F - 最大子矩形

Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u

Submit



Status

Description

Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*1 or greater located within the whole array. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the
sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.

As an example, the maximal sub-rectangle of the array:



0 -2 -7 0

9 2 -6 2

-4 1 -4 1

-1 8 0 -2

is in the lower left corner:



9 2

-4 1

-1 8

and has a sum of 15.

Input

The input consists of an N * N array of integers. The input begins with a single positive integer N on a line by itself, indicating the size of the square two-dimensional array. This is followed by N^2 integers separated by whitespace (spaces and newlines).
These are the N^2 integers of the array, presented in row-major order. That is, all numbers in the first row, left to right, then all numbers in the second row, left to right, etc. N may be as large as 100. The numbers in the array will be in the range [-127,127].

Output

Output the sum of the maximal sub-rectangle.

Sample Input

4

0 -2 -7 0 9 2 -6 2

-4 1 -4 1 -1



8 0 -2

Sample Output

15

<span style="color:#3333ff;">/*

_________________________________________________________________________________________________________________

       author      :       Grant Yuan

       time        :       2014.7.19

       source      :       Hdu1081

       algorithm   :       暴力枚举+动态规划

       explain     :       暴力枚举第k1行到第k2行每一列各个元素的和sum[i]，然后对sum[i]进行一次最大子序列求和

___________________________________________________________________________________________________________________

*/

#include<iostream>

#include<cstdio>

#include<cstring>

#include<cstdlib>

#include<functional>

#include<algorithm>

using namespace std;

int a[105][105];

int l;

int sum[105];

int dp[105];

int main()

{

	while(~scanf("%d",&l)){

		for(int i=0;i<l;i++)

			for(int j=0;j<l;j++)

			 scanf("%d",&a[i][j]);

		int ans=-9999999,ans1;

		for(int k1=0;k1<l;k1++)

			for(int k2=0;k2<l;k2++){

		   memset(dp,0,sizeof(dp));

		   memset(sum,0,sizeof(sum));

		 for(int i=0;i<l;i++){

			for(int j=k1;j<=k2;j++)

		     {

			   sum[i]+=a[i][j];

		         }

		   for(int m=0;m<l;m++)

		     {

		   	  dp[m+1]=max(dp[m]+sum[m],sum[m]);

		      }

		   ans1=dp[1];

		   for(int d=1;d<=l;d++)

			  if(dp[d]>ans1)

		ans1=dp[d];

		if(ans1>ans)

		      ans=ans1;}}

		printf("%d\n",ans);}

}

</span>