# Find index after traversing a permutation Array of 1 to N by K steps

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: 4
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: 5

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 `

Output:

```4
```

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