minimum-operations-to-sort-a-permutation

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Algorithms

You are given an integer array <code>nums</code> of length <code>n</code>, where <code>nums</code> is a permutation of the integers from 0 to <code>n - 1</code>.

You may perform only the following operations:

<ul>
	<li>Reverse the entire array.</li>
	<li>Rotate Left by One: Move the first element to the end of the array, and rest elements to left by one position.</li>
</ul>

Return an integer denoting the minimum number of operations required to sort the array in increasing order. If it is not possible to sort the array using only the given operations, return -1.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [0,2,1]

Output: 2

Explanation:

<ul>
	<li>Rotate Left by one: <code>[2, 1, 0]</code></li>
	<li>Reverse the array: <code>[0, 1, 2]</code></li>
</ul>

The array becomes sorted in 2 operations, which is minimal
</div>

Example 2:

<div class="example-block">
Input: nums = [1,0,2]

Output: 2

Explanation:

<ul>
	<li>Reverse the array: <code>[2, 0, 1]</code></li>
	<li>Rotate Left by one: <code>[0, 1, 2]</code></li>
</ul>

The array becomes sorted in 2 operations, which is minimal.
</div>

Example 3:

<div class="example-block">
Input: nums = [2,0,1,3]

Output: -1

Explanation:

It is impossible to reach <code>[2, 0, 1, 3]</code>. Thus, the answer is -1.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n == nums.length &lt;= 105</code></li>
	<li><code>0 &lt;= nums[i] &lt;= n - 1</code></li>
	<li><code>nums</code> is a permutation of integers from 0 to <code>n - 1</code>.</li>
</ul>