To The Max
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 14951 Accepted Submission(s): 6983
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.
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
DP
1 #include<iostream> 2 //#include<fstream> 3 #include<memory.h> 4 using namespace std; 5 int main() 6 { 7 //ifstream in("data.txt"); 8 int n,i,j,k; 9 int mat[102][102]={0}; 10 int a; 11 while(cin>>n) 12 { 13 memset(mat,0,sizeof(mat)); 14 for(i=1;i<=n;i++) 15 for(j=1;j<=n;j++) 16 { 17 cin>>a; 18 mat[i][j]=mat[i][j-1]+a; 19 } 20 int max=-128,sum; 21 for(i=1;i<=n;i++) 22 for(j=i;j<=n;j++) 23 { 24 sum=0; 25 for(k=1;k<=n;k++) 26 { 27 sum+=mat[k][j]-mat[k][i-1]; 28 if(sum>max) 29 max=sum; 30 if(sum<0) 31 sum=0; 32 } 33 } 34 cout<<max<<endl; 35 } 36 return 0; 37 }