POJ ---1050 To the Max
2014-03-23 10:31
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To the Max
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.
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
Sample Output
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 38914 | Accepted: 20534 |
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.
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
#include<iostream> #include<cstdio> #include<cstring> using namespace std; int map[105][105], sum[105][105]; int main(){ int n, maxn; /* freopen("in.c", "r", stdin); */ while(~scanf("%d", &n)){ for(int i = 1;i <=n;i ++){ for(int j = 1;j <= n;j ++){ scanf("%d", &map[i][j]); sum[i][j] = sum[i-1][j] + sum[i][j-1] + map[i][j] - sum[i-1][j-1]; } } maxn = -100000000; for(int i = 1;i <= n;i ++){ for(int j = 1;j <= n;j ++){ for(int k = i+1;k <= n;k ++){ for(int p = j+1;p <= n;p ++) maxn = max(sum[k][p]-sum[k][j-1]-sum[i-1][p] + sum[i-1][j-1], maxn); } } } printf("%d\n", maxn); } return 0; }
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