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Find index after traversing a permutation Array of 1 to N by K steps
• Last Updated : 20 May, 2021

Given an integer K and an index array arr[] of length N which contains elements in the range [1, N], the task is to find the index after traversing the array by K steps starting from the index 1.
Traversal of index array: In the traversal of the index array the next index to be visited is the value at the current index.
Examples:

Input: arr[] = {3, 2, 4, 1}, K = 5
Output:
Explanation:
Traversal to the indices starting from index 1:
1 => 3 => 4 => 1 => 3 => 4
Finally, after K traversals the index is 4
Input: arr[] = {6, 5, 2, 5, 3, 2}, K = 2
Output:

Approach: The key observation in the problem is that after traversing the index array N times it repeats itself. Therefore, we can find the value of the and then finally find the index after traversal.
Below is the implementation of the above approach:

## C++

 `// C++ implementation to find the``// index after traversing the index``// array K times` `#include``using` `namespace` `std;` `// Function to find the index after``// traversing the index array K times``int` `findIndexAfterKTrav(vector<``int``> arr,``                        ``int` `n, ``int` `k){``    ``k = k % n;``    ``int` `indi = 1;``    ` `    ``// Loop to traverse the index``    ``// array K times``    ``while` `(k){``        ``indi = arr[indi-1];``        ``k--;``    ``}``    ` `    ``return` `arr[indi-1];``}` `// Driver Code``int` `main() {``    ``int` `n = 4, k = 5;``    ``vector<``int``> arr{3, 2, 4, 1};` `    ``// Function Call``    ``cout << findIndexAfterKTrav(arr, n, k);``    ``return` `0;``}`

## Java

 `// Java implementation to find the``// index after traversing the index``// array K times``class` `GFG{``    ` `// Function to find the index after``// traversing the index array K times``public` `static` `int` `findIndexAfterKTrav(``int``[] arr,``                                      ``int` `n, ``int` `k)``{``    ``k = k % n;``    ``int` `indi = ``1``;``        ` `    ``// Loop to traverse the index``    ``// array K times``    ``while` `(k > ``0``)``    ``{``        ``indi = arr[indi - ``1``];``        ``k--;``    ``}``    ``return` `arr[indi - ``1``];``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``4``, k = ``5``;``    ``int``[] arr = { ``3``, ``2``, ``4``, ``1` `};``    ` `    ``// Function Call``    ``System.out.print(findIndexAfterKTrav(arr, n, k));``}``}` `// This code is contributed by divyeshrabadiya07`

## Python3

 `# Python3 implementation to find the``# index after traversing the index``# array K times` `# Function to find the index after``# traversing the index array K times``def` `findIndexAfterKTrav(arr, n, k):``    ` `    ``k ``=` `k ``%` `n;``    ``indi ``=` `1``;` `    ``# Loop to traverse the index``    ``# array K times``    ``while` `(k > ``0``):``        ``indi ``=` `arr[indi ``-` `1``];``        ``k ``-``=` `1``;` `    ``return` `arr[indi ``-` `1``];` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``n ``=` `4``;``    ``k ``=` `5``;``    ``arr ``=` `[ ``3``, ``2``, ``4``, ``1` `];` `    ``# Function Call``    ``print``(findIndexAfterKTrav(arr, n, k));` `# This code is contributed by Princi Singh`

## C#

 `// C# implementation to find the``// index after traversing the index``// array K times``using` `System;` `class` `GFG{``     ` `// Function to find the index after``// traversing the index array K times``public` `static` `int` `findIndexAfterKTrav(``int``[] arr,``                                      ``int` `n, ``int` `k)``{``    ``k = k % n;``    ``int` `indi = 1;``         ` `    ``// Loop to traverse the index``    ``// array K times``    ``while` `(k > 0)``    ``{``        ``indi = arr[indi - 1];``        ``k--;``    ``}``    ``return` `arr[indi - 1];``}`` ` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 4, k = 5;``    ``int``[] arr = { 3, 2, 4, 1 };``     ` `    ``// Function Call``    ``Console.Write(findIndexAfterKTrav(arr, n, k));``}``}` `// This code is contributed by Princi Singh`

## Javascript

 ``
Output:
`4`

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