To the Max
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 48554 | Accepted: 25678 |
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.
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
4 0 -2 -7 0 9 2 -6 2 -4 1 -4 1 -1 8 0 -2
Sample Output
15
Source
原题链接:http://poj.org/problem?id=1050
做这题前,先弄清楚HDU1003这题。
然后再把二维压缩为一维就可以了。
1,12,123,1234,2,23,234,3,34,4
按上面几种情况压缩,求出最大的即可。
AC代码:
/**
* 行有余力,则来刷题!
* 博客链接:http://blog.youkuaiyun.com/hurmishine
*
*/
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int maxn=100+5;
int a[maxn][maxn];
int dp[maxn];
int n;
int getMax(int *a)
{
int maxx=a[0];
int sum=a[0];
for(int i=1;i<n;i++)
{
if(sum+a[i]>a[i])
sum+=a[i];
else
sum=a[i];
if(sum>maxx)
maxx=sum;
}
return maxx;
}
int main()
{
while(cin>>n)
{
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
cin>>a[i][j];
}
int p;
int maxx=0;
for(int i=0;i<n;i++)
{
memset(dp,0,sizeof(dp));
for(int j=i;j<n;j++)
{
p=0;
for(int k=0;k<n;k++)
{
dp[p]+=a[j][k];
p++;
}
int ans=getMax(dp);
if(ans>maxx)
maxx=ans;
}
}
cout<<maxx<<endl;
}
return 0;
}