Nine degrees OJ topic 1250: Matrix transformation

Title Description:

For an integer matrix, there is an operation to add a moment to any element in the matrix, which needs to be adjacent (up or down) and one element,
A positive matrix is given to determine whether it can be obtained by the above operation from a full 0 matrix.

Input:

Output:

If the output "Yes" can be transformed, otherwise "No".
There are multiple sets of data, the first row of each group of data a positive integer n (n<=10), a n*n matrix, followed by n rows, n integers per row. When n is 0 o'clock, the test ends.

Sample input:

31 10 91 1 21 0 130 1 00 1 21 0 10

Sample output:

YesNo

1#include <cstdio>2#include <cstdlib>3#include <cstring>4#include <algorithm>5#include <iostream>6#include <cmath>7 intmatrix[ A][ A];8 intdir[][2] = {{0,1},{0,-1},{1,0},{-1,0}};9 Ten intMainintargcChar Const*argv[]) One { A     intN; -      while(SCANF ("%d", &n)! = EOF && N! =0)  { -         intx =0, y =0; the          for(inti =0; I < n; i++) { -              for(intj =0; J < N; J + +) { -scanf"%d",&matrix[i][j]); -                 if((i + j) &1) { +x = x +Matrix[i][j]; -                 } +                 Else { Ay = y +Matrix[i][j]; at                 } -             } -         } -         if(X! =y) { -Puts"No"); -             Continue; in         } -         BOOLIsOk =true; to          for(inti =0; I < n && isOk; i++) { +              for(intj =0; J < n && IsOk; J + +) { -                 intsum =0; the                  for(intp =0; P <4; p++) { *                     intTMPX = i + dir[p][0]; $                     intTmpy = j + dir[p][1];Panax Notoginseng                     if(Tmpx >=0&& tmpx < n && tmpy >=0&& Tmpy <N) { -sum = sum +Matrix[tmpx][tmpy]; the                     } +                 } A                 if(Matrix[i][j] >sum) { theIsOk =false; +                      Break; -                 } $             } $         } -         if(isOk) { -Puts"Yes"); the         } -         Else {WuyiPuts"No"); the         } -  Wu  -     } About     return 0; $}

The key to this problem is to find the necessary and sufficient conditions for judgment, there are two necessary and sufficient conditions here (excerpt from http://www.cnblogs.com/liangrx06/p/5083814.html),

(1) x=sum (A[i][j] where i+j is odd, y=sum (A[i][j]) where i+j is even, then there is x=y
(2) Any one element is not more than the surrounding four elements and

Nine degrees OJ topic 1250: Matrix transformation