BZOJ1047 [HAOI2007]理想的正方形

昨天刷水累死蒟蒻了。。。

每天一到题解总还是要写的。。。于是就是这个了！

二维RMQ，第一反应是二维线段树，妥妥MLE + TLE

想起来去年市选小题有一道一模一样的，我当时就是写二维线段树，然后MLE0分、、、真是悲剧

发现长度是固定的为n，和动态规划的某个叫单调队列的优化很像：

先求出每一列的某个点向下n个数的最大/小值，然后求出每一行某个点向右的n个单调队列的最大/小值，方法依旧是单调队列。。。

程序写的很烦。。。是照抄网上的。。。（太烦了不想写呢><）

/**************************************************************
    Problem: 1047
    User: rausen
    Language: C++
    Result: Accepted
    Time:1604 ms
    Memory:16600 kb
****************************************************************/
 
#include <cstdio>
#include <algorithm>
 
using namespace std;
const int N = 1005;
 
int mp[N][N];
int q[N][N], h[N], t[N], Q[N];
int mx[N][N], mn[N][N];
int s, e, a, b, n;
 
inline int read(){
    int x = 0, sgn = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9'){
        if (ch == '-') sgn = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9'){
        x = x * 10 + ch - '0';
        ch = getchar();
    }
    return sgn * x;
}
 
void getmax(){
    for (int i = 1; i <= b; ++i)
        h[i] = 1, t[i] = 0;
    for (int i = 1; i <= a; ++i){
        for (int j = 1; j <= b; ++j){
            while (h[j] <= t[j] && i - q[j][h[j]] >= n) ++h[j];
            while (h[j] <= t[j] && mp[q[j][t[j]]][j] <= mp[i][j]) --t[j];
            q[j][++t[j]] = i;
        }
        e = 0, s = 1;
        for (int j = 1; j <= b; ++j){
            while (s <= e && j - Q[s] >= n) ++s;
            while (s <= e && mp[q[Q[e]][h[Q[e]]]][Q[e]] <= mp[q[j][h[j]]][j]) --e;
            Q[++e] = j;
            mx[i][j] = mp[q[Q[s]][h[Q[s]]]][Q[s]];
        }
    }
}
 
void getmin(){
    for (int i = 1; i <= b; ++i)
        h[i] = 1, t[i] = 0;
    for (int i = 1; i <= a; ++i){
        for (int j = 1; j <= b; ++j){
            while (h[j] <= t[j] && i - q[j][h[j]] >= n) ++h[j];
            while (h[j] <= t[j] && mp[q[j][t[j]]][j] >= mp[i][j]) --t[j];
            q[j][++t[j]] = i;
        }
        e = 0, s = 1;
        for (int j = 1; j <= b; ++j){
            while (s <= e && j - Q[s] >= n) ++s;
            while (s <= e && mp[q[Q[e]][h[Q[e]]]][Q[e]] >= mp[q[j][h[j]]][j]) --e;
            Q[++e] = j;
            mn[i][j] = mp[q[Q[s]][h[Q[s]]]][Q[s]];
        }
    }
}
 
int main(){
    a = read(), b = read(), n = read();
    for (int i = 1; i <= a; ++i)
        for (int j = 1; j <= b; ++j)
            mp[i][j] = read();
     
    getmax();
    getmin();
    int ans = (int) 1e9;
    for (int i = n; i <= a; ++i)
        for (int j = n; j <= b; ++j)
            ans = min(ans, mx[i][j] - mn[i][j]);
    printf("%d
", ans);
    return 0;
}