547. Friend Circles 朋友圈

题目链接
tag:

• Medium；
• DFS;
• BFS;

question
  There are N students in a class. Some of them are friends, while some are not. Their friendship is transitive in nature. For example, if A is a direct friend of B, and B is a direct friend of C, then A is an indirect friend of C. And we defined a friend circle is a group of students who are direct or indirect friends.

  Given a N*N matrix M representing the friend relationship between students in the class. If M[i][j] = 1, then the ith and jth students are direct friends with each other, otherwise not. And you have to output the total number of friend circles among all the students.

Example 1:

Input:
[[1,1,0],
[1,1,0],
[0,0,1]]
Output: 2
Explanation:The 0th and 1st students are direct friends, so they are in a friend circle. The 2nd student himself is in a friend circle. So return 2.

Example 2:

Input:
[[1,1,0],
[1,1,1],
[0,1,1]]
Output: 1
Explanation:The 0th and 1st students are direct friends, the 1st and 2nd students are direct friends, so the 0th and 2nd students are indirect friends. All of them are in the same friend circle, so return 1.

Note:

• N is in range [1,200].
• M[i][i] = 1 for all students.
• If M[i][j] = 1, then M[j][i] = 1.

解法一：DFS：
  本题求朋友圈的个数，对于朋友圈的定义是可以传递的，比如A和B是好友，B和C是好友，那么即使A和C不是好友，那么他们三人也属于一个朋友圈。比较直接的解法就是 DFS 搜索，对于某个人，遍历其好友，然后再遍历其好友的好友，那么我们就能把属于同一个朋友圈的人都遍历一遍，同时标记出已经遍历过的人，然后累积朋友圈的个数，再去对于没有遍历到的人在找其朋友圈的人，这样就能求出个数。代码如下：

class Solution {
public:
    int findCircleNum(vector<vector<int>>& M) {
        // DFS
        int n = M.size(), res = 0;
        vector<bool> visited(n, false);
        for (int i=0; i<n; ++i) {
            if (visited[i])
                continue;
            helper(M, i, visited);
            ++res;
        }
        return res;
    }
    
    void helper(vector<vector<int>> &M, int k, vector<bool> &visited) {
        visited[k] = true;
        for (int i=0; i<M.size(); ++i) {
            if (!M[k][i] || visited[i])
                continue;
            helper(M, i, visited);
        }
    }
};

解法二：BFS
  我们也可以用 BFS 来遍历朋友圈中的所有人，思路和上面大同小异，代码如下：

class Solution {
public:
    int findCircleNum(vector<vector<int>>& M) {
        // BFS
        int n = M.size(), res = 0;
        vector<bool> visited(n, false);
        queue<int> q;
        for (int i=0; i<n; ++i) {
            if (visited[i])
                continue;
            q.push(i);
            while (!q.empty()) {
                int t = q.front(); q.pop();
                visited[t] = true;
                for (int j = 0; j < n; ++j) {
                    if (!M[t][j] || visited[j]) continue;
                    q.push(j);
                }
            }
            ++res;
        }
        return res;
    }
};