codeforces 570 D. Tree Requests 树状数组+dfs搜索序

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链接:http://codeforces.com/problemset/problem/570/D


D. Tree Requests
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Roman planted a tree consisting of n vertices. Each vertex contains a lowercase English letter. Vertex 1 is the root of the tree, each of the n?-?1 remaining vertices has a parent in the tree. Vertex is connected with its parent by an edge. The parent of vertex i is vertex pi, the parent index is always less than the index of the vertex (i.e., pi?<?i).

The depth of the vertex is the number of nodes on the path from the root to v along the edges. In particular, the depth of the root is equal to 1.

We say that vertex u is in the subtree of vertex v, if we can get from u to v, moving from the vertex to the parent. In particular, vertex v is in its subtree.

Roma gives you m queries, the i-th of which consists of two numbers vihi. Let‘s consider the vertices in the subtree vi located at depthhi. Determine whether you can use the letters written at these vertices to make a string that is a palindrome. The letters that are written in the vertexes, can be rearranged in any order to make a palindrome, but all letters should be used.

Input

The first line contains two integers nm (1?≤?n,?m?≤?500?000) — the number of nodes in the tree and queries, respectively.

The following line contains n?-?1 integers p2,?p3,?...,?pn — the parents of vertices from the second to the n-th (1?≤?pi?<?i).

The next line contains n lowercase English letters, the i-th of these letters is written on vertex i.

Next m lines describe the queries, the i-th line contains two numbers vihi (1?≤?vi,?hi?≤?n) — the vertex and the depth that appear in thei-th query.

Output

Print m lines. In the i-th line print "Yes" (without the quotes), if in the i-th query you can make a palindrome from the letters written on the vertices, otherwise print "No" (without the quotes).

Sample test(s)
input
6 5
1 1 1 3 3
zacccd
1 1
3 3
4 1
6 1
1 2
output
Yes
No
Yes
Yes
Yes
Note

String s is a palindrome if reads the same from left to right and from right to left. In particular, an empty string is a palindrome.

Clarification for the sample test.

In the first query there exists only a vertex 1 satisfying all the conditions, we can form a palindrome "z".

In the second query vertices 5 and 6 satisfy condititions, they contain letters "с" and "d" respectively. It is impossible to form a palindrome of them.

In the third query there exist no vertices at depth 1 and in subtree of 4. We may form an empty palindrome.

In the fourth query there exist no vertices in subtree of 6 at depth 1. We may form an empty palindrome.

In the fifth query there vertices 2, 3 and 4 satisfying all conditions above, they contain letters "a", "c" and "c". We may form a palindrome "cac".



题意:

告诉你一颗树的父子关系,1节点为根。再告诉你每一个点上的字母。

问 v节点 子树(包含v节点)在第h行的全部节点的字母是否能组成回文串。


做法:

先用dfs 搜索 把全部节点标个左标号和右标号。 这样标号以后。每一个节点 用左标号 当自己 新的标号。 然后  子树全部节点 的新标号 肯定在 子树根节点的 左右标号之间。

标号之后分层来做。

每层  对每一个字母分别做统计。

把该层全部节点 的 左标号 在树状数组中+1. 然后对于该层的全部询问 做 树状数组统计。(sum(rit[v])-sum(lft[v]-1))。   

假设是奇数 说明这个 字母在查询的区间内 有奇数个。

每一个查询  最多有一个奇数个的字母。否则不能构成回文串


#include <iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<vector>
#include<math.h>

using namespace std;
const int N = 500100;

int f[N];
vector<int> son[N];
int id;
int lft[N],rit[N];
int deps[N]; 
int ans[N];
char str[N];
vector<int> G[N];//深度
vector<pair<int,int> > Q[N];
void dfs(int nw,int dep)
{
	lft[nw]=id++;
	deps[nw]=dep;
	G[dep].push_back(nw);
	for(int i=0;i<son[nw].size();i++)
	{
		int to=son[nw][i];
		dfs(to,dep+1);
	}
	rit[nw]=id++;
}

int bit[2*N];

int lowbit(int x)
{
	return x&(-x);
}

void add(int wei,int x)
{

	while(wei<=id)
	{
		bit[wei]+=x;
		wei+=lowbit(wei);
	}
}

int sum(int wei)
{
	if(wei==0)
		return 0;
	int sum=0;
	while(wei>0)
	{
		sum+=bit[wei];
		wei-=lowbit(wei);
	}
	return sum;
}

int main()
{
	int n,m;
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		for(int i=2;i<=n;i++)
		{
			scanf("%d",f+i);
			son[f[i]].push_back(i);
		}
		scanf("%s",str+1);
		id=1;
		dfs(1,1);
		int dep=1;
		for(int i=1;i<=m;i++)
		{
			int vv,hh;
			scanf("%d%d",&vv,&hh);
			dep=max(hh,dep);
			Q[hh].push_back(make_pair<int,int>(vv,i));
		}

		for(int i=1;i<=dep;i++)
		{
			for(int j=0;j<26;j++)
			{
				if(j==25)
					int kkk=1;
				for(int k=0;k<G[i].size();k++)//每一个节点
				{
					if(str[G[i][k]]-'a'==j)
						add(lft[G[i][k]],1);
				}
				
				for(int k=0;k<Q[i].size();k++)
				{
					int v=Q[i][k].first;
					int ii=Q[i][k].second;
					if((sum(rit[v])-sum(lft[v]-1))&1) ans[ii]++;
				}

				 
				for(int k=0;k<G[i].size();k++)//每一个节点
				{
					if(str[G[i][k]]-'a'==j)
						add(lft[G[i][k]],-1);
				}
				// printf("jj %d \n",j);
			}

			//printf("ii %d \n",i);
		}

		for(int i=1;i<=m;i++)
		{
			if(ans[i]<=1)
				printf("Yes\n");
			else
				printf("No\n");
		}

	}
	return 0;
}



 


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