Partial order relation

Time Limit: 1000 ms Memory Limit: 65536 KiB

Submit Statistic

Problem Description

Given the relation matrix of binary relation on a finite set, it is determined whether the relation is a partial order relation.

Input

For multiple groups of test data, for each group of test data, enter the positive integer n (1 < = n < = 100) in the first row, and enter the relationship matrix of N rows and N columns in the second row to n+1 row.

Output

For each group of test data, if it is a partial order relationship, then output yes, otherwise, output no.

Sample Input

4
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
4
1 0 0 1
0 1 0 0
0 0 1 0
1 0 0 1

Sample Output

yes
no

Hint

Formal definition of partial order relation: let R be A binary relation on set A, if R satisfies reflexivity, antisymmetry and transitivity, then R is called partial order relation on A.

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
using namespace std;
int a[105][105];
int main()
{
    int n, i, j, flag, k;
    while(~scanf("%d", &n))
    {
        for(i = 1; i <= n; i++)
        {
            for(j = 1; j <= n; j++)
            {
                scanf("%d", &a[i][j]);
            }
        }
        flag = 1;
        for(i = 1; i <= n; i++)
        {///Reflexivity, 1 diagonal
            if(a[i][i] != 1)
                flag = 0;
        }
        for(i = 1; i <= n; i++)
        {
            for(j = 1; j <= n; j++)
            {
                if(a[i][j] == 1 && a[j][i] == 1 && i != j)
                {///Antisymmetry, if IRJ & & JRI, then i = j does not hold, then it does not have antisymmetry
                    flag = 0;
                }
                if(a[i][j] == 1)
                {///Symmetry, if IRJ & & JRK is iRk, if it doesn't hold, it doesn't have antisymmetry
                    for(k = 1; k <= n; k++)
                    {
                        if(a[j][k] == 1 && a[i][k] != 1)
                        {
                            flag = 0;
                        }
                    }
                }
            }
        }
        if(flag)  printf("yes\n");
        else  printf("no\n");
    }
    return 0;
}