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.
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
求出town judge 有两点要求,judge 不相信任何人,任何其他人都相信judge(注意其他人可以除了judge以外还相信其他人,而不仅仅只有一个judge)。也就是judge一定被n-1个人相信。这道题可以利用图论解决,trust数组其实就是各个结点的临接表,如果a相信b(a->b),则b的入度加一,a的出度加一(等价于入度减一),利用一个数组维护所有人(结点)的入度关系,然后寻找入度为n-1的结点即为judge。
class Solution {
public:
int findJudge(int n, vector<vector<int>>& trust) {
vector<int> graph(n+1,0);
for(auto tt:trust){
graph[tt[0]]--;
graph[tt[1]]++;
}
for(int i=1;i<n+1;++i){
if(graph[i]==n-1){
return i;
}
}
return -1;
}
};