997. Find the Town Judge
Description
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
. If a trust relationship does not exist in trust
array, then such a trust relationship does not exist.
Return the label of the town judge if the town judge exists and can be identified, or return -1
otherwise.
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
Constraints:
1 <= n <= 1000
0 <= trust.length <= 104
trust[i].length == 2
- All the pairs of
trust
are unique. ai != bi
1 <= ai, bi <= n
Solutions
Solution 1: Counting
We create two arrays $cnt1$ and $cnt2$ of length $n + 1$, representing the number of people each person trusts and the number of people who trust each person, respectively.
Next, we traverse the array $trust$, for each item $[a_i, b_i]$, we increment $cnt1[a_i]$ and $cnt2[b_i]$ by $1$.
Finally, we enumerate each person $i$ in the range $[1,..n]$. If $cnt1[i] = 0$ and $cnt2[i] = n - 1$, it means that $i$ is the town judge, and we return $i$. Otherwise, if no such person is found after the traversal, we return $-1$.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $trust$.
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