minimum-operations-to-make-array-modulo-alternating-i

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Algorithms

You are given an integer array <code>nums</code> and an integer <code>k</code>.

In one operation, you can increase or decrease any element of <code>nums</code> by 1.

An array is called modulo alternating if there exist two distinct integers <code>x</code> and <code>y</code> (<code>0 &lt;= x, y &lt; k</code>) such that:

<ul>
	<li>For every even index <code>i</code>, <code>nums[i] % k == x</code></li>
	<li>For every odd index <code>i</code>, <code>nums[i] % k == y</code></li>
</ul>

Return the minimum number of operations required to make <code>nums</code> modulo alternating.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [1,4,2,8], k = 3

Output: 2

Explanation:

<ul>
	<li>Let&#39;s choose <code>x = 1</code> for even indices and <code>y = 2</code> for odd indices.</li>
	<li>Perform the following operations:
	<ul>
		<li>Increment <code>nums[1] = 4</code> by 1, giving <code>nums = [1, 5, 2, 8]</code>.</li>
		<li>Decrement <code>nums[2] = 2</code> by 1, giving <code>nums = [1, 5, 1, 8]</code>.</li>
	</ul>
	</li>
	<li>Now, for even indices, <code>nums[i] % k = 1</code>, and for odd indices, <code>nums[i] % k = 2</code>.</li>
	<li>Thus, the total number of operations required is 2.</li>
</ul>
</div>

Example 2:

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

Output: 1

Explanation:

<ul>
	<li>Incrementing <code>nums[1]</code> by 1 gives <code>nums = [1, 2, 1]</code>, which satisfies the condition with <code>x = 1</code> and <code>y = 2</code>.</li>
	<li>Thus, the total number of operations required is 1.</li>
</ul>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 109</code></li>
	<li><code>2 &lt;= k &lt;= 100</code></li>
</ul>