luoguP3379 【模板】最近公共祖先（LCA）

思路

可以用倍增法去解决问题

代码

#include <bits/stdc++.h>
using namespace std;
int n, m, root, parent[30][600005], dep[600005], head[1000005];
int log_v;
int cnt = 0;
struct e {
	int to, next;
} edge[1000005];
int getint() {
	char ch = '*';
	while (!isdigit(ch = getchar()));
	int num = ch - '0';
	while (isdigit(ch = getchar()))num = num * 10 + ch - '0';
	return num;
}
void add (int x, int y) {
	cnt++;
	edge[cnt].to = y;
	edge[cnt].next = head[x];
	head[x] = cnt;
}
void dfs(int node, int father, int d) {
	parent[0][node] = father;
	dep[node] = d;
	for (int i = head[node]; i != -1; i = edge[i].next) {
		if (edge[i].to != father) dfs(edge[i].to, node, d + 1);
	}
}
void init() {
	dfs(root, -1, 0);
	for (int k = 0; k < log_v - 1; k++) {
		for (int i = 1; i <= n; i++) {
			if (parent[k][i] < 0) parent[k + 1][i] = -1;
			else parent[k + 1][i] = parent[k][parent[k][i]];
		}
	}
}
int LCA(int x, int y) {
	if (dep[x] > dep[y]) swap(x, y);
	for (int i = 0; i < log_v; i++) {
		if (((dep[y] - dep[x]) >> i) & 1) y = parent[i][y];
	}
	if (x == y) return x;
	for (int i = log_v; i >= 0; i--) {
		if (parent[i][x] != parent[i][y]) {
			x = parent[i][x];
			y = parent[i][y];
		}
	}
	return parent[0][x];
}
int main() {
	memset(head, -1, sizeof(head));
	n = getint();
	m = getint();
	root = getint();
	log_v = int(log10(n) / log10(2)) + 1;
	for (int i = 1; i <= n - 1; i++) {
		int x, y;
		x = getint();
		y = getint();
		add(x, y);
		add(y, x);
	}
	init();
	for (int i = 1; i <= m; i++) {
		int x, y;
		x = getint();
		y = getint();
		printf("%d\n", LCA(x, y));
	}
	return 0;
}