URAL1146 & POJ1050 Maximum Sum (maximum contiguous subsequence and)

Description

Given a 2-dimensional array of positive and negative integers, find the sub-rectangle with the largest sum. The sum of a rectangle is the sum of the "the elements in" that rectangle. The problem the sub-rectangle with the largest sum are referred to as the Maximal sub-rectangle. A Sub-rectangle is any contiguous sub-array of size 1x1 or greater located within the whole array. 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-hand corner and has the sum of 15.

Input

The input consists of an NX NArray of integers. The input begins with a single positive integer NOn a line by itself indicating the size of the square and the dimensional array. This was followed by N2 integers separated by white-space (newlines and spaces). These N2integers make to the array in row-major order (i.e., all numbers to the first row, left-to-right, then all numbers on the Second row, left-to-right, etc.). NMay is as large as 100. The numbers in the array would be in the range [−127, 127].

Output

The output is the sum of the maximal sub-rectangle. Test Instructions Analysis: The topic is relatively simple, given a n*n matrix, to find the matrix of the maximum and the neutron matrix. In the given example, the largest sub-matrix is

9	2
−4	1
−1	8

That is 15. Solution thinking: This is a two-dimensional array, to find the largest sub-matrix and, should think of using one-dimensional maximum sub-sequence and, then you can compress sub-matrices into sub-sequences, and then solve. 1) The matrix is shrunk to a column column, and the four columns are then evaluated for the maximum number of sub-sequences. 2) One-dimensional maximal sub-sequence and. The code is as follows:

#include <stdio.h>
#define MAX_N
int arr[max_n][max_n];
int Rowssum[max_n]; and
int N for each line;
int calc (int x, int y);
Int main ()
{
     //freopen ("Input.txt", "R", stdin);
      scanf ("%d", &n);
      int i = 0;
      Int j = 0;
      int max =-1270000;
      int sum = 0;
      for (i=0;i<n;i++)
      {
            for (j=0;j<n;j++)
             {
            &NBS P     &NBSP;SCANF ("%d", &arr[i][j]);
             }
     }

      for (i=0;i<n;i++)
      {
           for (j=i ; j<n;j++)
          {
                 sum = Calc (i,j); Calculation of column I to column J Maximum and
                 if (Sum>max)
      & nbsp         {
                      max = sum;                {
         
    &NBSP ; }
      printf ("%d\n", Max);
      return 0;
}

int calc (int x, int y)
{
int i = 0;
int j = 0;
int resultvalue =-1270000;
int thissum = 0;
for (i=0;i<n;i++)
{
Rowssum[i] = 0;
for (j=x;j<=y;j++)
{
Rowssum[i] = Rowssum[i] + arr[i][j];
}
}

Rowssum represents the and of each row for the specified column I to J.

Rowssum[] The maximum subsequence of this one-dimensional array and
for (i=0;i<n;i++)
{
Thissum = Thissum + rowssum[i];
if (Thissum>resultvalue)
{
Resultvalue = Thissum;
}
if (thissum<0)
{
thissum = 0;
}
}

return resultvalue;

}

URAL1146 & POJ1050 Maximum Sum (maximum contiguous subsequence and)