277. Find the Celebrity

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.

First approach takes O(n^2), for each pair of person, if A doesn't know B, then A is a potential candidate of the Celebrity, then the question is reduced to half size, continue this approach until the size reduced to 1. Then sweep the array to make sure the Celebrity is known by others, otherwise, he/she is fake 'Celebrity'

The following solution is based on a simple assumption. if know(L,R) return false, then L must be the Celebrity otherwise there is no Celebrity.

/* The knows API is defined in the parent class Relation.
      boolean knows(int a, int b); */

public class Solution extends Relation {
    public int findCelebrity(int n) {
        int l=0, r = n-1;
        while(l < r){
            if(knows(l, r)){
                l++;
            }else{
                r--;
            }
        }
        for(int i=0; i< n; i++){
            if(i == l) continue;
            if(knows(l, i) || !knows(i , l)) return -1;
        }
        return l;

    }
}