Codeforces 1006E Military Problem

In this problem you will have to help Berland army with organizing their command delivery system.

There are n officers in Berland army. The first officer is the commander of the army, and he does not have any superiors. Every other officer has exactly one direct superior. If officer a is the direct superior of officer b, then we also can say that officer b is a direct subordinate of officer a Officer x is considered to be a subordinate (direct or indirect) of officer y

if one of the following conditions holds:

• officer y is the direct superior of officer x
• the direct superior of officer x is a subordinate of officer y
• For example, on the picture below the subordinates of the officer 3 are: 5,6,7,8,9.

  The structure of Berland army is organized in such a way that every officer, except for the commander, is a subordinate of the commander of the army.

  Formally, let's represent Berland army as a tree consisting of n vertices, in which vertex u corresponds to officer u. The parent of vertex u corresponds to the direct superior of officer u. The root (which has index 1) corresponds to the commander of the army.

  Berland War Ministry has ordered you to give answers on q queries, the i-th query is given as (ui,ki), where ui is some officer, and ki is a positive integer.

  To process the i-th query imagine how a command from ui spreads to the subordinates of ui. Typical DFS (depth first search) algorithm is used here.
• Suppose the current officer is a and he spreads a command. Officer a chooses b — one of his direct subordinates (i.e. a child in the tree) who has not received this command yet. If there are many such direct subordinates, then a chooses the one having minimal index. Officer a gives a command to officer b. Afterwards, b uses exactly the same algorithm to spread the command to its subtree. After b finishes spreading the command, officer a chooses the next direct subordinate again (using the same strategy). When officer a cannot choose any direct subordinate who still hasn't received this command, officer a finishes spreading the command.

  finishes spreading the command.

  Let's look at the following example:

  If officer 1 spreads a command, officers receive it in the following order: [1,2,3,5,6,8,7,9,4].

  If officer 3 spreads a command, officers receive it in the following order: [3,5,6,8,7,9].

  If officer 7 spreads a command, officers receive it in the following order: [7,9].

  If officer 9 spreads a command, officers receive it in the following order: [9] .

• To answer the i-th query (ui,ki), construct a sequence which describes the order in which officers will receive the command if the ui-th officer spreads it. Return the ki-th element of the constructed list or -1 if there are fewer than ki elements in it.

  You should process queries independently. A query doesn't affect the following queries.

  Input

  The first line of the input contains two integers n and q (2≤n≤2⋅105,1≤q≤2⋅105 ) — the number of officers in Berland army and the number of queries.

  The second line of the input contains n−1 integers p2,p3,…,pn (1≤pi<i), where pi is the index of the direct superior of the officer having the index i. The commander has index 1

  and doesn't have any superiors.The next q lines describe the queries. The i-th query is given as a pair (ui,ki) (1≤ui,ki≤n), where ui is the index of the officer which starts spreading a command, and ki is the index of the required officer in the command spreading sequence.

  Output

  Print q numbers, where the i-th number is the officer at the position ki in the list which describes the order in which officers will receive the command if it starts spreading from officer ui. Print "-1" if the number of officers which receive the command is less than ki.

  You should process queries independently. They do not affect each other.

  Example

  Input

  9 6
  1 1 1 3 5 3 5 7
  3 1
  1 5
  3 4
  7 3
  1 8
  1 9
  

  Output

  3
  6
  8
  -1
  9
  4

題意：給你每一個官員的直系上屬，每一個官員發出一個命令的時候，他會先對他的直系下屬裏編號最小的發出命令，然後他的直系下屬也執行這樣的操作完後，他再對下一個直系下屬發出命令。然後讓你求從第u個官員發出，第k個（包括自己）是哪個官員。

解題思路：這個題意給你表述的就是你dfs下的順序，那麼你就dfs後給每一個節點表一個號，並且把每一個號對應的節點給統計好，這樣方便查詢答案。然後我們對每一次查詢只需要看在這個序列中有沒有第k個官員。

 

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<vector>
#include<map>
using namespace std;
const int maxn=2e5+10;
vector<int> ve[maxn];
map<int,int> mp;
int n,m,l[maxn],r[maxn],cnt;
void dfs(int u){
	l[u]=cnt++;
	mp[cnt-1]=u;
	for(int i=0;i<ve[u].size();i++){
		int v=ve[u][i];
		dfs(v);
	}
	r[u]=cnt;
}
int main(){
	int i,j;
	scanf("%d%d",&n,&m);
	mp.clear();
	for(i=1;i<=n;i++) ve[i].clear();
	int u,v;
	for(i=2;i<=n;i++){
		scanf("%d",&u);
		ve[u].push_back(i);
	}
	cnt=1;
	dfs(1);
	while(m--){
		scanf("%d%d",&u,&v);
		if(r[u]-l[u]<v){
			printf("-1\n");
		}
		else{
			int t=l[u]+v-1;
			printf("%d\n",mp[t]);
		}
	}
	return 0;
}