【LCA最近公共祖先】 poj1470 Closest Common Ancestors

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本文讨论了一次编程过程中因将数组头节点的名称错误输入而导致的时间浪费问题，并介绍了如何通过tarjan算法进行离线操作来解决此类问题。文章详细解释了tarjan算法的实现过程，包括边的添加、查询的构建、深度优先搜索以及LCA（最近公共祖先）的查找。同时，文中还展示了如何通过tarjan算法优化节点间的连接关系，减少不必要的计算，提高程序效率。

昨晚写错了，把数组名head2写成了head，浪费了一个来小时。。。

tarjan离线搞，不言语：

#include <cstdio>
#include <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
using namespace std;

const int MAX = 1024;
struct edge {
	int from;
	int to;
	int next;
	edge(int _from, int _to, int _next) {
		from = _from;
		to = _to;
		next = _next;
	}
};
struct query {
	int u;
	int v;
	int id;
	int next;
	query(int _u, int _v, int _id, int _next) {
		u = _u;
		v = _v;
		id = _id;
		next = _next;
	}
};
vector<edge> G;
vector<query> my;
int head[MAX], head2[MAX];
int LCA[MAX*MAX];
int in[MAX]; //in degree
int father[MAX];
int n, m, root;

inline void add_edge(int a, int b) {
	G.push_back(edge(a, b, head[a]));
	head[a] = G.size() - 1;
}

inline void add_query(int a, int b, int id) {
	my.push_back(query(a, b, id, head2[a]));
	head2[a] = my.size() - 1;
}

inline int read() {
	char ch;
	while ((ch = getchar()) < '0' || ch > '9') {

	}
	int x = ch - '0';
	while ((ch = getchar()) >= '0' && ch <= '9') {
		x = (x << 3) + (x << 1) + ch - '0';
	}
	return x;
}

int find(int x) {
	return x == father[x] ? x : father[x] = find(father[x]);
}

void tarjan(int u) {
	father[u] = u;
	for (int j = head2[u]; ~j; j = my[j].next) {
		//printf("vis %d\n", my[j].v);
		if (~father[my[j].v]) {
			LCA[my[j].id] = find(my[j].v);
			//printf("LCA[%d] = %d\n", my[j].id, LCA[my[j].id]);
		}
	}
	for (int j = head[u]; ~j; j = G[j].next) {
		if (father[G[j].to] == -1) {
			tarjan(G[j].to);
			father[G[j].to] = u;
		}
	}
}

int main() {
	//freopen("1470.in", "r", stdin);
	while (~scanf(" %d", &n)) {
		memset(father, -1, sizeof(father));
		memset(head, -1, sizeof(head));
		memset(head2, -1, sizeof(head2));
		memset(in, 0, sizeof(in));
		G.clear();
		my.clear();
		
		int u, v;
		for (int i = 1; i <= n; ++i) {
			u = read();
			int c = read();
			while (c--) {
				v = read();
				add_edge(u, v);
				//add_edge(v, u);
				++in[v];
			}
		}
		
		m = read();
		for (int i = 1; i <= m; ++i) {
			u = read();
			v = read();
			add_query(u, v, i);
			add_query(v, u, i);
		}
		
		for (int i = 1; i <= n; ++i) {
			if (in[i] == 0) {
				root = i;
				break;
			}
		}

		tarjan(root);
		map<int, int> ans;
		for (int i = 1; i <= m; ++i) {
			ans[LCA[i]]++;
		}
		for (map<int, int>::iterator it = ans.begin(); it != ans.end(); ++it) {
			printf("%d:%d\n", it->first, it->second);
		}
		if (m) getchar();
	}
	return 0;
}