## Saturday, August 28, 2010

### poj_1050_ToTheMax.cpp

poj1050, uva00108,

## Problem:

To the Max
 Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 22580 Accepted: 11759
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
```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

## Solution:

Dynamic programming.

## Source Code:

```
//Thu Mar 11 12:12:25 CST 2010
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
using namespace std;
int MaxSum(int n, int a[])
{
int i, max = -12800, sum = 0;
for (i = 0; i < n; i++)
{
if (sum > 0)
sum += a[i];
else
sum = a[i];
if (max < sum)
max = sum;
}
return max;
}
int MaxSum2(int n, int a[][100])
{
int max = -12800;
int b[100];
int i, j, k;
for (i = 0; i < n; i++) //Start from row# i.
{
for (j = 0; j < n; j++)
b[j] = 0; //The sum of elements from row i to row k. j control the column.
for (k = i; k < n; k++)
{
for (j = 0; j < n; j++)
b[j] += a[k][j];
int sum = MaxSum(n, b);
if (max < sum)
max = sum;
}
}
return max;
}
int main(int argc, char* argv[])
{
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
int n;
int a[100][100];
while (cin >> n)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
cin >> a[i][j];
}
}
cout << MaxSum2(n, a) << endl;
}
fclose(stdin);
fclose(stdout);
return 0;
}

```