## May 10, 2020

### #LeetCode:Find the Town Judge

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][0] != trust[i][1]
1 <= trust[i][0], trust[i][1] <= N

Algorithm
We can solve this problem by visualizing the graph. Draw N vertices's and start drawing the relationships.

[1,3] means vertex 1 trust vertex 3.
[2,3] means vertex 2 trust vertex 3.

Now create two arrays, indegree and outdegree.

• indegree[x] represents the numbers of edges incoming to a vertex x.
• outdegree[x] represents the numbers of edges outgoing from vertex x.

We need to check:
if(indegree[x]==N-1 && outdegree[i]==0){
return x;
}

i.e if the number of edges incoming to the vertex is N-1 (which means N-1 person are trusting x), but there is no outgoing edge (x is not trusting anyone), then that edge represents a judge.

Java Solution