JZOJ [4820]. 【NOIP2016提高A組模擬10.15】最大化

Description

Input

Output

Sample Input

樣例輸入1：
3 2
4 0
-10 8
-2 -2

Sample Output

樣例輸出1：
4

Data Constraint

The Solution

先n^2枚舉矩形的左右兩邊l,r，然後在行上找最值

即先確定兩邊，再處理行。

我們可以得到前i行l~r的總和。記爲si

我們可以用前綴和來弄。

如果si>sj且i>j則(i-j)*(r-l+1)可以更新答案

維護單調遞減棧

用一個數組f記錄j

每次在其中二分找j

複雜度是O(n3log)

CODE

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#define fo(i,a,b) for (int i=a;i<=b;i++)
#define N 405
#define INF 1000000000

using namespace std;

typedef long long ll;

int n,m,top;
ll a[N][N],Stack[N],Pre[N],f[N],ans = 0;

int Find(ll x)
{
    int l = 1, r = top,res = -1;
    while (l <= r)
    {
        int mid = (l + r) >> 1;
        if (Stack[mid] < x) res = mid , r = mid - 1;
        else l = mid + 1;
    }
    return res;
}

void Work(int x,int y)
{
    top = 0;
    fo(i,1,n) Pre[i] += a[i][y];
    Stack[0] = INF;
    ll sum = 0;
    fo(i,1,n)
    {
        sum += Pre[i];
        if (sum > 0) ans = max(ans,(ll)i * (y-x+1));
        else
        {
            int t = Find(sum);
            if (t != -1) ans = max(ans,(ll)(i-f[t]) * (y-x+1));
        }
        if (sum < Stack[top]) Stack[++ top] = sum,f[top] = i;
    }
}

int main()
{
    freopen("max.in","r",stdin);
    freopen("max.out","w",stdout);
    scanf("%d%d",&n,&m);
    fo(i,1,n) fo(j,1,m) scanf("%lld",&a[i][j]);
    fo(i,1,m)
    {
        fill(Pre,Pre+1+N,0);
        fo(j,i,m) Work(i,j);
    }
    printf("%lld\n",ans);
    return 0;
}