277. Find the Celebrity

Suppose you are at a party with n people (labeled from 0 to n - 1 ) and among them, there may exist one celebrity. The definition of a celebrity is that all the other n - 1 people know him/her but he/she does not know any of them.

Now you want to find out who the celebrity is or verify that there is not one. The only thing you are allowed to do is to ask questions like: "Hi, A. Do you know B " to get information of whether A knows B. You need to find out the celebrity (or verify there is not one) by asking as few questions as possible (in the asymptotic sense).

You are given a helper function bool knows(a, b) which tells you whether A knows B. Implement a function int findCelebrity(n) . There will be exactly one celebrity if he/she is in the party. Return the celebrity's label if there is a celebrity in the party. If there is no celebrity, return -1 .

Example 1:

Input: 

graph = 
[
  [1,1,0],
  [0,1,0],
  [1,1,1]
]

Output: 

1

Explanation: 

There are three persons labeled with 0, 1 and 2. graph[i][j] = 1 means person i knows person j, otherwise graph[i][j] = 0 means person i does not know person j. The celebrity is the person labeled as 1 because both 0 and 2 know him but 1 does not know anybody.

Example 2:

Input: 

graph = 
[
  [1,0,1],
  [1,1,0],
  [0,1,1]
]

Output: 

-1

Explanation: 

There is no celebrity.

Note:

1. The directed graph is represented as an adjacency matrix, which is an  n x n matrix where a[i][j] = 1 means person  i knows person  j while  a[i][j] = 0 means the contrary.
2. Remember that you won't have direct access to the adjacency matrix.

1、题目描述¶

假设你是一个专业的狗仔，参加了一个 n 人派对，其中每个人被从 0到 n - 1标号。在这个派对人群当中可能存在一位 “名人”。所谓 “名人” 的定义是：其他所有 n - 1 个人都认识他/她，而他/她并不认识其他任何人。

现在你想要确认这个 “名人” 是谁，或者确定这里没有 “名人”。而你唯一能做的就是问诸如 “A 你好呀，请问你认不认识 B呀？” 的问题，以确定 A 是否认识 B。你需要在（渐近意义上）尽可能少的问题内来确定这位 “名人” 是谁（或者确定这里没有 “名人”）。

在本题中，你可以使用辅助函数bool knows(a, b)获取到 A 是否认识B。请你来实现一个函数int findCelebrity(n)。

派对最多只会有一个 “名人” 参加。若 “名人” 存在，请返回他/她的编号；若 “名人” 不存在，请返回 -1。

示例 1:



输入: graph = [
  [1,1,0],
  [0,1,0],
  [1,1,1]
]
输出: 1
解析: 有编号分别为 0、1 和 2 的三个人。graphi = 1 代表编号为 i 的人认识编号为 j 的人，而 graphi = 0 则代表编号为 i 的人不认识编号为 j 的人。“名人” 是编号 1 的人，因为 0 和 2 均认识他/她，但 1 不认识任何人。
示例 2:



输入: graph = [
  [1,0,1],
  [1,1,0],
  [0,1,1]
]
输出: -1
解析: 没有 “名人”

注意:

• 该有向图是以邻接矩阵的形式给出的，是一个 n × n 的矩阵， a[i][j] = 1 代表 i 与 j 认识，a[i][j] = 0 则代表 i 与 j 不认识。 请记住，您是无法直接访问邻接矩阵的。