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\n",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;

}