POJ 1050 to the Max

to the Max

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 45906		Accepted: 24276

Description

Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*1 o R greater located within the whole array. 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.
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:

7 |
-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 in a line by itself, indicating the size of the square two-dimensional a Rray. This was followed by n^2 integers separated by whitespace (spaces and newlines). These is the n^2 integers of the array, presented in Row-major order. That's, all numbers on the first row, left-to-right, then all numbers-second row, left-to-right, etc. N may be as large as 100. The numbers in the array would be in the range [-127,127].

Output

Output the sum of the maximal sub-rectangle.

Sample Input

40-2-7 0 9 2-6 2-4 1-4  1-18  0-2

Sample Output

15

Source

Greater New York 2001

Translation:

Total time limit:

1000ms

Memory Limit:

65536kB

Describe

The size of the known matrix is defined as the and of all elements in the matrix. Given a matrix, your task is to find the largest non-empty (size is at least 1 * 1) sub-matrices.

For example, the following matrix of 4 * 4

0-2-7 0
9 2-6 2
-4 1-4 1
-1 8 0-2

The maximum sub-matrix is

7 |
-4 1
-1 8

The size of this sub-matrix is 15.

Input

The input is a matrix of n * N. The first line of input gives N (0 < n <= 100). Then, in a few rows later, the n integers of the first row are given first from left to right, and then the n integers of the second row are given from left to right ... ) gives the N2 integers in the matrix, separated by whitespace characters (spaces or blank lines) between the integers. The range of integers in the known matrix is in [-127, 127].

Output

The size of the output maximum sub-matrix.

Sample input

40-2-7 0 9 2-6 2-4 1-4  1-18  0-2

Sample output

15

First Kind

/*prepare an array f[i,j] to save to i,j Matrix and (similar to prefix and) for a sub-matrix [x1,y1,x2,y2]//x1,x2 represents the upper left and bottom right corner of the horizontal axis has s[x1,y1,x2,y2] = f[x2,y2]-F[x1-1, Y2]-f[x2,y1-1] + f[x1,y1];*/#include<cstdio>#include<iostream>using namespacestd;#defineN 101intans=-0x7f, n,a[n][n],f[n][n];intMain () {scanf ("%d",&N);  for(intI=1; i<=n;i++)         for(intj=1; j<=n;j++) {scanf ("%d",&A[i][j]); F[I][J]=f[i-1][j]+f[i][j-1]-f[i-1][j-1]+A[i][j]; }     for(intI=1; i<=n;i++)         for(intj=1; j<=n;j++)             for(intk=0; k+i<=n;k++)                 for(intL=0; l+j<=n;l++){                    intxx=i+k,yy=j+l; Ans=max (ans,f[xx][yy]-f[i-1][yy]-f[xx][j-1]+f[i-1][j-1]); } printf ("%d\n", ans); return 0;}

The second Kind

#include <cstdio>#include<iostream>using namespacestd;#defineN 101inta[n][n],n,ans=0;intMain () {scanf ("%d",&N);  for(intI=1, x;i<=n;i++)         for(intj=1; j<=n;j++) scanf ("%d", &x), a[i][j]=a[i-1][j]+x; //Column prefixes and  for(intI=1; i<=n;i++)         for(intj=i;j<=n;j++){            inttmp=0;  for(intk=1; k<=n;k++){                intnum=a[j][k]-a[i-1][k]; if(tmp>0) tmp+=num; Elsetmp=num; Ans=Max (ans,tmp); }} printf ("%d\n", ans); return 0;}

POJ 1050 to the Max