图论--LCA--树上倍增法（在线）

拒绝无脑抄袭，Ctrl+C可以，先看明白

本文链接： https://blog.csdn.net/weixin_43627118/article/details/102702410

/*
 * LCA在线算法(倍增法) 
 */
const int MAXN = 10010;
const int DEG = 20;
 
struct Edge
{
    int to, next;
} edge[MAXN * 2];
 
int head[MAXN], tot;
void addedge(int u, int v)
{
    edge[tot].to = v;
    edge[tot].next = head[u];
    head[u] = tot++;
}
 
void init()
{
    tot = 0;
    memset(head, -1, sizeof(head));
}
 
int fa[MAXN][DEG];      //  fa[i][j]表示结点i的第2^j个祖先
int deg[MAXN];          //  深度数组
 
void BFS(int root)
{
    queue<int>que;
    deg[root] = 0;
    fa[root][0] = root;
    que.push(root);
    while (!que.empty())
    {
        int tmp = que.front();
        que.pop();
        for (int i = 1; i < DEG; i++)
        {
            fa[tmp][i] = fa[fa[tmp][i - 1]][i - 1];
        }
        for (int i = head[tmp]; i != -1; i = edge[i].next)
        {
            int v = edge[i].to;
            if (v == fa[tmp][0])
            {
                continue;
            }
            deg[v] = deg[tmp] + 1;
            fa[v][0] = tmp;
            que.push(v);
        }
    }
}
 
int LCA(int u, int v)
{
    if (deg[u] > deg[v])
    {
        swap(u, v);
    }
    int hu = deg[u], hv = deg[v];
    int tu = u, tv = v;
    for (int det = hv-hu, i = 0; det ; det >>= 1, i++)
    {
        if (det & 1)
        {
            tv = fa[tv][i];
        }
    }
    if (tu == tv)
    {
        return tu;
    }
    for (int i = DEG - 1; i >= 0; i--)
    {
        if (fa[tu][i] == fa[tv][i])
        {
            continue;
        }
        tu = fa[tu][i];
        tv = fa[tv][i];
    }
    return fa[tu][0];
}
 
bool flag[MAXN];
 
int main()
{
    int T;
    int n;
    int u, v;
    scanf("%d", &T);
 
    while(T--)
    {
        scanf("%d", &n);
        init();
        memset(flag, false, sizeof(flag));
        for (int i = 1; i < n; i++)
        {
            scanf("%d%d", &u, &v);
            addedge(u, v);
            addedge(v, u);
            flag[v] = true;
        }
        int root;
        for (int i = 1; i <= n; i++)
        {
            if (!flag[i])
            {
                root = i;
                break;
            }
        }
        BFS(root);
        scanf("%d%d", &u, &v);
        printf("%d\n", LCA(u, v));
    }
    return 0;
}