Tags: "leetcode", "graph", access_time 2-min read

# Find the Town Judge

#### Created: May 10, 2020 by [lek-tin]

##### Last updated: May 10, 2020

In a town, there are N people labelled 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 `trust`, an array of pairs `trust[i]` = [a, b] representing that the person labelled `a` trusts the person labelled `b`.

If the town judge exists and can be identified, return the label of the town judge. Otherwise, return `-1`.

#### Example 1:

``````Input: N = 2, trust = [[1,2]]
Output: 2
``````

#### Example 2:

``````Input: N = 3, trust = [[1,3],[2,3]]
Output: 3
``````

#### Example 3:

``````Input: N = 3, trust = [[1,3],[2,3],[3,1]]
Output: -1
``````

#### Example 4:

``````Input: N = 3, trust = [[1,2],[2,3]]
Output: -1
``````

#### Example 5:

``````Input: N = 4, trust = [[1,3],[1,4],[2,3],[2,4],[4,3]]
Output: 3
``````

#### Note:

• `1 <= N <= 1000`
• `trust.length <= 10000`
• `trust[i]` are all different
• `trust[i] != trust[i]`
• `1 <= trust[i]`, `trust[i] <= N`

### Solution (hashset)

Java

``````class Solution {
public int findJudge(int N, int[][] trust) {
HashMap<Integer, HashSet<Integer>> lookup = new HashMap<Integer, HashSet<Integer>>();
for (int i = 0; i < trust.length; i++) {
int from = trust[i];
int to = trust[i];
if (lookup.get(from) == null) {
lookup.put(from, new HashSet<Integer>());
}
}

int missingCount = 0;
int judge = -1;
for (int i = 1; i <= N; i++) {
if (lookup.get(i) == null) {
if (missingCount == 1) return -1;
missingCount++;
judge = i;
continue;
}
}

for (Map.Entry<Integer, HashSet<Integer>> entry: lookup.entrySet()) {
HashSet<Integer> values = entry.getValue();
if (!values.contains(judge)) return -1;
}

return judge;
}
}
``````

### Solution (indegrees)

Java

``````public int findJudge(int N, int[][] trust) {
// early stop
if (trust.length < N - 1) {
return -1;
}

int[] indegrees = new int[N + 1];
int[] outdegrees = new int[N + 1];

for (int[] relation : trust) {
int from = relation;
int to = relation;
outdegrees[from]++;
indegrees[to]++;
}

for (int i = 1; i <= N; i++) {
if (indegrees[i] == N - 1 && outdegrees[i] == 0) {
return i;
}
}
return -1;
}
``````