题目 3161: 蓝桥杯2023年第十四届省赛真题-子矩阵

题目

代码

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1010, mod = 998244353;
int g[N][N];
int rmin[N][N], rmax[N][N];
ll mmin[N][N], mmax[N][N];
int q[N * N];
int hh, tt;
int n, m, a, b;
int main()
{
  cin >> n >> m >> a >> b;
  for (int i = 1; i <= n; i++)
  {
    for (int j = 1; j <= m; j++)
    {
      cin >> g[i][j];
    }
  }

  for (int i = 1; i <= n; i++)
  {
    hh = 0, tt = -1;
    for (int j = 1; j <= m; j++)
    {
      if (hh <= tt && j - q[hh] + 1 > b)
        hh++;
      while (hh <= tt && g[i][q[tt]] >= g[i][j])
        tt--;
      q[++tt] = j;
      if (j >= b)
        rmin[i][j - b + 1] = g[i][q[hh]];
    }
  }

  for (int j = 1; j <= m; j++)
  {
    hh = 0, tt = -1;
    for (int i = 1; i <= n; i++)
    {
      if (hh <= tt && i - q[hh] + 1 > a)
        hh++;
      while (hh <= tt && rmin[q[tt]][j] >= rmin[i][j])
        tt--;
      q[++tt] = i;
      if (i >= a)
        mmin[i - a + 1][j] = rmin[q[hh]][j];
    }
  }

  for (int i = 1; i <= n; i++)
  {
    hh = 0, tt = -1;
    for (int j = 1; j <= m; j++)
    {
      if (hh <= tt && j - q[hh] + 1 > b)
        hh++;
      while (hh <= tt && g[i][q[tt]] <= g[i][j])
        tt--;
      q[++tt] = j;
      if (j >= b)
        rmax[i][j - b + 1] = g[i][q[hh]];
    }
  }

  for (int j = 1; j <= m; j++)
  {
    hh = 0, tt = -1;
    for (int i = 1; i <= n; i++)
    {
      if (hh <= tt && i - q[hh] + 1 > a)
        hh++;
      while (hh <= tt && rmax[q[tt]][j] <= rmax[i][j])
        tt--;
      q[++tt] = i;
      if (i >= a)
        mmax[i - a + 1][j] = rmax[q[hh]][j];
    }
  }

  ll ans = 0;
  for (int i = 1; i + a - 1 <= n; i++)
  {
    for (int j = 1; j + b - 1 <= m; j++)
    {
      ans = (ans + (mmin[i][j] * mmax[i][j]) % mod) % mod;
    }
  }

  cout << ans;
}