Find the Town Judge Problem & Solution

In a town, there are n people labeled from 1 to n. There is a rumor that one of these people is secretly the town judge.

If the town judge exists, then:

  • The town judge trusts nobody.
  • Everybody (except for the town judge) trusts the town judge.
  • There is exactly one person that satisfies properties 1 and 2.

You are given an array trust where trust[i] = [ai, bi] representing that the person labeled ai trusts the person labeled bi.

Return the label of the town judge if the town judge exists and can be identified, or return -1 otherwise.

See the find the town judge problem on LeetCode.

C++ Solution

#pragma GCC optimize("Ofast")
#pragma GCC optimization("unroll-loops")
#pragma GCC target("avx,avx2,fma")

static const int _=[](){std::ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);return 0;}();

class Solution {
public:
  int findJudge(int n, vector<vector<int>>& trust) {
    vector<int> incoming(n, 0);
    vector<int> outgoing(n, 0);
    for (int i = 0; i < trust.size(); ++i) {
      ++incoming[trust[i][1] - 1];
      ++outgoing[trust[i][0] - 1];
    }

    for (int i = 0; i < n; ++i) {
      if (incoming[i] == n - 1 &&
          outgoing[i] == 0) {
        return i + 1;
      }
    }

    return -1;
  }
};