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  • codeforces 570 D Tree Requests

    题意:给出一棵树。每一个结点都有一个字母,有非常多次询问,每次询问。以结点v为根的子树中高度为h的后代是否可以经过调整变成一个回文串。


    做法:
    推断能否够构成一个回文串的话,仅仅须要知道是否有大于一个的奇数数目的字母就可以。为了非常快的訪问到一个区间。记录前缀和就可以。为了省内存,状压奇偶就可以。


    为了非常快的找到以结点v为根的子树中高度为h的后代,须要dfs整棵树。然后记录每一个结点第一次訪问它的时间戳以及离开它的时间戳,就能够二分出来。




    为了省内存,能够离线处理询问。

    #include<map>
    #include<string>
    #include<cstring>
    #include<cstdio>
    #include<cstdlib>
    #include<cmath>
    #include<queue>
    #include<vector>
    #include<iostream>
    #include<algorithm>
    #include<bitset>
    #include<climits>
    #include<list>
    #include<iomanip>
    #include<stack>
    #include<set>
    #include<bitset>
    using namespace std;
    int head[500010],tail;
    struct Edge
    {
    	int to,next;
    }edge[500010];
    void add(int from,int to)
    {
    	edge[tail].to=to;
    	edge[tail].next=head[from];
    	head[from]=tail++;
    }
    int in[500010],ot[500010];
    int cnt;
    struct node
    {
    	int id,tm;
    	node(){}
    	node(int id,int tm)
    	{
    		this->id=id;
    		this->tm=tm;
    	}
    	bool operator <(node a)const
    	{
    		return tm<a.tm;
    	}
    };
    vector<node>bx[500010];
    void dfs(int from,int step)
    {
    	in[from]=++cnt;
    	bx[step].push_back(node(from,cnt));
    	for(int i=head[from];i!=-1;i=edge[i].next)
    	{
    		int to=edge[i].to;
    		dfs(to,step+1);
    	}
    	ot[from]=++cnt;
    }
    bool num[500010][26];
    char s[500010];
    void create(int h)
    {
    	int n=bx[h].size();
    	for(int i=0;i<n;i++)
    	{
    		if(i==0)
    		{
    			for(int j=0;j<26;j++)
    				num[i][j]=0;
    		}
    		else
    		{
    			for(int j=0;j<26;j++)
    				num[i][j]=num[i-1][j];
    		}
    		int id=bx[h][i].id-1;
    		num[i][s[id]-'a']^=1;
    	}
    }
    bool work(int v,int h)
    {
    	if(bx[h].empty())
    		return 1;
    	int l=upper_bound(bx[h].begin(),bx[h].end(),node(-1,in[v]))-bx[h].begin();
    	if(l==bx[h].size()||bx[h][l].tm>ot[v])
    		return 1;
    	int r=lower_bound(bx[h].begin(),bx[h].end(),node(-1,ot[v]))-bx[h].begin();
    	l--;r--;
    	bool flag=0;
    	for(int i=0;i<26;i++)
    	{
    		bool t;
    		if(l<0)
    			t=num[r][i];
    		else
    			t=(num[l][i]^num[r][i]);
    		if(t&1)
    		{
    			if(flag)
    				return 0;
    			flag=1;
    		}
    	}
    	return 1;
    }
    struct Q
    {
    	int id,v,h;
    	bool operator <(Q a)const
    	{
    		return h<a.h;
    	}
    }q[500010];
    bool ans[500010];
    int main()
    {
    	int n,m;
    	scanf("%d%d",&n,&m);
    	memset(head,-1,sizeof(head));
    	for(int i=2;i<=n;i++)
    	{
    		int p;
    		scanf("%d",&p);
    		add(p,i);
    	}
    	scanf("%s",s);
    	dfs(1,1);
    	for(int i=0;i<m;i++)
    	{
    		scanf("%d%d",&q[i].v,&q[i].h);
    		q[i].id=i;
    	}
    	sort(q,q+m);
    	int p=-1;
    	for(int i=0;i<m;i++)
    	{
    		if(q[i].h!=p)
    		{
    			p=q[i].h;
    			create(p);
    		}
    		ans[q[i].id]=work(q[i].v,q[i].h);
    	}
    	for(int i=0;i<m;i++)
    		if(ans[i])
    			puts("Yes");
    		else
    			puts("No");
    }


    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 then - 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 the i-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".




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  • 原文地址:https://www.cnblogs.com/clnchanpin/p/6958452.html
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