luogu3379 最近公共祖先（LCA） tarjan 倍增

最新推荐文章于 2024-12-06 22:51:15 发布

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最新推荐文章于 2024-12-06 22:51:15 发布

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本文介绍了使用Tarjan算法进行树形结构的连通性分析和倍增算法求最近公共祖先（LCA）。通过具体代码实现，展示了如何利用这两种算法解决实际问题。

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tarjan不多言

#include <iostream>
#include <cstdio>
using namespace std;
struct Edge{
    int too, nxt;
}edge[1000005];
struct Ques{
    int nxt, too, ran;
}ques[1000005];
int getint(){
    char ch=getchar();
    int re=0;
    while(ch<'0' || ch>'9')    ch = getchar();
    while(ch>='0' && ch<='9'){
        re = re*10 + ch - '0';
        ch = getchar();
    }
    return re;
}
int n, m, ecnt, qcnt, ehea[500005], qhea[500005], fa[500005], uu, vv;
int s, ans[500005];
bool vis[500005];
void add_edge(int fro, int too){
    edge[++ecnt].nxt = ehea[fro];
    edge[ecnt].too = too;
    ehea[fro] = ecnt;
}
void add_ques(int fro, int too, int ran){
    ques[++qcnt].nxt = qhea[fro];
    ques[qcnt].too = too;
    ques[qcnt].ran = ran;
    qhea[fro] = qcnt;
}
int myfind(int x){
    return fa[x]==x?x:fa[x]=myfind(fa[x]);
}
void tarjan(int u){
    vis[u] = true;
    for(int i=ehea[u]; i; i=edge[i].nxt){
        int t=edge[i].too;
        if(!vis[t]){
            tarjan(t);
            fa[t] = u;
        }
    }
    for(int i=qhea[u]; i; i=ques[i].nxt){
        int t=ques[i].too;
        if(vis[t])
            ans[ques[i].ran] = myfind(t);
    }
}
int main(){
    n = getint();
    m = getint();
    s = getint();
    for(int i=1; i<n; i++){
        uu = getint();
        vv = getint();
        add_edge(uu, vv);
        add_edge(vv, uu);
        fa[i] = i;
    }
    fa[n] = n;
    for(int i=1; i<=m; i++){
        uu = getint();
        vv = getint();
        add_ques(uu, vv, i);
        add_ques(vv, uu, i);
    }
    tarjan(s);
    for(int i=1; i<=m; i++)
        printf("%d\n", ans[i]);
    return 0;
}

倍增亦不多言

#include <iostream>
#include <cstdio>
using namespace std;
int n, m, s, grand[500005][22], deep[500005], hea[500005], cnt, uu, vv;
struct Edge{
    int too, nxt;
}edge[1000005];
int getint(){
    char ch=getchar();
    int re=0;
    while(ch<'0' || ch>'9') ch = getchar();
    while(ch>='0' && ch<='9'){
        re = re*10 + ch - '0';
        ch = getchar();
    }
    return re;
}
void add_edge(int fro, int too){
    edge[++cnt].nxt = hea[fro];
    edge[cnt].too = too;
    hea[fro] = cnt;
}
void builddepth(int u){
    for(int i=hea[u]; i; i=edge[i].nxt){
        int t=edge[i].too;
        if(!deep[t]){
            deep[t] = deep[u] + 1;
            grand[t][0] = u;
            builddepth(t);
        }
    }
}
void init(){
    deep[s] = 1;
    builddepth(s);
    for(int i=1; i<=19; i++)
        for(int j=1; j<=n; j++)
            grand[j][i] = grand[grand[j][i-1]][i-1];
}
int getlca(int x, int y){
    if(deep[x]<deep[y]){
        x ^= y;
        y ^= x;
        x ^= y;
    }
    for(int i=19; i>=0; i--)
        if(deep[grand[x][i]]>=deep[y])
            x = grand[x][i];
    if(x==y)    return x;
    for(int i=19; i>=0; i--)
        if(grand[x][i]!=grand[y][i]){
            x = grand[x][i];
            y = grand[y][i];
        }
    return grand[x][0];
}
int main(){
    n = getint();
    m = getint();
    s = getint();
    for(int i=1; i<n; i++){
        uu = getint();
        vv = getint();
        add_edge(uu, vv);
        add_edge(vv, uu);
    }
    init();
    for(int i=1; i<=m; i++){
        uu = getint();
        vv = getint();
        printf("%d\n", getlca(uu, vv));
    }
    return 0;
}