To The Max
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 7620 Accepted Submission(s): 3692
Problem Description
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.
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.
Input
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].
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
8 0 -2
Sample Output
15
这道题目是求二维数组的最大子矩阵的和，最大子矩阵一定是在1~n行之间，所以要任选连续的几行压缩成一位数组求最大连续子段和。
代码:
#include <iostream>
#include <cstdio>
using namespace std;
#define N 105
int arr[N][N],b[N];
int dp(int *a,int m) //求一维数组的最大子段和
{
int i,sum,max;
sum = 0;
max = 0;
for(i=0; i<N; i++)
{
sum += a[i];
if(sum<0)
sum = 0;
if(sum>max)
max = sum;
}
return max;
}
int main()
{
int i,j,k,n,sum,max;
while(scanf("%d",&n)!=EOF)
{
for(i=0; i<n; i++)
for(j=0; j<n; j++)
scanf("%d",&arr[i][j]);
max = 0;
for(i=0; i<n; i++)
{
memset(b,0,sizeof(b));
for(j=i; j<n; j++)
{
for(k=0; k<n; k++)
b[k] += arr[j][k];
sum = dp(b,n);
if(sum>max)
max = sum;
}
}
printf("%d\n",max);
}
return 0;
}