To the Max
2010-07-14 15:54
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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
Sample Output
代码
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
40 -2 -7 0 9 2 -6 2-4 1 -4 1 -18 0 -2
Sample Output
15
/********代码******枚举*****DP***************/
代码
#include<stdio.h> int main() { int n,i,j,k,l,ii,h,max,Max; int map[101][101],sum[101],s[101]; while(scanf("%d",&n)!=EOF){ for(i=0;i<n;i++){ for(j=0;j<n;j++) scanf("%d",&map[i][j]); } Max=0; for(i=0;i<n;i++){ for(j=i;j<n;j++){ //从第i列到第j列 for(k=0;k<n;k++) sum[k]=s[k]=0; max=-127; for(k=0;k<n;k++){ for(l=i;l<=j;l++) s[k]+=map[k][l]; //s[k]为敌k行的值(从第i列到第j列) if(sum[k]>0) sum[k+1]=sum[k]+s[k]; //sum[k]为到k行是的最大值(从第i列到第j列) else sum[k+1]=s[k]; if(sum[k+1]>max)max=sum[k+1]; //max记录最大值(从第i列到第j列) } if(max>Max) //Max记录总的最大值 Max=max; } } printf("%d\n",Max); } return 0; }
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