CareerCup

public class FindTheCelebrity {

	public static void main(String[] args){
		int[] input = new int[] {1,2,3,4,5,6};
		
		FindTheCelebrity ftc = new FindTheCelebrity();

		int left = 0;
		int right = input.length-1;
		while(left<right) {
			if (ftc.knows(input[left], input[right])) {
				left++;
			} else{
				right--;
			}
		}
		
		int id = right;
		for(int i=0; i<input.length; i++) {
			if(i != right) {
				if(!ftc.knows(input[i], input[right])) {
					id = -1;
				}
				if(ftc.knows(input[right], input[i])){
					id = -1;
				}
			}
		}
		
		System.out.println("Candidate " + right);
		System.out.println(id == -1 ? -1 : input[id]);
	}
	
	public boolean knows(int a, int b) {
		int[][] map = new int[][] {{0,1,0,1,0,1},
			   					   {0,0,0,0,0,0},
			   					   {0,1,0,0,0,1},
			   					   {0,1,0,1,0,1},
			   					   {0,1,0,0,1,0},
			   					   {0,1,0,0,0,0}};
		return map[a-1][b-1] == 1;
	}
	
}

We could represent the persons as the array of Qubits:
00: Celebrity - knows nobody in the room
01: No celebrity - knows only celebrity
10: No celebrity - knows everybody but no celebrity
11: No celebrity - knows the celebrity and everybody else

If we sort the array - then we know where to look for the celebrity.

Based on your question, the problem is asking us to find the celebrity given the person list and the person number. So, this can be done in O(N+N) = O(N) time where N = number of rows/cols. If this was problem was finding the celebrity given the matrix, then it would be a different problem. I present a solution in Python below.

I assume I am given an adjacency matrix. My solution in Python:

def determineCelebrity(peopleList, person):
    # Scan the adjacency matrix
    actualPersonIndex = person - 1
    # Scan the cols and make sure everyone knows the person
    for i in range(len(peopleList)):
        if i != actualPersonIndex and peopleList[i][actualPersonIndex] != 1:
            return False
    # Make sure the celebrity knows no one else in the party
    return all(x == 0 for x in peopleList[actualPersonIndex])

Test code:

celebrityMatrix = \
[
    [0, 1, 0, 1, 0, 1],
    [0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 1],
    [0, 1, 0, 1, 0, 1],
    [0, 1, 0, 0, 1, 0],
    [0, 1, 0, 0, 0, 0]
]
print(determineCelebrity(celebrityMatrix, 5)) # False
print(determineCelebrity(celebrityMatrix, 2)) # True
print(determineCelebrity(celebrityMatrix, 3)) # False

1. Given problem of finding whether the given person is celebrity or not can be solved in 0(n) just by checking row corresponding to that person should be all 0's, and column should be all 1's.

2. If the problem is to find the celebrity, then also complexity will be O(n), ie. starting from the first person, iterate it's row and find out the first 1 say at element i, all elements/persons before that one cannot be celebrity as first person does not know them, so direct skip to i, and start iterating its row from i+1 th position and keep skipping .

class FindTheCeleb
{
	public static void main (String[] args) throws java.lang.Exception{
	    
	    /*
	    Assumption: whoIknow matrix 
	    Everyone knows themselves, so a 1 for themselves
	    Everyone may or maynot know the others in the party thus 0/1 for the rest of the fields 
	    
	    */
		Integer[][] whoIknow=new Integer[][]{{1,0,0,0,0,0},
		                     {1,1,0,0,1,0},
		                     {1,1,1,0,0,0},
		                     {1,0,0,1,1,0},
		                     {1,0,0,1,1,0},
		                     {1,0,0,1,1,1}};
		                     
		Integer[] people= new Integer[]{1,2,3,4,5,6};
		
		Integer testPerson1 = 4;
		Integer testPerson2 = 1;
		System.out.println("Person "+ testPerson1 + 
		                    (isCelebrity(whoIknow, testPerson1)? " is a isCelebrity": " is not a celebrity"));
		                    
		System.out.println("Person "+ testPerson2 + 
		                    (isCelebrity(whoIknow, testPerson2)? " is a isCelebrity": " is not a celebrity"));
	}
	
	public static boolean isCelebrity(Integer[][] whoIknow, Integer testPerson){
	    int i=0;
	    for(;i<whoIknow.length;i++){
	        //System.out.println(whoIknow[i][testPerson-1]);
	        if(whoIknow[i][testPerson-1]==0){
	            //System.out.println("testPerson=" + testPerson);
	            return false;
	        }
	    }
	    
	   return true;
	}
}

public class FinaCelebrity {

    public static void main(String[] args) {

        // initialize Person instances assuming Tom is the celebrity
        // John
        Person john = new Person("John");
        john.friendsList.add("Eric");
        john.friendsList.add("Kevin");
        john.friendsList.add("Tom");
        john.friendsList.add("Joey");

        // Eric
        Person eric = new Person("Eric");
        eric.friendsList.add("John");
        eric.friendsList.add("BM");
        eric.friendsList.add("Tom");

        // Jeff
        Person jeff = new Person("Jeff");
        jeff.friendsList.add("Amy");
        jeff.friendsList.add("Tom");

        // Tom (the celebrity who knows no one in the room, so no friends)
        Person tom = new Person("Tom");

        // add persons into people
        ArrayList<Person> people = new ArrayList<Person>();
	people.add(john);
        people.add(eric);
        people.add(jeff);

        // check if a person is the celebrity
        String name = tom.name;
        if (findCelebrity(people, john))
            System.out.println(name + " is celebrity");
        else
            System.out.println(name + " is NOT celebrity");
    }

    // find if a person is celebrity among people
    static public boolean findCelebrity(ArrayList<Person> people, Person person) {

        // check if the person doesn't know any in the room
        if (!person.friendsList.isEmpty())
            return false;

        // check if everyone know the person
        int len = people.size();
        for (int i = 0; i < len; i++) {
            if (people.get(i).name != person.name) { // skip himself
                if (!people.get(i).friendsList.contains(person.name)) // check if person is included in the friend list
                    return false;
            }
        }

        return true;
    }

    static class Person {

        ArrayList<String> friendsList = new ArrayList<String>();

        String name;

        public Person(String _name) {
            name = _name;
        }

        public boolean knowSomeone(String person) {
            if (friendsList.contains(person))
                return true;
            else
                return false;
        }
    }
}

Assuming Person has a property Knows that is a HashSet<Person>:

bool IsCelebrity(Person person, IEnumerable<Person> room)
{
    return !person.Knows.Any() // person doesn't know anyone
          &&        // all people in room either knows or is the person
          room.All(r => r == person || r.Knows.Contains(person));
}

O(n) where n is number of people in room (Knows.Contains is O(1) as its a HashSet).