# Find the Kth node in the DFS traversal of a given subtree in a Tree

Given a tree with N nodes, and two integers K and V. The task is to find the Kth node in the DFS traversal of the vertex V.
Consider the below Tree:

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 .

Print “-1” if the numbers in the DFS of vertex V are less than K.
Examples:

```Input : Tree: Shown in above image, V = 3, K = 4
Output : 8

Input : Tree: Shown in above image, V = 7, K = 3
Output : -1
```

Approach : Let’s construct a vector : to store the DFS traversal of the complete tree from vertex 1. Let tinv be the position of the vertex V in the vector p (the size of the vector p in moment we call DFS from the vertex V) and toutv be the position of the first vertex pushed to the vector after leaving the subtree of vertex V (the size of the vector p in moment when we return from DFS from the vertex V). Then it is obvious that the subtree of the vertex V lies in the interval [tinv, toutv).
So, to find the Kth node in the DFS of the subtree of node V, we will have to return the Kth node in the interval [tinv, toutv).

Below is the implementation of the above approach:

 `// 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<``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 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 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 `

Output:
```8
```

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Improved By : mohit kumar 29, jrishabh99

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