CodeForces 429B Working out(dp,四个角递推)

B. Working out

Summer is coming! It's time for Iahub and Iahubina to work out, as they both want to look hot at the beach. The gym where they go is a matrix a with n lines and m columns. Let number a[i][j] represents the calories burned by performing workout at the cell of gym in the i-th line and the j-th column.

Iahub starts with workout located at line 1 and column 1. He needs to finish with workout a[n][m]. After finishing workout a[i][j], he can go to workout a[i + 1][j] or a[i][j + 1]. Similarly, Iahubina starts with workout a[n][1] and she needs to finish with workout a[1][m]. After finishing workout from cell a[i][j], she goes to either a[i][j + 1] or a[i - 1][j].

There is one additional condition for their training. They have to meet in exactly one cell of gym. At that cell, none of them will work out. They will talk about fast exponentiation (pretty odd small talk) and then both of them will move to the next workout.

If a workout was done by either Iahub or Iahubina, it counts as total gain. Please plan a workout for Iahub and Iahubina such as total gain to be as big as possible. Note, that Iahub and Iahubina can perform workouts with different speed, so the number of cells that they use to reach meet cell may differs.

Input

The first line of the input contains two integers n and m (3 ≤ n, m ≤ 1000). Each of the next n lines contains m integers: j-th number from i-th line denotes element a[i][j] (0 ≤ a[i][j] ≤ 10⁵).

Output

The output contains a single number — the maximum total gain possible.

Sample test(s)

Input

3 3
100 100 100
100 1 100
100 100 100

Output

800

dp思路：可以枚举每个可能相遇的点所产生的最大情况
dp1[i][j] 从（1,1）到（i,j）的最大值
dp2[i][j] 从（n,m）到（i,j）的最大值
dp3[i][j] 从（m,1）到（i,j）的最大值
dp1[i][j] 从（1,n）到（i,j）的最大值

ans为最终结果：
由于遍历的每个点是，可以分为四个部分，（1,1）->（i,j）+（i,j）->(n,m) + (n,1)->(i,j) + （1,m）->(i,j)
因此可以用ans更新四部分和的最大值

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <string>
#define LL long long
#define WW freopen("in.txt","r",stdin)
#define RR freopen("out.txt","w",stdout)
#define INF 0x3f3f3f3f

using namespace std;

const int maxn = 1010;

int dp1[maxn][maxn],dp2[maxn][maxn],dp3[maxn][maxn],dp4[maxn][maxn];
int a[maxn][maxn];

int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=m;j++)
        {
            scanf("%d",&a[i][j]);
        }
    }

    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=m;j++)
        {
            dp1[i][j] = max(dp1[i-1][j],dp1[i][j-1]) + a[i][j];
        }
    }

    for(int i=n;i>=1;i--)
    {
        for(int j=m;j>=1;j--)
        {
            dp2[i][j] = max(dp2[i+1][j],dp2[i][j+1]) + a[i][j];
        }
    }

    for(int i=1;i<=n;i++)
    {
        for(int j=m;j>=1;j--)
        {
             dp3[i][j] = a[i][j] + max(dp3[i-1][j], dp3[i][j+1]);
        }
    }

    for(int i=n;i>=1;i--)
    {
        for(int j=1;j<=m;j++)
        {
            dp4[i][j] = a[i][j] + max(dp4[i][j-1], dp4[i+1][j]);
        }
    }
    int ans = 0;
    for(int i=2;i<n;i++)
    {
        for(int j=2;j<m;j++)
        {
            ans = max(ans,dp1[i-1][j]+dp2[i+1][j]+dp3[i][j+1]+dp4[i][j-1]);
            ans = max(ans,dp1[i][j-1]+dp2[i][j+1]+dp3[i-1][j]+dp4[i+1][j]);
        }
    }
    printf("%d\n",ans);
    return 0;
}