URAL1146——DP——Maximum Sum

Description

Given a 2-dimensional array of positive and negative integers, find the sub-rectangle with the largest sum. 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. A sub-rectangle is any contiguous sub-array of size 1 × 1 or greater located within the whole array.

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-hand corner and has the 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 white-space (newlines and spaces). These N ² integers make up the array in row-major order (i.e., all numbers on the first row, left-to-right, then all numbers on 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

The output is the sum of the maximal sub-rectangle.

Sample Input

input	output
4 0 -2 -7 0 9 2 -6 2 -4 1 -4 1 -1 8 0 -2	15

 大意：问你最大的矩阵和，坑死我了WA了n发。。原来做的方法错了。没有考虑当答案为负值的时候

dp[i][j][k]表示i行j列从k个元素开始往前的和，三重循环保证所有情况都遍历到

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int dp[150][150][150];
int a[150][150];
const int inf = 0x3f3f3f3f;
int main()
{
    int n;
    while(~scanf("%d",&n)){
        for(int i = 1; i <= n ; i++)
            for(int j = 1; j <= n ;j++)
                scanf("%d",&a[i][j]);
        memset(dp,0,sizeof(dp));
        int ans = -inf;
        for(int i = 1; i <= n ; i++){
            for(int j = 1; j <= n ;j++){
                int sum = 0;
                for(int k = j; k >= 1; k--){
                    sum += a[i][k];
                    dp[i][j][k] = max(sum + dp[i-1][j][k],sum);
                    ans = max(ans,dp[i][j][k]);
                }
            }
        }
        printf("%d
",ans);
    }
    return 0;
}

错误代码也来一发....祭奠我8个WA一个CE..

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int main()
{
    int a[150][150];
    int n,m;
    scanf("%d",&n);
    for(int i = 1; i <= n ;i++){
        for(int j = 1; j <= n ;j++){
         scanf("%d",&m);
         a[i][j] = a[i-1][j] + m;
        }
    }

    int max1 = 0;
    int sum;
    for(int i = 1; i <= n ;i++){
        for(int j = i+1 ; j<= n ;j++){
            int sum = 0;
            for(int k = 1; k <= n;k++){
              int temp = a[j][k] - a[i][k];
               sum += temp;
              if(sum < 0) sum = 0;
              if(sum  > max1) max1 = sum;
            }
        }
    }
    printf("%d",max1);
   return 0;
}