Union Find

Description from wiki: a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets

you can easily solve leetcode: 547. Number of Provinces w/ UF.
get UF template at github/sky-bro/AC/Algorithms/Union Find

Template

UF datastructure is very simple, it has only two key functions: U and F.

use U (union) to connect two nodes, so they belong to the same set;
use F (find) to find the root of a node (or the group id of the node)

We use ids to store the parent of every node, ids[i] is the i-th node’s parent. if ids[i] == i means i is the root if its group, we can say the group id is i.

So, different root/group id means nodes are in different groups, whereas same root/group id means two nodes are in the same group.

simle

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class UF {
 private:
  vector<int> ids;

 public:
  UF(int n) {
    ids.resize(n);
    iota(ids.begin(), ids.end(), 0);
  }

  int F(int x) { return ids[x] == x ? x : (ids[x] = F(ids[x])); }

  void U(int p, int q) { ids[F(p)] = ids[F(q)]; }
};

full

part from U and F, based on your needs, you can add these functions:

int group_count(), count the number of sets/groups – initialize group_cnt as n (each node as a group), every time U unions two different groups, --group_count.
int count(int x), count the size of the group of node x – when U unions two different groups, add one group’s size to another (the new root).
bool connected(int p, int q), check if two nodes are in the same group.

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class UF {
 private:
  vector<int> ids, cnts;
  int cnt;

 public:
  UF(int n) {
    ids.resize(n);
    iota(ids.begin(), ids.end(), 0);
    cnt = n;
    cnts.resize(n, 1);
  }

  int F(int x) { return ids[x] == x ? x : (ids[x] = F(ids[x])); }

  void U(int p, int q) {
    int pid = F(p), qid = F(q);
    if (pid != qid) {
      ids[qid] = pid;
      --cnt;
      cnts[pid] += cnts[qid];
    }
  }

  int group_count() { return cnt; }
  int count(int x) { return cnts[F(x)]; }
  bool connected(int p, int q) { return F(p) == F(q); }
};

Solution to lc problem 547

you can also solve this problem with dfs: github/sky-bro/AC/leetcode.com/0547 Friend Circles/main.cpp, lc has changed the name of this problem to “Number of Provinces”

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// union find
class Solution {
 private:
  int n, cnt;
  vector<int> ids;
  void U(int p, int q) {
    int pid = F(p), qid = F(q);
    if (pid != qid) {
      --cnt;
      ids[pid] = ids[qid];
    }
  }
  int F(int x) { return x == ids[x] ? x : (ids[x] = F(ids[x])); }

 public:
  int findCircleNum(vector<vector<int>>& isConnected) {
    n = cnt = isConnected.size();
    ids.resize(n);
    iota(ids.begin(), ids.end(), 0);
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (isConnected[i][j]) {
          U(i, j);
        }
      }
    }
    return cnt;
  }
};

Union Find

Template

simle

full

Solution to lc problem 547

more problems for exercise