模板_LCA(最近公共祖先)

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倍增算法

#include<cstdio>#include<vector>#include<algorithm>#include<iostream>using namespace std;#define N 100005#define M 21struct LCA{    vector<int> g[N];    int root,ans,n,m;    int d[N],f[N][M];    void dfs(int x,int dp){        d[x]=dp;        for(int i=0;i<g[x].size();i++){            if(!d[g[x][i]]){                dfs(g[x][i],dp+1);                f[g[x][i]][0]=x;            }        }    }    void work(){        for(int i=1;i<=20;i++)            for(int j=1;j<=n;j++)                f[j][i]=f[f[j][i-1]][i-1];    }    int lca(int u,int v){        if(d[u]<d[v])   swap(u,v);        int l=d[u]-d[v];        if(l)        for(int i=0;i<=20;i++)            if(l&(1<<i))    u=f[u][i];        if(u==v) return u;        for(int i=20;i>=0;i--){            if(f[u][i]!=f[v][i])                u=f[u][i],v=f[v][i];        }        return f[u][0];    }    void init(){        scanf("%d",&n);int x,y;        for(int i=1;i<=n;i++){            scanf("%d",&x);            if(x) g[x].push_back(i);            else root=i;        }        dfs(root,0);work();ans=0;        scanf("%d",&m);        while(m--){            scanf("%d%d",&x,&y);            ans=lca(x^ans,y^ans);            printf("%d\n",ans);        }    }}s;int main(){    s.init();    return 0;}

离线算法Tarjan HDU_P2586

#include<cstdio>#include<cstring>#include<queue>#include<vector>#include<iostream>using namespace std;#define N 40005struct Tarjan{    struct qEdge{int fr,to,lca;};    struct Edge{int fr,to,dis;};    vector<Edge> edge;vector<qEdge> qedge;    vector<int> qs[N];vector<int> g[N];    int p[N];long long d[N],ans[N];bool b[N];int n,m;    void Add_qEdge(int fr,int to){        qedge.push_back((qEdge){fr,to,0});        int ll=qedge.size();        qs[fr].push_back(ll-1);        qs[to].push_back(ll-1);    }    void Add_Edge(int fr,int to,int d){        edge.push_back((Edge){fr,to,d});edge.push_back((Edge){to,fr,d});        m=edge.size();        g[fr].push_back(m-2);g[to].push_back(m-1);    }    long long abs(long long x){return x>=0?x:-x;}    void dfs(int u,int f,long long w){        d[u]=w;        for(int i=0;i<g[u].size();i++){            Edge &e=edge[g[u][i]];            if(e.to==f) continue;            dfs(e.to,u,w+e.dis);        }    }    int Find(int x){return p[x]==x?x:p[x]=Find(p[x]);}    void Tarjan_Lca(int u){        p[u]=u;b[u]=true;        for(int i=0;i<g[u].size();i++){            Edge &e=edge[g[u][i]];            if(!b[e.to]){                Tarjan_Lca(e.to);                p[e.to]=u;            }        }        for(int i=0;i<qs[u].size();i++){            qEdge &e=qedge[qs[u][i]];            if(u==e.fr&&b[e.to]){                e.lca=Find(e.to);                ans[qs[u][i]]=abs(d[u]+d[e.to]-2*d[e.lca]);            }            if(u==e.to&&b[e.fr]){                e.lca=Find(e.fr);                ans[qs[u][i]]=abs(d[u]+d[e.fr]-2*d[e.lca]);            }        }    }    void init(){        edge.clear();qedge.clear();        for(int i=0;i<=n;i++) g[i].clear(),qs[i].clear();        memset(d,0,sizeof(d));memset(ans,0,sizeof(ans));    };    void Solve(int n,int m){        this->n=n;this->m=m;int x,y,z;        for(int i=0;i<=n;i++) p[i]=i;        for(int i=1;i<n;i++){            scanf("%d%d%d",&x,&y,&z);            Add_Edge(x,y,z);        }        for(int i=0;i<m;i++){            scanf("%d%d",&x,&y);            Add_qEdge(x,y);        }        dfs(1,0,0);Tarjan_Lca(1);        for(int i=0;i<m;i++) printf("%lld\n",ans[i]);        init();    }}s;int main(){    int t,n,m;scanf("%d",&t);    while(t--){        scanf("%d%d",&n,&m);        s.Solve(n,m);    }    return 0;}

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