277_Find the Celebrity

277. Find the Celebrity

Level: medium

Tag: array

Question

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.

Idea

Three steps:

• find the possible celebrity

  • Use the first loop is to exclude n - 1labels that are not possible to be a celebrity.

  • After the first loop,xis the only candidate.

• Verify if this possible celebrity doesn't know anyone

• Verify if everyone knows this possible celebrity

Complexity

• Time:$O(n)$

• Space:$O(1)$

Solution

# The knows API is already defined for you.
# @param a, person a
# @param b, person b
# @return a boolean, whether a knows b
# def knows(a, b):

class Solution(object):
    def findCelebrity(self, n):
        """
        :type n: int
        :rtype: int
        """
        x = 0

        # find the only possible celebrity
        for i in xrange(n):
            if knows(x, i):
                x = i

        # verify if this possible celebrity doesn't know anyone
        # important: use range(x) because all the positions after x has been tested in first loop
        if any(knows(x, i) for i in range(x)):    
            return -1

        # verify if everyone knows this possible celebrity
        if any(not knows(i, x) for i in range(n)):
            return -1

        return x