算法-并查集

并查集Union Find

• 简单地数据结构
• 很实用的数据结构

UF

class UF{public:    explicit UF(int number);    int find(int x);    bool connected(int x, int y);    void unions(int x, int y);private:    vector<int> id;    vector<int> rank;}UF::UF(int number){    id.resize(number);    iota(id.begin(),id.end(),0);    rank.resize(number,1);}int UF::find(int x){    while(id[x]!=x)         x=find(id[x]);    return id[x];}//iterative/*int UF::find(int x){    while(id[x]!=x){        id[x]=id[id[x]];        x=id[x];    }    return id[x];}*/bool UF:: connected(int x,int y){    return find(x)==find(y);}void UF::unions(int x, int y){    int root1=find(x);    int root2=find(y);    if(root1==root2) return;    if(rank[root1]<rank[root2]){        id[root1]=root2;        rank[root2]+=rank[root1];    }else{        id[root2]=id[root1];        rank[root1]+=rank[root2];    }   }

Number of Connected Components in an Undirected Graph

• 并查集的直接应用

int countComponents(int n,vector<pair<int, int>>& edges){    int cnt=0;    UF(n);    for(auto edge:edges)        unions(edge.first,edge.second);    for(int i=0;i<n;i++)         if(id[i]==i)             cnt++;    return cnt;}

Graph Valid Tree

• 考察一：无环图
• 考察二：树的边的个数edges=vertices-1

bool ValidTree(int n, vector<pair<int, int>>& edges){    if(edges.empty() || edges.size()!=n-1) return false;    UF(n);    for(auto edge:edges){        int x=find(edge.first);        int y=find(edge.second);        if(x==y) return false;        id[x]=y;    }    return true;}