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【最大子矩陣和】HDU1081-To The Max
To The Max
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 8193 Accepted Submission(s): 3981
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.
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].
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
Sample Output
15
Source
Greater New York 2001
最大子矩陣和
關於最大子矩陣和的做法探討詳細請看：https://blog.csdn.net/acmman/article/details/38580931
AC代碼：
#include <stdio.h>
#include <string.h>
#include <limits.h>
#define MAXN 200
int a[MAXN][MAXN],temp[MAXN];
int n;
int getsum()
{
int i,sum=0,max=0;
for(i=0;i<n;i++)
{
sum+=temp[i];
if(sum>max) max=sum;
if(sum<0) sum=0;
}
return max;
}
int main()
{
int i,j,ans,k;
while(scanf("%d",&n)!=EOF)
{
memset(a,0,sizeof(a));
for(i=0;i<n;i++)
for(j=0;j<n;j++)
scanf("%d",&a[i][j]);
ans=INT_MIN;
for(i=0;i<n;i++)//從第i行開始
{
memset(temp,0,sizeof(temp));
for(j=i;j<n;j++)//從 i行到 n-1行都嚐試一次
{
for(k=0;k<n;k++)//把 j至 k行的每一列都加起來，就是矩陣壓縮
temp[k]+=a[j][k];
int pre=getsum();//計算壓縮矩陣形成的一維數組的最長連續序列
if(ans<pre)//更新最大值
ans=pre;
}
}
printf("%d\n",ans);
}
return 0;
}
最後更新：2017-04-03 05:39:54