To the Max
Time Limit: 2 Seconds Memory Limit: 65536 KB
Problem
Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1 x 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.
The input consists of an N x 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.
Input
4
0 -2 -7 0 9 2 -6 2
-4 1 -4 1 -1
8 0 -2
Output
15
代码如下:
# include<stdio.h>
# include<string.h>
# define N
int main(){
int a[N][N],b[N];
int n,i,j,k;
while(scanf("%d",&n)!=EOF)
{
for(i=;i<n;i++)
for(j=;j<n;j++)
scanf("%d",&a[i][j]);
int max= -;
for(i=;i<n;i++) //第i行到第j行的最大子矩阵和
{
memset(b,,sizeof(b));
for(j=i;j<n;j++)
{
int sum=;
for(k=;k<n;k++)
{
b[k] += a[j][k];
sum += b[k];
if(sum<) sum=b[k];
if(sum>max) max=sum;
}
}
}
printf("%d\n",max);
}
return ;
}