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/* 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) {
        
    }
}
  1. Best. Two pass.
  • 1st for: decides candidate; note candidate to be k; so 0 to k-1 don’t know k, k+1 to n-1 also don’t know k because candidate = k.
  • 2nd: this candidate doesn’t know others, check if all others know this person.
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public int findCelebrity(int n) {
    int candidate = 0;
    for (int i = 1; i < n; ++i) {
        if (knows(candidate, i)) candidate = i;
    }
    for (int i = 0; i < n; ++i) {
        if (candidate != i && (knows(candidate, i) || !knows(i, candidate))) return -1; 
    }
    return candidate;
}
  1. Stack. Two pass.
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/* 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) {
        if (n <= 0) return -1;
        if (n == 1) return 0;
        
        Stack<Integer> st = new Stack<>();
        for (int i = 0; i < n; ++i) {
            st.push(i);
        }
        
        int a = 0, b = 0;
        while (st.size() > 1) {
            a = st.pop(); b = st.pop();
            if (knows(a, b)) st.push(b); else st.push(a);
        }
        
        int c = st.pop();
        for (int i = 0; i < n; ++i) {
            if (c != i && (knows(c, i) || !knows(i, c))) return -1;
        }
        return c;
    }
}

Why stack not list? list: add, remove could take O(n), stack pop is O(1)