Question

Write a program in java to determine whether a given function F from the set {0,1,2,3,...,m} to (0,1,2,3,...,n} is one-to-one and/or onto. The inputs to your program will be:

- an integer m

- an integer n, and

- a two dimensional boolean array F of size (m+1) x (n+1), where F[ i , j ] = 1 if F(i) = j.

Answer 1

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;

public class Main
{
public static boolean checkOneToOne(int m, int n, int F[][]) {
// check if every column has less than or equal to one 1.
for (int j = 0; j <= n; j++) {
int count_one = 0;
for (int i = 0; i <= m; i++) {
count_one += F[i][j];
}
if (count_one > 1)
return false;
}
return true;
}
  
public static boolean checkOnto(int m, int n, int F[][]) {
// check if every column has atleast one 1.
for (int j = 0; j <= n; j++) {
int count_one = 0;
for (int i = 0; i <= m; i++) {
count_one += F[i][j];
}
if (count_one == 0)
return false;
}
return true;
}
  
   public static void main(String[] args) throws IOException {
       BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       System.out.print("Enter m: ");
       int m = Integer.parseInt(br.readLine());
       System.out.print("Enter n: ");
       int n = Integer.parseInt(br.readLine());
       int F[][] = new int[m + 1][n + 1];
       for (int i = 0; i <= m; i++) {
       for (int j = 0; j <= n; j++) {
       System.out.print("Enter F[" + i + ", " + j +"]: ");
       F[i][j] = Integer.parseInt(br.readLine());
       }
       }
       if (checkOneToOne(m, n, F))
       System.out.println("Function is one-to-one.");
       else
       System.out.println("Function is not one-to-one.");
       if (checkOnto(m, n, F))
       System.out.println("Function is onto.");
       else
       System.out.println("Function is not onto.");
       br.close();
   }
}