给定一棵具有N个节点以及两个整数K和V的树。任务是在顶点V的DFS遍历中找到第K个节点。
考虑下面的树：
DFS of node number 1 is [1, 2, 3, 5, 6, 8, 7, 9, 4].
DFS of node number 3 is [3, 5, 6, 8, 7, 9]
DFS of node number 7 is [7, 9]
DFS of node number 9 is [9].
如果顶点V的DFS中的数字小于K，则打印“ -1”。
例子：
Input : Tree: Shown in above image, V = 3, K = 4
Output : 8
Input : Tree: Shown in above image, V = 7, K = 3
Output : -1方法：让我们构造一个向量p ：存储从顶点1开始的完整树的DFS遍历。令tin v为顶点p在向量p中的位置(向量p的大小，在此时刻，我们从顶点调用DFS的大小) V)和tout v是离开顶点V的子树后被推到向量的第一个顶点的位置(当我们从顶点V从DFS返回时，向量p的大小)。显然，顶点V的子树位于区间[tin v ，tout v )中。
因此，要在节点V的子树的DFS中找到第K个节点，我们将必须在间隔[tin v ，tout v )中返回第K个节点。
下面是上述方法的实现：
C++
// C++ program to find the Kth node in the
// DFS traversal of the subtree of given
// vertex V in a Tree
#include
using namespace std;
#define N 100005
// To store nodes
int n;
vector tree[N];
// To store the current index of vertex in DFS
int currentIdx;
// To store the starting index and ending
// index of vertex in the DFS traversal array
vector startIdx, endIdx;
// To store the DFS of vertex 1
vector p;
// Function to add edge between two nodes
void Add_edge(int u, int v)
{
tree[u].push_back(v);
tree[v].push_back(u);
}
// Initialize the vectors
void intisalise()
{
startIdx.resize(n);
endIdx.resize(n);
p.resize(n);
}
// Function to perform DFS of a vertex
// 1. stores the DFS of the vertex 1 in vector p,
// 2. store the start index of DFS of every vertex
// 3. store the end index of DFS of every vertex
void Dfs(int ch, int par)
{
p[currentIdx] = ch;
// store staring index of node ch
startIdx[ch] = currentIdx++;
for (auto c : tree[ch]) {
if (c != par)
Dfs(c, ch);
}
// store ending index
endIdx[ch] = currentIdx - 1;
}
// Function to find the Kth node in DFS of vertex V
int findNode(int v, int k)
{
k += startIdx[v] - 1;
// check if kth number exits or not
if (k <= endIdx[v])
return p[k];
return -1;
}
// Driver code
int main()
{
// number of nodes
n = 9;
// add edges
Add_edge(1, 2);
Add_edge(1, 3);
Add_edge(1, 4);
Add_edge(3, 5);
Add_edge(3, 7);
Add_edge(5, 6);
Add_edge(5, 8);
Add_edge(7, 9);
intisalise();
// store DFS of 1st node
Dfs(1, 0);
int v = 3, k = 4;
cout << findNode(v, k);
return 0;
} Java
// Java program to find the Kth node in the
// DFS traversal of the subtree of given
// vertex V in a Tree
import java.util.*;
class GFG{
static int N = 100005;
// To store nodes
static int n;
static ArrayList<
ArrayList> tree = new ArrayList<>();
// To store the current index of vertex in DFS
static int currentIdx;
// To store the starting index and ending
// index of vertex in the DFS traversal array
static int[] startIdx;
static int[] endIdx;
// To store the DFS of vertex 1
static int[] p;
// Function to add edge between two nodes
static void Add_edge(int u, int v)
{
tree.get(u).add(v);
tree.get(v).add(u);
}
// Initialize the vectors
static void intisalise()
{
startIdx = new int[n + 1];
endIdx = new int[n + 1];
p = new int[n + 1];
}
// Function to perform DFS of a vertex
// 1. stores the DFS of the vertex 1 in vector p,
// 2. store the start index of DFS of every vertex
// 3. store the end index of DFS of every vertex
static void Dfs(int ch, int par)
{
p[currentIdx] = ch;
// store staring index of node ch
startIdx[ch] = currentIdx++;
for(int c : tree.get(ch))
{
if (c != par)
Dfs(c, ch);
}
// store ending index
endIdx[ch] = currentIdx - 1;
}
// Function to find the Kth node
// in DFS of vertex V
static int findNode(int v, int k)
{
k += startIdx[v] - 1;
// Check if kth number exits or not
if (k <= endIdx[v])
return p[k];
return -1;
}
// Driver code
public static void main(String[] args)
{
// Number of nodes
n = 9;
for(int i = 0; i <= n; i++)
tree.add(new ArrayList());
// Add edges
Add_edge(1, 2);
Add_edge(1, 3);
Add_edge(1, 4);
Add_edge(3, 5);
Add_edge(3, 7);
Add_edge(5, 6);
Add_edge(5, 8);
Add_edge(7, 9);
intisalise();
// Store DFS of 1st node
Dfs(1, 0);
int v = 3, k = 4;
System.out.println(findNode(v, k));
}
}
// This code is contributed by jrishabh99 Python3
# Python3 program to find the Kth node in the
# DFS traversal of the subtree of given
# vertex V in a Tree
N = 100005
n = 10
tree = [[]for i in range(N)]
# To store the current index of vertex in DFS
currentIdx = 0
# To store the starting index and ending
# index of vertex in the DFS traversal array
startIdx = [0 for i in range(n)]
endIdx = [0 for i in range(n)]
# To store the DFS of vertex 1
p = [0 for i in range(n)]
# Function to add edge between two nodes
def Add_edge(u, v):
tree[u].append(v)
tree[v].append(u)
# Initialize the vectors
def intisalise():
pass
# Function to perform DFS of a vertex
# 1. stores the DFS of the vertex 1 in vector p,
# 2. store the start index of DFS of every vertex
# 3. store the end index of DFS of every vertex
def Dfs(ch, par):
global currentIdx
p[currentIdx] = ch
# store staring index of node ch
startIdx[ch] = currentIdx
currentIdx += 1
for c in tree[ch]:
if (c != par):
Dfs(c, ch)
# store ending index
endIdx[ch] = currentIdx - 1
# Function to find the Kth node in
# DFS of vertex V
def findNode(v, k):
k += startIdx[v] - 1
# check if kth number exits or not
if (k <= endIdx[v]):
return p[k]
return -1
# Driver code
# number of nodes
n = 9
# add edges
Add_edge(1, 2)
Add_edge(1, 3)
Add_edge(1, 4)
Add_edge(3, 5)
Add_edge(3, 7)
Add_edge(5, 6)
Add_edge(5, 8)
Add_edge(7, 9)
intisalise()
# store DFS of 1st node
Dfs(1, 0)
v, k = 3, 4
print(findNode(v, k))
# This code is contributed by mohit kumarC#
// C# program to find the Kth node in the
// DFS traversal of the subtree of given
// vertex V in a Tree
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{
// To store nodes
static int n;
static ArrayList tree = new ArrayList();
// To store the current index of vertex in DFS
static int currentIdx;
// To store the starting index and ending
// index of vertex in the DFS traversal array
static int[] startIdx;
static int[] endIdx;
// To store the DFS of vertex 1
static int[] p;
// Function to add edge between two nodes
static void Add_edge(int u, int v)
{
((ArrayList)tree[u]).Add(v);
((ArrayList)tree[v]).Add(u);
}
// Initialize the vectors
static void intisalise()
{
startIdx = new int[n + 1];
endIdx = new int[n + 1];
p = new int[n + 1];
}
// Function to perform DFS of a vertex
// 1. stores the DFS of the vertex 1 in vector p,
// 2. store the start index of DFS of every vertex
// 3. store the end index of DFS of every vertex
static void Dfs(int ch, int par)
{
p[currentIdx] = ch;
// store staring index of node ch
startIdx[ch] = currentIdx++;
foreach(int c in (ArrayList)tree[ch])
{
if (c != par)
Dfs(c, ch);
}
// store ending index
endIdx[ch] = currentIdx - 1;
}
// Function to find the Kth node
// in DFS of vertex V
static int findNode(int v, int k)
{
k += startIdx[v] - 1;
// Check if kth number exits or not
if (k <= endIdx[v])
return p[k];
return -1;
}
// Driver code
public static void Main(string[] args)
{
// Number of nodes
n = 9;
for(int i = 0; i <= n; i++)
tree.Add(new ArrayList());
// Add edges
Add_edge(1, 2);
Add_edge(1, 3);
Add_edge(1, 4);
Add_edge(3, 5);
Add_edge(3, 7);
Add_edge(5, 6);
Add_edge(5, 8);
Add_edge(7, 9);
intisalise();
// Store DFS of 1st node
Dfs(1, 0);
int v = 3, k = 4;
Console.Write(findNode(v, k));
}
}
// This code is contributed by rutvik_56输出：
8