SPOJ10707 COT2-Count on a tree II

COT2 - Count on a tree II

中文题意

离线询问一颗树上路径(u,v)中经过所有点的权值的种类数。

题解

树上莫队。即在树的欧拉序列上进行莫队。同一个点加第一次时增加，第二次时减去增加的影响。

错误记录

用了tarjan LCA，并偷懒将询问和莫队都用一个node表示。意味着每一个询问都要开两个node，写莫队排序sort的时候注意结构体数组长度！莫队排序后两个相同的node不一定相邻，因为可能出现node[i].l/size和node[j].l/size相等，但是node[i].l和node[j].l并不相等的情况。卡了半天。

题目信息不全，权值据说是1e9，别忘了离散化

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdlib>
#include <iostream>
#include <cmath>

void swap(int &a, int &b){int tmp = a;a = b, b = tmp;}
int max(int a, int b){return a > b ? a : b;}
int min(int a, int b){return a < b ? a : b;}
void read(int &x)
{
	x = 0;char ch = getchar(), c = ch;
	while(ch < '0' || ch > '9') c = ch, ch = getchar();
	while(ch <= '9' && ch >= '0') x = x * 10 + ch - '0', ch = getchar();
	if(c == '-') x = -x;
}

const int INF = 0x3f3f3f3f;
const int MAXN = 1000000;
const int MAXM = 1000000;

struct Edge
{
	int u, v, nxt;
	Edge(int _u, int _v, int _nxt){u = _u, v = _v, nxt = _nxt;}
	Edge(){}
}edge[MAXN << 1];
int head[MAXN], cnt;
void insert(int a, int b)
{
	edge[++ cnt] = Edge(a, b, head[a]), head[a] = cnt;
	edge[++ cnt] = Edge(b, a, head[b]), head[b] = cnt;
}

int tong[MAXN], val[MAXN], num[MAXN], id[MAXN];
int fa[MAXN], seq[MAXN], st[MAXN], et[MAXN], t, sum;
int n, m;

void dfs(int x)
{
	seq[++ t] = x;
	st[x] = t;
	for(int pos = head[x];pos;pos = edge[pos].nxt)
	{
		int v = edge[pos].v;
		if(v == fa[x]) continue;
		fa[v] = x;
		dfs(v);
	}
	seq[++ t] = x;
	et[x] = t;
}

int cmp(int a, int b)
{
	return val[a] < val[b];
}

struct Node
{
	int l, r, id, lca, nxt, u, v, need_lca;
	Node(int _u, int _v, int _id, int _nxt){u = _u, v = _v, id = _id, nxt = _nxt;}
	Node(){}
	void init()
	{
		if(lca == u)
			l = st[lca], r = st[v], need_lca = 0;
		else if(lca == v)
			l = st[lca], r = st[u], need_lca = 0;
		else
		{
			if(st[u] < st[v]) l = et[u], r = st[v];
			else l = et[v], r = st[u];
			need_lca = 1;
		}
		return ;
	}
}node[MAXM];
int head_node[MAXM], cnt_node = 1;

void insert_node(int u, int v, int id)
{
	node[++ cnt_node] = Node(u, v, id, head_node[u]), head_node[u] = cnt_node;
	node[++ cnt_node] = Node(v, u, id, head_node[v]), head_node[v] = cnt_node;
}

int ans[MAXM];

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

int vis[MAXN];

void dfs_tarjan(int x)
{
	vis[x] = 1;
	for(int pos = head[x];pos;pos = edge[pos].nxt)
	{
		int v = edge[pos].v;
		if(vis[v]) continue;
		dfs_tarjan(v);
		int f1 = find(x), f2 = find(v);
		fa[f2] = f1;
	}
	for(int pos = head_node[x];pos;pos = node[pos].nxt)
	{
		int v = node[pos].v;
		if(vis[v])
			node[pos].lca = node[pos ^ 1].lca = find(v);
	}
}

void tarjan_lca()
{
	for(int i = 1;i <= n;++ i) fa[i] = i;
	dfs_tarjan(1);
}

int size;

int cmp2(Node& a, Node& b)
{
	return a.l/size == b.l/size ? a.r < b.r : a.l/size < b.l/size;
}

int w[MAXN];

void add(int x)
{
	if(w[x] == 0) tong[val[x]] += 1;
	else if(w[x] == 1) tong[val[x]] -= 1;

	if(tong[val[x]] == 1 && w[x] == 0) ++ sum;
	if(tong[val[x]] == 0 && w[x] == 1) -- sum; 

	++ w[x];
}

void del(int x)
{
	if(w[x] == 1) tong[val[x]] -= 1;
	else if(w[x] == 2) tong[val[x]] += 1;

	if(tong[val[x]] == 1 && w[x] == 2) ++ sum;
	if(tong[val[x]] == 0 && w[x] == 1) -- sum;

	-- w[x];
}

bool is_cal[MAXM << 1];

int main()
{
	read(n), read(m);
	for(int i = 1;i <= n;++ i) read(val[i]), id[i] = i;
	for(int i = 1;i < n;++ i)
	{
		int tmp1, tmp2;
		read(tmp1), read(tmp2);
		insert(tmp1, tmp2);
	}
	std::sort(id + 1, id + 1 + n, cmp);

	for(int i = 1, j = 1;i <= n;)
	{
		num[j] = val[id[i]];
		while(val[id[i]] == num[j]) val[id[i]] = j, ++ i;
		++ j;
	}

	dfs(1);

	for(int i = 1;i <= m;++ i)
	{
		int tmp1, tmp2;
		read(tmp1), read(tmp2);
		insert_node(tmp1, tmp2, i);
	}

	tarjan_lca();

	for(int i = 2;i <= cnt_node;++ i)
		node[i].init();

	size = sqrt(n);
	if(size == 0) size = 1;
	std::sort(node + 2, node + 1 + cnt_node, cmp2);

	int l = 1, r = 1;
	add(seq[1]);
	for(int i = 2;i <= cnt_node;++ i)
	{
		if(is_cal[node[i].id]) continue;
		is_cal[node[i].id] = 1;
		while(l < node[i].l) del(seq[l]), ++ l;
		while(l > node[i].l) -- l, add(seq[l]);
		while(r < node[i].r) ++ r, add(seq[r]);
		while(r > node[i].r) del(seq[r]), -- r;

		if(node[i].need_lca) add(node[i].lca);
		ans[node[i].id] = sum;
		if(node[i].need_lca) del(node[i].lca);
	}
	for(int i = 1;i <= m;++ i)
		printf("%d\n", ans[i]);

	return 0;
}