Question

I need to check if relation is transitive or not?

Would you please suggest some algorithm to check the transitivity of relations?

I am storing relation as a boolean matrix there is 1 if elements are related other wise 0 like in graphs.

Thanks.

Answer 1

Much simpler algorithm as my Map/Set version (deleted), now with boolean matrix. Maybe this is easier to understand, even if you don’t know Java?

public class Trans {    final static int SIZE = 4;    static boolean isTransitive(boolean[][] function)   {     for (int i = 0; i < SIZE; i++)     {       for (int j = 0; j < SIZE; j++)       {         if (function[i][j])         {           for (int k = 0; k < SIZE; k++)           {             if (function[j][k] && !function[i][k])             {               return false;             }           }         }       }     }     return true;   }    public static void main(String[] args)   {     boolean[][] function = new boolean[SIZE][SIZE];     for (int i = 0; i < SIZE; i++)     {       function[i] = new boolean[SIZE];     }     function[0][1] = true;     function[1][2] = true;     function[0][2] = true;     function[0][3] = true;     function[1][3] = true;        System.out.println(isTransitive(function));   } }