算法整理-并查集和分治

一. Friend Cycle

用一个数组存储root结点，采用压缩路径的方法，查找的时间复杂度为O(1)， 合并的时间复杂度为O(1)

class Solution {
public:
    int findCircleNum(vector<vector<int>>& M) {
        int len = M.size();
        if (len == 0) return 0;
        vector<int> parent(len, 0);
        for (int i=0; i<len; i++) {
             parent[i] = i;
        }
        int count = len;
        for (int i=0; i<len; i++)
          for (int j=i+1; j<len; j++) {
              if (M[i][j] == 1) {
                  int parent1 = findParent(i, parent);
                  int parent2 = findParent(j, parent);
                  if (parent1 != parent2) {
                      parent[parent2] = parent1;
                      count--;
                  }

              } 
          }
          return count;
    }

private:
    int findParent(int pos, vector<int> &parent){
        if (parent[pos] == pos) return pos;
        
        int root = findParent(parent[pos], parent);
        parent[pos] = root;
        return root;
        
    }

};

二.  逆序对