# Lexicographically Smallest Permutation of length N such that for exactly K indices, a[i] > a[i] + 1

• Difficulty Level : Basic
• Last Updated : 14 May, 2021

Given two integers N and K, the task is to generate a permutation of N numbers (Every number from 1 to N occurs exactly once) such that the number of indices where a[i]>a[i+1] is exactly K. Print “Not possible” if no such permutation is possible.
Examples:

```Input: N = 5, K = 3
Output: 5 4 3 1 2
Starting 3 indices satisfying the condition
a[i] > a[i]+1

Input: N = 7, k = 4
Output: 7 6 5 4 1 2 3```

Approach: Since the permutation should be lexicographically smallest with the condition satisfied for k indices i.e. a[i] > a[i+1]. So for that starting K+1 digits should be in decreasing order and remaining should be in increasing order. So just print the K numbers from N to 1. Then print numbers from 1 to N-K.

For example: N = 6, K = 4
Print K numbers from N to 1 i.e. 6, 5, 4, 3
Print N-K numbers from 1 to N-K i.e. 1, 2
Permutation will be 654312 i.e. Starting 4 indices satisfy a[i] > a[i+1] for i = 1 to k.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ` `using` `namespace` `std;`   `void` `printPermutation(``int` `n, ``int` `k)` `{` `    ``int` `i, mx = n;` `    ``for` `(i = 1; i <= k; i++) ``// Decreasing part` `    ``{` `        ``cout << mx << ``" "``;` `        ``mx--;` `    ``}` `    ``for` `(i = 1; i <= mx; i++) ``// Increasing part` `        ``cout << i << ``" "``;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `N = 5, K = 3;`   `    ``if` `(K >= N - 1)` `        ``cout << ``"Not Possible"``;`   `    ``else` `        ``printPermutation(N, K);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the above approach`   `import` `java.io.*;`   `class` `GFG {`     `static` `void` `printPermutation(``int` `n, ``int` `k)` `{` `    ``int` `i, mx = n;` `    ``for` `(i = ``1``; i <= k; i++) ``// Decreasing part` `    ``{` `        ``System.out.print( mx + ``" "``);` `        ``mx--;` `    ``}` `    ``for` `(i = ``1``; i <= mx; i++) ``// Increasing part` `        ``System.out.print( i + ``" "``);` `}`   `// Driver Code`   `    ``public` `static` `void` `main (String[] args) {` `            ``int` `N = ``5``, K = ``3``;`   `    ``if` `(K >= N - ``1``)` `        ``System.out.print( ``"Not Possible"``);`   `    ``else` `        ``printPermutation(N, K);` `    ``}` `}`   `// This code is contributed by inder_verma..`

## Python3

 `# Python3 implementation of the` `# above approach ` `def` `printPermutation(n, k): `   `    ``mx ``=` `n ` `    ``for` `i ``in` `range``(``1``, k ``+` `1``): ``# Decreasing part ` `        ``print``(mx, end ``=` `" "``) ` `        ``mx ``-``=` `1` `    `  `    ``for` `i ``in` `range``(``1``, mx ``+` `1``): ``# Increasing part ` `        ``print``(i, end ``=` `" "``) `   `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``:`   `    ``N, K ``=` `5``, ``3`   `    ``if` `K >``=` `N ``-` `1``: ` `        ``print``(``"Not Possible"``) `   `    ``else``:` `        ``printPermutation(N, K) `   `# This code is contributed` `# by Rituraj Jain`

## C#

 `// C# implementation of the above approach` `using` `System;` `class` `GFG {`     `static` `void` `printPermutation(``int` `n, ``int` `k)` `{` `    ``int` `i, mx = n;` `    ``for` `(i = 1; i <= k; i++) ``// Decreasing part` `    ``{` `        ``Console.Write( mx + ``" "``);` `        ``mx--;` `    ``}` `    ``for` `(i = 1; i <= mx; i++) ``// Increasing part` `        ``Console.Write( i + ``" "``);` `}`   `// Driver Code`   `    ``public` `static` `void` `Main () {` `            ``int` `N = 5, K = 3;`   `    ``if` `(K >= N - 1)` `        ``Console.WriteLine( ``"Not Possible"``);`   `    ``else` `        ``printPermutation(N, K);` `    ``}` `}`   `// This code is contributed by inder_verma..`

## PHP

 `= ``\$N` `- 1)` `        ``echo` `"Not Possible"``;`   `    ``else` `        ``printPermutation(``\$N``, ``\$K``);`     `// This code is contributed by inder_verma..` `?>`

## Javascript

 ``

Output:

`5 4 3 1 2`

Time Complexity: O(N)

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