P3379 【模板】最近公共祖先（LCA，树链剖分）_p3379 【模板】最近公共祖先(lca)树链剖分-优快云博客

本文详细介绍了一种求解最近公共祖先(LCA)问题的有效算法，并提供了完整的C++代码实现。通过预处理重链剖分，该算法能在O(log N)的时间复杂度内找到任意两点的最近公共祖先。

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核心函数

int lca(int u, int v)
{
    while (top[u] != top[v])//如果u,v在不同的重链，向上跳
    {
        if (dep[top[u]] < dep[top[v]])
            swap(u, v);
        u = fa[top[u]];
    }
    //u,v在同一条链上了（重链没有分叉&&此时的u,v不是最开始的u,v了）
    if (dep[u] < dep[v])
        return u;
    else
        return v;
}

代码

#include <bits/stdc++.h>

using namespace std;
//-----pre_def----
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> PII;
typedef pair<double, double> PDD;
#define fir(i, a, b) for (int i = (a); i <= (b); i++)
#define rif(i, a, b) for (int i = (a); i >= (b); i--)
#define endl '\n'
#define init_h memset(h, -1, sizeof h), idx = 0;
#define lowbit(x) x &(-x)

//---------------
const int N = 5e5 + 10;
int n, m, root;
int h[N], e[N << 1], ne[N << 1], idx;
int top[N], fa[N], sz[N], son[N], dep[N];
void add(int a, int b)
{
    e[idx] = b;
    ne[idx] = h[a];
    h[a] = idx++;
}
void dfs1(int u, int father, int depth)
{
    dep[u] = depth, fa[u] = father, sz[u] = 1;
    for (int i = h[u]; ~i; i = ne[i])
    {
        int t = e[i];
        if (t == father)
            continue;
        dfs1(t, u, depth + 1);
        sz[u] += sz[t];
        if (son[u] == 0 || sz[son[u]] < sz[t])
        {
            son[u] = t;
        }
    }
}
void dfs2(int u, int v)
{
    top[u] = v;
    if (son[u] == 0)
        return;
    dfs2(son[u], v);
    for (int i = h[u]; ~i; i = ne[i])
    {
        int t = e[i];
        if(t==fa[u]||t==son[u]) continue;
        dfs2(t,t);
    }
}

int lca(int u, int v)
{
    while (top[u] != top[v])
    {
        if (dep[top[u]] < dep[top[v]])
            swap(u, v);
        u = fa[top[u]];
    }
    
    if (dep[u] < dep[v])
        return u;
    else
        return v;
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
    int StartTime = clock();
#endif
    scanf("%d%d%d", &n, &m, &root);
    init_h;
    fir(i, 1, n - 1)
    {
        int a, b;
        scanf("%d%d", &a, &b);
        add(a, b);
        add(b, a);
    }
    dfs1(root, -1, 1);
    dfs2(root,root);
    while(m--)
    {
        int a,b;
        scanf("%d%d",&a,&b);
        printf("%d\n",lca(a,b));
    }
#ifndef ONLINE_JUDGE
    printf("Run_Time = %d ms\n", clock() - StartTime);
#endif
    return 0;
}