Dado un árbol con N Nodes y dos enteros K y V . La tarea es encontrar el Node Kth en el recorrido DFS del vértice V .
Considere el siguiente árbol:
DFS del Node número 1 es [1, 2, 3, 5, 6, 8, 7, 9, 4].
El DFS del número de Node 3 es [3, 5, 6, 8, 7, 9]
El DFS del número de Node 7 es [7, 9] El
DFS del número de Node 9 es [9].
Imprime “-1” si los números en el DFS del vértice V son menores que K.
Ejemplos:
Input : Tree: Shown in above image, V = 3, K = 4 Output : 8 Input : Tree: Shown in above image, V = 7, K = 3 Output : -1
Enfoque : construyamos un vector p : para almacenar el recorrido DFS del árbol completo desde el vértice 1. Sea tin v la posición del vértice V en el vector p (el tamaño del vector p en el momento en que llamamos DFS desde el vértice V) y tout v sea la posición del primer vértice empujado al vector después de dejar el subárbol del vértice V (el tamaño del vector p en el momento en que regresamos de DFS desde el vértice V). Entonces es obvio que el subárbol del vértice V está en el intervalo [tin v , tout v ).
Entonces, para encontrar el Node K-ésimo en el DFS del subárbol del Node V, tendremos que devolver el Node K-ésimo en el intervalo [tin v , tout v ].
A continuación se muestra la implementación del enfoque anterior:
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 starting 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<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 starting 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
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 starting 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 starting 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
Javascript
<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 starting 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>
Producción:
8
Publicación traducida automáticamente
Artículo escrito por pawan_asipu y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA