[ NOIP ][ LCA ] 倍增算法求最近公共祖先（LCA）

核心：

　　pre[i][j] 为节点 i 向上2的j次方处的祖先。

　　pre[i][j] = pre[pre[i][j-1]][j-1]

#include <bits\stdc++.h>
const int maxn = 10000 + 10;
using namespace std;
int pre[maxn][50], n, root, dis[maxn], dep[maxn];
vector<int> v[maxn];
void dfs(int p) {
	vector<int>::iterator it;
	for(it = v[p].begin(); it != v[p].end(); it++) {
		int s = *it;
		dep[s] = dep[p] + 1;
		dis[s] = dis[p] + 1;
		dfs(s);
	}
}
void init() {
	for(int j = 1; (1 << j) <= n; j++) 
		for(int i = 1; i <= n; i++) pre[i][j] = pre[pre[i][j-1]][j-1];
}
void add(int a, int b) {
	v[a].push_back(b);
	pre[b][0] = a;
}
int lca(int a, int b) {
	if(dep[a] > dep[b]) swap(a, b);
	int m = dep[b] - dep[a];
	for(int i = 0; (1 << i) <= m; i++) {
		if(m & (1 << i)) b = pre[b][i];
	}
	if(a != b) {
		for(int i = (int)log2(n); i >= 0; i--) {
			if(pre[a][i] != pre[b][i]) {
				a = pre[a][i];
				b = pre[b][i];
			}
		}
		a = pre[a][0];
	}
	return a;
}
int main() {
	cin >> n >> root;
	for(int i = 1; i < n; i++) {
		int a, b;
		cin >> a >> b;
		add(a, b);
	}
	init();
	dfs(root);
	cout << "LCA is located on node : " << lca(16, 9) << endl;
	system("pause");
	return 0;
}