#include <stdio.h>
#include <stdlib.h>
#include<time.h>
#include<math.h>
#define max 9000
int mat[max][max];
int main() {
int i, j, m, n;
int isReflexive=1,isSymmetric=1,isTransitive=1,isequivalence=1;
printf("Enter the column dimension of the matrix: ");
scanf("%d", &n);
double total_time;
clock_t start,end;
start=clock();
for(i = 0; i < n;i++) {
for(j = 0; j < n;j++) {
mat[i][j]=rand()%2;
}
}
printf("The randomly generated matrix is : \n");
for(i = 0; i < n;i++) {
for(j = 0; j < n;j++) {
printf("%d ",mat[i][j]);
}
printf("\n");
}
//equivalence
//Reflexive
for(i = 0; i < n;i++) //o(n)
if(mat[i][i]==0)
{isReflexive=0;}
//Symmetric
for(i = 0; i < n;i++) { //o(n^2)
for(j = 0; j < n;j++){
if(mat[i][j]!=mat[j][i])
isSymmetric=0;
}
//Transitive
for(i = 0; i < n;i++) { // o(n^3)
for(j = 0; j < n;j++){
for( int k=0;k<n;k++){
if(mat[i][j] && mat[j][k] && !mat[k][i])
isTransitive=0;
}
}
}
if(!isReflexive || !isTransitive || !isSymmetric)
isequivalence=0;
}
int x,y;
for (i = 0; i < m; i++) {
for( j = 0; j < n; j++) {
if (mat[i][j] != mat[j][i])
x = 1;
else if (mat[i][j] == -mat[j][i])
y = 1;
}
}
if (y == 1)
printf("\n\nThe matrix is Anti Symmetric.\n ");
else
printf("\n\nNot anti symmetric\n");
if(isReflexive)
{printf("Reflexive\n");}
if(!isReflexive)
{printf("Not Reflexive\n");}
if(isTransitive)
{printf("Transitive\n");}
if(!isTransitive)
{printf("Not Transitive\n");}
if(isSymmetric)
{printf("Symmetric\n");}
if(!isSymmetric)
{printf("Not Symmetric\n");}
if(isequivalence)
{printf("Equivalent");}
if(!isequivalence)
{printf("Not Equivalent");}
printf("\n");
end=clock();
total_time=((double)(end-start)/CLOCKS_PER_SEC)*pow(10,3);
printf("\n Execution time is : %1f ms \n",total_time);
printf("\n");
return 0;
}