LC 1489. Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree (tarjan, 最小生成树)

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referenct to @617280219

1. Sort and group edges by weight. In each step we process one group of edges
2. Discard the edges whose ends are already connected
3. Run Tarjan's bridge finding algorithm on each connnected part of the subgraph. Add bridges to critical and the rest to pseudo-critical
4. Use union-find to connect the edges' two ends.

class Solution {
public:
    struct Edge{
        int u;
        int v;
        int id;
    };
    int N;
    int fa[100];
    int cri[200];
    int pcri[200];
    int dict[100];
    int low[100];
    int timer;
    
    int find(int p){
        if(p==fa[p]) return p;
        fa[p]=find(fa[p]);
        return fa[p];
    }
    
    bool uni(int p, int q){
        int proot=find(p);
        int qroot=find(q);
        if(proot==qroot) return false;
        fa[proot]=qroot;
        return true;
    }
    
    void tarjan(int u,  vector<vector<pair<int,int>>> &adj, int parent){
        ++timer;
        dict[u]=low[u]=timer;
        for(auto& p:adj[u]){
            if(p.first==parent) continue;
            if(dict[p.first]!=-1){
                low[u]=min(low[u],dict[p.first]);
            }else{
                tarjan(p.first,adj,u);
                if(dict[u]<low[p.first] && pcri[p.second]!=1){
                    cri[p.second]=1;
                }
                low[u]=min(low[u],low[p.first]);
            }
        }
    }
    
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        int en=edges.size();
        N=n;
        map<int,vector<Edge>> mp;
        for(int i=0;i<en;i++){
            auto &e=edges[i];
            mp[e[2]].push_back(Edge{e[0],e[1],i});
        }
        for(int i=0;i<N;i++) fa[i]=i;
        for(auto& m:mp){
            vector<Edge>& es=m.second;
            unordered_map<int,vector<int>> pathes;
            for(auto& e:es){
                int ur=find(e.u);
                int vr=find(e.v);
                if(ur==vr) continue;
                if(ur<vr) swap(ur,vr);
                pathes[ur*N+vr].push_back(e.id);
            }
            vector<vector<pair<int,int>>> adj(N);
            vector<Edge> n_edges;
            for(auto& p:pathes){
                if(p.second.size()>1){
                    for(int i:p.second) pcri[i]=1;
                }
                int ur=p.first/N;
                int vr=p.first%N;
                int id=p.second[0];
                adj[ur].push_back({vr,id});
                adj[vr].push_back({ur,id});
                n_edges.push_back(Edge{ur,vr,id});
                uni(ur,vr);
            }
            memset(dict,-1,sizeof(dict));
            timer=0;
            for(auto& e:n_edges){
                if(dict[e.u]==-1){
                    tarjan(e.u,adj,-1);
                }
            }
            for(auto& e:n_edges){
                if(cri[e.id]==0) pcri[e.id]=1;
            }
        }
        vector<vector<int>> res;
        vector<int> res1,res2;
        for(int i=0;i<en;i++) {
            if(cri[i]) res1.push_back(i);
            else if(pcri[i]) res2.push_back(i);
        }
        res.push_back(res1);
        res.push_back(res2);
        return res;
    }
};