在树中给定子树的 DFS 遍历中找到第 k 个节点
原文:https://www . geeksforgeeks . org/find-the-kth-node-in-DFS-遍历树中给定的子树/
给定一个节点为 N 的树，以及两个整数 K 和 V 。任务是在顶点 V 的 DFS 遍历中找到 Kth 节点。 考虑下面的树:
节点号 1 的 DFS 是[1，2，3，5，6，8，7，9，4]。 3 号节点的 DFS 为[3，5，6，8，7，9] 7 号节点的 DFS 为[7，9] 9 号节点的 DFS 为[9]。
如果顶点 V 的 DFS 中的数字小于 k，则打印“-1”。
示例:
Input : Tree: *Shown in above image*, V = 3, K = 4
Output : 8
Input : Tree: *Shown in above image*, V = 7, K = 3
Output : -1
逼近:我们构造一个向量 p :存储从顶点 1 开始的完全树的 DFS 遍历。设 tin v 为顶点 V 在向量 p 中的位置(向量 p 的大小在我们从顶点 V 返回 DFS 的瞬间)，tout v 为离开顶点 V 的子树后第一个被推送到向量的顶点的位置(向量 p 的大小在我们从顶点 V 返回 DFS 的瞬间)。那么很明显顶点 V 的子树位于区间【tin v ，tout v 】。 所以，要在节点 V 的子树的 DFS 中找到第 k 个节点，我们就要返回区间【tin v ，tout v 中的第 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 <bits/stdc++.h>
using namespace std;
#define N 100005
// To store nodes
int n;
vector<int> 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<int> startIdx, endIdx;
// To store the DFS of vertex 1
vector<int> 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 语言(一种计算机语言，尤用于创建网站)
// 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<Integer>> 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<Integer>());
// 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
Python 3
# 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 kumar
C
// 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
java 描述语言
<script>
// Javascript program to find the Kth node in the
// DFS traversal of the subtree of given
// vertex V in a Tree
let N = 100005;
// To store nodes
let n=10;
let tree = [];
// To store the current index of vertex in DFS
let currentIdx=0;
// To store the starting index and ending
// index of vertex in the DFS traversal array
let startIdx;
let endIdx;
// To store the DFS of vertex 1
let p;
// Function to add edge between two nodes
function Add_edge(u,v)
{
tree[u].push(v);
tree[v].push(u);
}
// Initialize the vectors
function intisalise()
{
startIdx = new Array(n + 1);
endIdx = new Array(n + 1);
p = new Array(n + 1);
for(let i=0;i<(n+1);i++)
{
startIdx[i]=0;
endIdx[i]=0;
p[i]=0;
}
}
// 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
function Dfs(ch,par)
{
p[currentIdx] = ch;
// store staring index of node ch
startIdx[ch] = currentIdx++;
for(let c=0;c<tree[ch].length;c++)
{
if (tree[ch] != par)
Dfs(tree[ch], ch);
}
// store ending index
endIdx[ch] = currentIdx - 1;
}
// Function to find the Kth node
// in DFS of vertex V
function 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;
for(let i = 0; i <= n; i++)
tree.push([]);
// 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);
let v = 3, k = 4;
document.write(findNode(v, k));
// This code is contributed by unknown2108
</script>
Output:
8
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