Gym 102152L

题意：
给一个$n\ast m$矩阵数组，让求子矩阵大小为$h\ast w$的最小中位数，确保$n\ast m$为奇数。

思路：
二分+求二维数组的前缀和。
二分答案x,然后判断二维矩阵中那个大于x的位置为1，然后二维矩阵的前缀和，二分大于x的数量，若子矩阵中有数量大于$(h\ast w+1)/2$则缩小，反则扩大。

参考代码：

/*
 * @Author: vain
 * @Date: 2020-08-26 11:58:46
 * @LastEditTime: 2020-09-10 19:04:49
 * @LastEditors: sueRimn
 * @Description: In User Settings Edit
 * @FilePath: \main\demo.cpp
 */
//#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
using namespace std;
typedef long long ll;
//#define ll long long
typedef unsigned long long ull;
const int N = 1e3 + 20;
const ll maxn = 1e5 + 20;
const ll mod = 1e9 + 7;
ll head[maxn], stac[maxn];
int a[maxn], b[maxn], c[maxn];
//typedef pair p;
//priority_queue, greater
 > m;
//ll sum[maxn];
int max(int a, int b) {
      return a > b ? a : b; }
ll min(ll a, ll b) {
      return a < b ? a : b; }
ll gcd(ll a, ll b) {
      return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) {
      return a * b / gcd(a, b); }
void swap(ll &x, ll &y) {
      x ^= y, y ^= x, x ^= y; }
map<string, ll> pll, che, mp;
int ik[N], q[N], cnt;
int lowbit(int x) {
      return (x) & (-x); }
vector<int> fc;
//ull h[maxn], p[maxn];
const ull base = 13331;
//char s1[maxn];
ll ksm(ll a, ll b)
{
     
    ll res = 1;
    while (b)
    {
     
        if (b & 1)
            res = a * res;
        b >>= 1;
        a = a * a;
    }
    return res;
}
int f[N][N], solv[N][N], stk[N];
int get(int x)
{
     
    int ans = 0;
    while (x)
    {
     
        if (x & 1)
            ans++;
        x >>= 1;
    }
    return ans;
}
void init(int x, int n, int m)
{
     
    for (int i = 1; i <= n; i++)
    {
     
        for (int j = 1; j <= m; j++)
        {
     
            if (f[i][j] <= x)
                solv[i][j] = 1;
            else
                solv[i][j] = 0;
        }
    }
    for (int i = 1; i <= n; i++)
    {
     
        for (int j = 1; j <= m; j++)
        {
     
            solv[i][j] = solv[i][j - 1] + solv[i - 1][j] - solv[i - 1][j - 1] + solv[i][j];
        }
    }
}
bool check(int x, int n, int m, int h, int w)
{
     
    init(x, n, m);
    for (int i = h; i <= n; i++)
    {
     
        for (int j = w; j <= m; j++)
        {
     
            int ans = solv[i][j] - solv[i][j - w] - solv[i - h][j] + solv[i - h][j - w];
            if (ans >= (h * w + 1) / 2)
                return true;
        }
    }
    return false;
}
int main()
{
     
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);
    srand(time(NULL));
    //cout << ksm(2, 20) << endl;
    int n, m, t, s, q, h, w;
    cin >> n >> m >> h >> w;
    for (int i = 1; i <= n; i++)
    {
     
        for (int j = 1; j <= m; j++)
        {
     
            cin >> f[i][j];
        }
    }
    int l = 1, r = n * m, ans = 0;
    while (l <= r)
    {
     
        int mid = l + r >> 1;
        if (check(mid, n, m, h, w))
        {
     
            ans = mid, r = mid - 1;
        }
        else
            l = mid + 1;
    }
    cout << ans << endl;
    // cin >> t;zz
    // while (t--)
    // {
     

    // }
}