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  1. #include <bits/stdc++.h>
  2. using namespace std;
  3.  
  4. using ll = long long;
  5.  
  6. bool isPerfectSquare(ll x) {
  7.     if (x < 0) return false;
  8.     ll r = sqrt((long double)x);
  9.     while (r * r < x) ++r;
  10.     while (r * r > x) --r;
  11.     return r * r == x;
  12. }
  13.  
  14. bool isPrime(ll x) {
  15.     if (x < 2) return false;
  16.     if (x % 2 == 0) return x == 2;
  17.     for (ll i = 3; i * i <= x; i += 2) {
  18.         if (x % i == 0) return false;
  19.     }
  20.     return true;
  21. }
  22.  
  23. int main() {
  24.     ios::sync_with_stdio(false);
  25.     cin.tie(nullptr);
  26.  
  27.     int N;
  28.     cin >> N;
  29.  
  30.     vector<vector<int>> a(N + 1, vector<int>(N + 1));
  31.     vector<ll> row(N + 1, 0), col(N + 1, 0);
  32.  
  33.     for (int i = 1; i <= N; ++i) {
  34.         for (int j = 1; j <= N; ++j) {
  35.             cin >> a[i][j];
  36.             row[i] += a[i][j];
  37.             col[j] += a[i][j];
  38.         }
  39.     }
  40.  
  41.     ll diag1 = 0, diag2 = 0;
  42.     for (int i = 1; i <= N; ++i) {
  43.         diag1 += a[i][i];
  44.         diag2 += a[i][N - i + 1];
  45.     }
  46.  
  47.     bool ok = true;
  48.  
  49.     // Điều kiện 1
  50.     if (row[1] != row[N]) ok = false;
  51.     if (!isPerfectSquare((row[1] + row[N]) * 2LL)) ok = false;
  52.  
  53.     // Điều kiện 2
  54.     if (col[1] == col[N]) ok = false;
  55.     if (!isPrime(col[1] + col[N])) ok = false;
  56.  
  57.     if (N % 2 == 0) {
  58.         int mid = N / 2;
  59.         if (!isPerfectSquare(row[mid] * col[mid])) ok = false;
  60.         if (diag1 == diag2) ok = false;
  61.     } else {
  62.         int mid = (N + 1) / 2;
  63.         if (!isPrime(row[mid] + col[mid])) ok = false;
  64.         if (diag1 != diag2) ok = false;
  65.     }
  66.  
  67.     cout << (ok ? "Yes" : "No") << '\n';
  68.  
  69.     return 0;
  70. }
  71.  
Success #stdin #stdout 0.31s 113832KB
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https://ideone.com/kUEqRJ
language:
C++14 (gcc 8.3)
created:
1 day ago
visibility:
public

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