Find the Celebrity
LinkedinThe problem
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 the celebrity, but the celebrity does not know any of them. Now you want to find out who the celebrity is or verify that there is not one. You are only allowed to ask questions like: "Hi, A. Do you know B?" to get information about 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 an integer n and a helper function **bool knows(a, b) **that tells you whether a knows b. Implement a function int findCelebrity(n). There will be exactly one celebrity if they are at the party. Return the celebrity's label if there is a celebrity at the party. If there is no celebrity, return -1. Note that the n x n 2D array graph given as input is not directly available to you, and instead only accessible through the helper function knows. graph[i][j] == 1 represents person i knows person j, wherease graph[i][j] == 0 represents person j does not know person i.
Input: graph = [[1,1,0],[0,1,0],[1,1,1]] Output: 1 Explanation: There are three persons labeled with 0, 1 and 2. graph[i][j] = 1 means person i knows person j, otherwise graph[i][j] = 0 means person i does not know person j. The celebrity is the person labeled as 1 because both 0 and 2 know him but 1 does not know anybody.
Input: graph = [[1,0,1],[1,1,0],[0,1,1]] Output: -1 Explanation: There is no celebrity.
Input: graph = [[1,0,1],[1,1,1],[1,1,1]]
- n == graph.length == graph[i].length
- 2 <= n <= 100
- graph[i][j] is 0 or 1.
- graph[i][i] == 1
cpp
/* The knows API is defined for you.
bool knows(int a, int b); */
class Solution {
public:
int findCelebrity(int n) {
// Your code goes here
}
};java
/* The knows API is defined in the parent class Relation.
boolean knows(int a, int b); */
class Solution extends Relation {
public int findCelebrity(int n) {
// Your code goes here
}
}python
# 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
"""
# Your code goes herejavascript
/**
* Definition for knows()
*
* @param {integer} person a
* @param {integer} person b
* @return {boolean} whether a knows b
* knows = function(a, b) {
* ...
* };
*/
/**
* @param {function} knows()
* @return {function}
*/
var solution = function(knows) {
/**
* @param {integer} n Total people
* @return {integer} The celebrity
*/
return function(n) {
// Your code goes here
};
};csharp
/* The knows API is defined for you.
bool Knows(int a, int b); */
public class Solution {
public int FindCelebrity(int n) {
}
}go
func findCelebrity(n int) int {
}Stuck? Show a way to structure it+
- 01Start with candidate 0.
- 02For each person i, replace candidate when candidate knows i.
- 03Verify the survivor knows nobody else.
- 04Verify every other person knows the survivor; otherwise return -1.
Reference answer
Then expect these follow-ups
Why does one comparison eliminate at least one person?
Tests: proof of elimination
How many knows calls does the full algorithm use?
Tests: complexity accounting
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