FindTheCelebrity.java

package array;

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

/**
 * Created by gouthamvidyapradhan on 25/11/2017.
 *
 * Suppose you are at a party with n people (labeled from 0 to n - 1) and among them, there may exist one celebrity.
 * The definition of a celebrity is that all the other n - 1 people know him/her but he/she does not know any of them.

 Now you want to find out who the celebrity is or verify that there is not one. The only thing you are allowed to do
 is to ask questions like: "Hi, A. Do you know B?" to get information of whether A knows B. You need to find out the
 celebrity (or verify there is not one) by asking as few questions as possible (in the asymptotic sense).

 You are given a helper function bool knows(a, b) which tells you whether A knows B. Implement a function int
 findCelebrity(n),  your function should minimize the number of calls to knows.

 Note: There will be exactly one celebrity if he/she is in the party. Return the celebrity's label if there is a
 celebrity in the party.  If there is no celebrity, return -1.
 */
public class FindTheCelebrity {

    private static Map<Integer, Set<Integer>> map = new HashMap<>();

    /**
     * Main method
     * @param args
     */
    public static void main(String[] args) {
        //initialize relationship
        map.put(0, new HashSet<>());
        map.put(1, new HashSet<>());
        map.put(2, new HashSet<>());
        map.put(3, new HashSet<>());
        map.put(4, new HashSet<>());
        map.put(5, new HashSet<>());
        map.put(6, new HashSet<>());
        map.get(0).add(3);
        map.get(0).add(1);
        map.get(0).add(2);
        map.get(0).add(4);
        map.get(0).add(5);
        map.get(0).add(6);

        map.get(1).add(0);
        map.get(1).add(3);
        map.get(1).add(2);

        map.get(2).add(1);
        map.get(2).add(3);
        map.get(2).add(4);

        map.get(4).add(2);
        map.get(4).add(3);
        map.get(4).add(5);

        map.get(5).add(4);
        map.get(5).add(3);
        map.get(5).add(6);

        map.get(6).add(5);
        map.get(6).add(3);
        map.get(6).add(0);

        System.out.println(new FindTheCelebrity().findCelebrity(0));
    }

    /**
     * Find celebrity
     * @param n
     * @return
     */
    public int findCelebrity(int n) {
        int candidate = -1, i = 0, next = 1;
        while(i < n){
            if(next >= n) break;
            if(knows(i, next) && !knows(next, i)){
                i = next;
                next = i + 1;
            } else if((!knows(i, next) && !knows(next, i)) ||  (knows(i, next) && knows(next, i))){
                i = next + 1;
                next = i + 1;
            } else {
                next++;
            }
            candidate = i;
        }
        if(candidate == -1 ||  candidate >= n)
            return -1;
        for(int j = 0; j < candidate; j ++){
            if(!knows(j, candidate) || knows(candidate, j)){
                candidate = -1;
                break;
            }
        }
        return candidate;
    }

    private boolean knows(int a, int b){
        return map.get(a).contains(b);
    }
}