
Yes
| 102,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
t = int(input())
for T in range(t):
n = int(input())
a = [int(x) for x in input().split()]
a1 = a[:]
a1.sort()
if a == a1:
print(0)
continue
count = 0
for i in range(n):
if i > 0 and a[i - 1] == i and a[i] != i + 1 and count == 1:
count = 2
if a[i] != i + 1 and count == 0:
count = 1
print(count)
```
Yes
| 102,198 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 β€ t β€ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 β€ n β€ 2 β
10^5) β the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 β€ a_{i} β€ n) β the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 β
10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
import math
from collections import deque
import sys
sys.setrecursionlimit(10**4)
def Divisors(n) :
l=[]
i = 2
while i <= math.sqrt(n):
if (n % i == 0) :
if (n // i == i) :
l.append(i)
else :
l.append(i)
l.append(n//i)
i = i + 1
return l
def SieveOfEratosthenes(n):
l=[]
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
for p in range(2, n+1):
if prime[p]:
l.append(p)
return l
def primeFactors(n):
l=[]
while n % 2 == 0:
l.append(2)
n = n / 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
l.append(i)
n = n / i
if n > 2:
l.append(n)
return(l)
def Factors(n) :
result = []
for i in range(2,(int)(math.sqrt(n))+1) :
if (n % i == 0) :
if (i == (n/i)) :
result.append(i)
else :
result.append(i)
result.append(n//i)
result.append(1)
return result
def maxSubArraySum(a):
max_so_far = 0
max_ending_here = 0
size=len(a)
for i in range(0, size):
max_ending_here = max_ending_here + a[i]
if (max_so_far < abs(max_ending_here)):
max_so_far = max_ending_here
return max_so_far
def longestsubarray(arr, n, k):
current_count = 0
# this will contain length of
# longest subarray found
max_count = 0
for i in range(0, n, 1):
if (arr[i] % k != 0):
current_count += 1
else:
current_count = 0
max_count = max(current_count,
max_count)
return max_count
#print(SieveOfEratosthenes(100))
#print(Divisors(100))
#print(primeFactors(100))
#print(Factors(100))
#print(maxSubArraySum(a))
def main():
n=int(input())
l=list(map(int,input().split()))
l1=[]
f=0
for i in range(1,n+1):
if l[i-1]!=i:
l1.append(0)
f=1
else:
l1.append(1)
if f==0:
print(0)
return
for i in range(0,n):
if l1[i]!=1:
break
s=i
for i in range(n-1,-1,-1):
if l1[i]!=1:
break
p=i
c=0
for i in range(s,p+1):
if l1[i]==1:
c+=1
if c==0:
print(1)
else:
print(2)
t=int(input())
for i in range(0,t):
main()
```
Yes
| 102,199 |
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