Nearest Common Ancestors 【POJ - 1330】【LCA模板】

 POJ - 1330

一、Tarjan求LCA

//47ms
#include <iostream>
#include <cstdio>
#include <vector>
using namespace std;

inline int read()
{
    int x = 0, f = 1; char c = getchar();
    while(c < '0' || c > '9') { if(c == '-') f = -f; c = getchar(); }
    while(c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
    return x * f;
}

const int maxN = 10004;

int n;

struct EDGE{
    int adj, to;
    EDGE(int a = -1, int b = 0) : adj(a), to(b) {}
}edge[maxN << 1];
int head[maxN], cnt;

void add_edge(int u, int v)
{
    edge[cnt] = EDGE(head[u], v);
    head[u] = cnt ++ ;
}

int root[maxN], du[maxN];

int Find(int x) { return root[x] == x ? x : root[x] = Find(root[x]); }
bool Same(int x, int y) { return Find(x) == Find(y); }
void Merge(int x, int y) { root[Find(y)] = Find(x); }

int lca;
bool vis[maxN];
vector<int>ques[maxN];

void init()
{
    for(int i = 0; i <= n; ++ i )
    {
        head[i] = -1;
        root[i] = i;
        vis[i] = false;
        du[i] = 0;
        ques[i].clear();
    }
    cnt = lca = 0;
}

void Tarjan(int u, int fa)
{
    if(lca) return ;
    vis[u] = true;
    for(int i = head[u]; ~i; i = edge[i].adj)
    {
        int v = edge[i].to;
        Tarjan(v, u);
        if(!Same(u, v)) Merge(u, v);
    }
    if(!ques[u].empty())
    {
        int siz = ques[u].size();
        for(int i = 0; i < siz; ++ i)
        {
            int v = ques[u][i];
            if(vis[v]) lca = Find(v);
            return ;
        }
    }
}

int main()
{
    int TAT; TAT = read();
    while(TAT --)
    {
        n = read();
        init();
        for(int i = 0; i < n - 1; ++ i )
        {
            int u, v;
            u = read(); v = read();
            add_edge(u, v);
            ++ du[v];
        }
        int u, v; u = read(); v = read();
        ques[u].push_back(v);
        ques[v].push_back(u);
        for(int i = 1; i <= n; ++ i)
        {
            if(!du[i])
            {
                Tarjan(i, 0);
                printf("%d\n", lca);
                break;
            }
        }
    }
    return 0;
}

---

二、欧拉序+ST求LCA

这种写法POJ 交C ++ 会报错CE：原因是log2找不到头文件？？？我很迷……

//63ms
#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;

inline int read()
{
    int x = 0, f = 1; char c = getchar();
    while(c < '0' || c > '9') { if(c == '-') f = -f; c = getchar(); }
    while(c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
    return x * f;
}

const int maxN = 10004;
int n, root, du[maxN];

struct EDGE{
    int adj, to;
    EDGE(int a = -1, int b = 0) : adj(a), to(b) {}
}edge[maxN];
int head[maxN], cnt;

void add_edge(int u, int v)
{
    edge[cnt] = EDGE(head[u], v);
    head[u] = cnt ++ ;
}

int deep[maxN], first[maxN];
int _min[maxN << 1][20], id[maxN << 1][20];
int Euler[maxN << 1], tot;

void init()
{
    for(int i = 0; i <= n; ++ i )
    {
        head[i] = -1;
        deep[i] = 0;
        du[i] = 0;
    }
    cnt = tot = 0;
}

void dfs(int u, int fa)
{
    deep[u] = deep[fa] + 1;
    Euler[ ++ tot] = deep[u];
    _min[tot][0] = deep[u]; id[tot][0] = u;
    first[u] = tot;
    for(int i = head[u]; ~i; i = edge[i].adj)
    {
        if(edge[i].to == fa) continue;
        dfs(edge[i].to, u);
    }
    Euler[ ++ tot] = deep[fa];
    _min[tot][0] = deep[fa]; id[tot][0] = fa;
}

void ST_pre()
{
    dfs(root, 0);
    for(int j = 1; (1 << j) < tot; ++ j )
    {
        for(int i = 1; i + (1 << j - 1) < tot; ++ i )
        {
            if(_min[i][j - 1] >= _min[i + (1 << j - 1)][j - 1])
            {
                _min[i][j] = _min[i + (1 << j - 1)][j - 1];
                id[i][j] = id[i + (1 << j - 1)][j - 1];
            }
            else
            {
                _min[i][j] = _min[i][j - 1];
                id[i][j] = id[i][j - 1];
            }
        }
    }
}

int LCA(int u, int v)
{
    int l = min(first[u], first[v]);
    int r = max(first[u], first[v]);
    int k = log2(r - l + 1);
    if(_min[l][k] <= _min[r - (1 << k) + 1][k])
        return id[l][k];
    else
        return id[r - (1 << k) + 1][k];
}

int main()
{
    int TAT; TAT = read();
    while(TAT -- )
    {
        n = read();
        init();
        for(int i = 0; i < n - 1; ++ i )
        {
            int u, v; u = read(); v = read();
            add_edge(u, v);
            ++ du[v];
        }
        for(int i = 1; i <= n; ++ i )
            if(du[i] == 0) { root = i; break; }
        ST_pre();
        int u, v; u = read(); v = read();
        printf("%d\n", LCA(u, v));
    }
    return 0;
}

三、倍增求解LCA

//16ms
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;

inline int read()
{
    int x = 0, f = 1; char c = getchar();
    while( c < '0' || c > '9' ) { if(c == '-') f = -f; c = getchar(); }
    while(c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
    return x * f;
}

const int maxN = 10004;
int n, root, du[maxN];

struct EDGE{
    int adj, to;
    EDGE(int a = -1, int b = 0): adj(a), to(b) {}
}edge[maxN];
int head[maxN], cnt;

void init()
{
    for(int i = 0; i <= n; ++ i )
    {
        head[i] = -1;
        du[i] = 0;
    }
    cnt = 0;
}

void add_edge(int u, int v)
{
    edge[cnt] = EDGE(head[u], v);
    head[u] = cnt ++ ;
}

int deep[maxN], f[maxN][25];

void dfs(int u, int fa)
{
    deep[u] = deep[fa] + 1;
    f[u][0] = fa;
    for(int i = head[u]; ~i; i = edge[i].adj)
    {
        int v = edge[i].to;
        dfs(v, u);
    }
}

void pre()
{
    deep[root] = 0;
    dfs(root, 0);
    for(int j = 1; j <= 20; ++ j )
        for(int i = 1; i <= n; ++ i )
            f[i][j] = f[f[i][j - 1]][j - 1];
}

int LCA(int u, int v)
{
    if(deep[u] < deep[v]) swap(u, v);
    for(int i = 20; i >= 0; -- i )
        if(deep[f[u][i]] >= deep[v]) 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];
}


int main()
{
    int TAT; TAT = read();
    while(TAT -- )
    {
        n = read();
        init();
        for(int i = 0; i < n - 1; ++ i )
        {
            int u, v; u = read(); v = read();
            add_edge(u, v);
            ++ du[v];
        }
        for(int i = 1; i <= n; ++ i ) if(du[i] == 0) { root = i; break; }
        pre();
        int u, v; u = read(); v = read();
        printf("%d\n", LCA(u, v));
    }
    return 0;
}