Guess the Permutation (Codeforces 618B)
Tags: Others, constructive algorithms

Bob has a permutation of integers from 1 to n. Denote this permutation as p. The i-th element of p will be denoted as pi. For all pairs of distinct integers i, j between 1 and n, he wrote the number ai, j = min(pi, pj). He writes ai, i = 0 for all integer i from 1 to n.Bob gave you all the values of ai, j that he wrote down. Your job is to reconstruct any permutation that could have generated these values. The input will be formed so that it is guaranteed that there is at least one solution that is consistent with the information given.

Input: The first line of the input will contain a single integer n (2 ≤ n ≤ 50).The next n lines will contain the values of ai, j. The j-th number on the i-th line will represent ai, j. The i-th number on the i-th line will be 0. It's guaranteed that ai, j = aj, i and there is at least one solution consistent with the information given.

Output: Print n space separated integers, which represents a permutation that could have generated these values. If there are multiple possible solutions, print any of them.

Note: In the first case, the answer can be {1, 2} or {2, 1}.In the second case, another possible answer is {2, 4, 5, 1, 3}.

Sample Inputs:
2
0 1
1 0

5
0 2 2 1 2
2 0 4 1 3
2 4 0 1 3
1 1 1 0 1
2 3 3 1 0

Sample Outputs:
2 1

2 5 4 1 3

Solution (Python):
n = int(input())
square = []
p = []
for i in range(n):
    a = [int(x) for x in input().split()]
    square.append(a)
for i in range(n):
    lst = square[i]
    for a in range(n):
        if lst.count(a) == n - a:
            p.append(a)
for k in range(n):
    if p[k] == n - 1:
        p[k] = n
        break
print(*p)

Solution (Python):
def solve():
    n = int(input())
    base = [0 for _ in range(n)]
    for i in range(n):
        lst = list(map(int, input().strip().split()))
        for (id, l) in enumerate(lst):
            base[id] = max(base[id], l)
    abc = set(base)
    vals = set((i for i in range(1, n + 1)))
    vals = sorted(list(vals - abc))
    for i in range(len(base) - 1, -1, -1):
        if base[i] in abc:
            abc.remove(base[i])
        else:
            for v in vals:
                if base[i] < v:
                    base[i] = v
                    vals.remove(v)
    for b in base:
        print(b, end=' ')
if __name__ == '__main__':
    solve()

Solution (Python):
n = int(input())
for i in range(n):
    a = input()
    a = a.split()
    a = [int(x) for x in a]
    a_s = set(a)
    if len(a_s) == n:
        b = a.copy()
        b[a.index(0)] = n
        break
for i in b:
    print(i, end=' ')