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hdu 1081 To The Max

2024-08-07 00:05:50   217人阅读

最大子矩阵和……


一直听说dp啊什么……


好吧……暴力


一个很巧妙的思想


由于有负数肯定是不太好的


所以，a[i][j]:第i行前j个数的和


然后，从第1行开始到最后一行，枚举第i列跟第j列(j<i)，与第k行围起来的矩阵和，


用t记录当前结果，若t为负数，则t=a[k][i]-a[k][j]


若t为正数，t+=a[k][i]-a[k][j]


每次更新t后，更新答案ans即可

#include<iostream>
#include<map>
#include<string>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
int a[1000][1000];
const int inf=1<<31;
int main()
{
    int i,j,k,n,t,ans;
    while(cin>>n)
    {
        memset(a,0,sizeof(a));
        for(i=1;i<=n;i++)
            for(j=1;j<=n;j++)
            {
                cin>>t;
                a[i][j]=a[i][j-1]+t;
            }
        ans=inf;
        for(i=1;i<=n;i++)    
            for(j=0;j<i;j++)
            {
                t=-1;
                for(k=1;k<=n;k++)
                {
                    if(t<0)
                        t=a[k][i]-a[k][j];
                    else
                        t+=a[k][i]-a[k][j];
                    ans=max(ans,t);
                }
            }
        cout<<ans<<endl;
    }
    return 0;
}


To The Max

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 8571    Accepted Submission(s): 4161


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

hdu 1081 To The Max


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