# Find array with k number of merge sort calls

• Difficulty Level : Hard
• Last Updated : 22 Jul, 2022

Given two numbers n and k, find an array containing values in [1, n] and requires exactly k calls of recursive merge sort function.

Examples:

```Input : n = 3
k = 3
Output : a[] = {2, 1, 3}
Explanation:
Here, a[] = {2, 1, 3}
First of all, mergesort(0, 3) will be called,
which then sets mid = 1 and calls mergesort(0,
1) and mergesort(1, 3), which do not perform
any recursive calls because segments (0, 1)
and (1, 3) are sorted.
Hence, total mergesort calls are 3.

Input : n = 4
k = 1
Output : a[] = {1, 2, 3, 4}
Explanation:
Here, a[] = {1, 2, 3, 4} then there will be
1 mergesort call — mergesort(0, 4), which
will check that the array is sorted and then
end.```

If we have a value of k even, then there is no solution since the number of calls is always odd (one call in the beginning and each call makes either 0 or 2 recursive calls).
If k is odd, let’s try to start with a sorted permutation and try to “unsort” it. Let’s make a function unsort(l, r) that will do it. When we “unsort” a segment, we can either keep it sorted (if we already made enough calls), or make it non-sorted and then call unsort(l, mid) and unsort(mid, r), if we need more calls. When we make a segment non-sorted, it’s better to keep both halves sorted; an easy way to handle this is to swap two middle elements.
It’s easy to see that the number of unsort calls is equal to the number of mergesort calls to sort the resulting permutation, so we can use this approach to try getting exactly k calls.

Below is the code for the above problem.

## CPP

 `// C++ program to find an array that can be``// sorted with k merge sort calls.``#include ``using` `namespace` `std;` `void` `unsort(``int` `l, ``int` `r, ``int` `a[], ``int``& k)``{``    ``if` `(k < 1 || l + 1 == r)``        ``return``;` `    ``// We make two recursive calls, so``    ``// reduce k by 2.``    ``k -= 2;` `    ``int` `mid = (l + r) / 2;``    ``swap(a[mid - 1], a[mid]);``    ``unsort(l, mid, a, k);``    ``unsort(mid, r, a, k);``}` `void` `arrayWithKCalls(``int` `n, ``int` `k)``{``    ``if` `(k % 2 == 0) {``        ``cout << ``" NO SOLUTION "``;``        ``return``;``    ``}` `    ``// Create an array with values``    ``// in [1, n]``    ``int` `a[n+1];``    ``a = 1;``    ``for` `(``int` `i = 1; i < n; i++)``        ``a[i] = i + 1;``    ``k--;` `    ``// calling unsort function``    ``unsort(0, n, a, k);` `    ``for` `(``int` `i = 0; i < n; ++i)``        ``cout << a[i] << ``' '``;``}` `// Driver code``int` `main()``{``    ``int` `n = 10, k = 17;``    ``arrayWithKCalls(n, k);``    ``return` `0;``}`

## Java

 `// Java program to find an array that can be``// sorted with k merge sort calls.``class` `GFG {``    ` `    ``static` `void` `unsort(``int` `l, ``int` `r, ``int` `a[], ``int` `k)``    ``{``        ` `        ``if` `(k < ``1` `|| l + ``1` `== r)``            ``return``;` `        ``// We make two recursive calls, so``        ``// reduce k by 2.``        ``k -= ``2``;` `        ``int` `mid = (l + r) / ``2``;``        ``int` `temp = a[mid - ``1``];``        ``a[mid - ``1``] = a[mid];``        ``a[mid] = temp;``        ` `        ``unsort(l, mid, a, k);``        ``unsort(mid, r, a, k);``    ``}` `    ``static` `void` `arrayWithKCalls(``int` `n, ``int` `k)``    ``{``        ``if` `(k % ``2` `== ``0``) {``            ``System.out.print(``"NO SOLUTION"``);``            ``return``;``        ``}` `        ``// Create an array with values``        ``// in [1, n]``        ``int` `a[] = ``new` `int``[n + ``1``];``        ``a[``0``] = ``1``;``        ` `        ``for` `(``int` `i = ``1``; i < n; i++)``            ``a[i] = i + ``1``;``        ``k--;` `        ``// calling unsort function``        ``unsort(``0``, n, a, k);` `        ``for` `(``int` `i = ``0``; i < n; ++i)``            ``System.out.print(a[i] + ``" "``);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ` `        ``int` `n = ``10``, k = ``17``;``        ` `        ``arrayWithKCalls(n, k);``    ``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python program to find``# an array that can be``# sorted with k merge``# sort calls.` `def` `unsort(l,r,a,k):` `    ``if` `(k < ``1` `or` `l ``+` `1` `=``=` `r):``        ``return`` ` `    ``# We make two recursive calls, so``    ``# reduce k by 2.``    ``k ``-``=` `2`` ` `    ``mid ``=` `(l ``+` `r) ``/``/` `2``    ``temp ``=` `a[mid ``-` `1``]``    ``a[mid``-``1``] ``=` `a[mid]``    ``a[mid] ``=` `temp` `    ``unsort(l, mid, a, k)``    ``unsort(mid, r, a, k)` `def` `arrayWithKCalls(n,k):` `    ``if` `(k ``%` `2` `=``=` `0``):``        ``print``(``"NO SOLUTION"``)``        ``return``    ` ` ` `    ``# Create an array with values``    ``# in [1, n]``    ``a ``=` `[``0` `for` `i ``in` `range``(n ``+` `2``)]``    ``a[``0``] ``=` `1``    ``for` `i ``in` `range``(``1``, n):``        ``a[i] ``=` `i ``+` `1``    ``k``-``=``1`` ` `    ``# calling unsort function``    ``unsort(``0``, n, a, k)`` ` `    ``for` `i ``in` `range``(n):``        ``print``(a[i] ,``" "``,end``=``"")` `# Driver code` `n ``=` `10``k ``=` `17``arrayWithKCalls(n, k)` `# This code is contributed``# by Anant Agarwal.`

## C#

 `// C# program to find an array that can``// be sorted with k merge sort calls.``using` `System;` `class` `GFG {``    ` `    ``static` `void` `unsort(``int` `l, ``int` `r,``                       ``int` `[]a, ``int` `k)``    ``{``        ``if` `(k < 1 || l + 1 == r)``            ``return``;` `        ``// We make two recursive calls,``        ``// so reduce k by 2.``        ``k -= 2;` `        ``int` `mid = (l + r) / 2;``        ``int` `temp = a[mid - 1];``        ``a[mid - 1] = a[mid];``        ``a[mid] = temp;``        ` `        ``unsort(l, mid, a, k);``        ``unsort(mid, r, a, k);``    ``}` `    ``static` `void` `arrayWithKCalls(``int` `n, ``int` `k)``    ``{``        ``if` `(k % 2 == 0)``        ``{``            ``Console.WriteLine(``"NO SOLUTION"``);``            ``return``;``        ``}` `        ``// Create an array with``        ``// values in [1, n]``        ``int` `[]a = ``new` `int``[n + 1];``        ``a = 1;``        ` `        ``for` `(``int` `i = 1; i < n; i++)``            ``a[i] = i + 1;``        ``k--;` `        ``// calling unsort function``        ``unsort(0, n, a, k);` `        ``for` `(``int` `i = 0; i < n; ++i)``            ``Console.Write(a[i] + ``" "``);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ` `        ``int` `n = 10, k = 17;``        ` `        ``arrayWithKCalls(n, k);``    ``}``}` `// This code is contributed by vt_m.`

## Javascript

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Output

`3 1 4 6 2 8 5 9 7 10 `

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