minimum-cost-to-make-arrays-identical

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Algorithms

You are given two integer arrays <code>arr</code> and <code>brr</code> of length <code>n</code>, and an integer <code>k</code>. You can perform the following operations on <code>arr</code> any number of times:

<ul>
	<li>Split <code>arr</code> into any number of contiguous subarrays and rearrange these subarrays in any order. This operation has a fixed cost of <code>k</code>.</li>
	<li>
	Choose any element in <code>arr</code> and add or subtract a positive integer <code>x</code> to it. The cost of this operation is <code>x</code>.
	</li>
</ul>

Return the minimum total cost to make <code>arr</code> equal to <code>brr</code>.

&nbsp;
Example 1:

<div class="example-block">
Input: arr = [-7,9,5], brr = [7,-2,-5], k = 2

Output: 13

Explanation:

<ul>
	<li>Split <code>arr</code> into two contiguous subarrays: <code>[-7]</code> and <code>[9, 5]</code> and rearrange them as <code>[9, 5, -7]</code>, with a cost of 2.</li>
	<li>Subtract 2 from element <code>arr[0]</code>. The array becomes <code>[7, 5, -7]</code>. The cost of this operation is 2.</li>
	<li>Subtract 7 from element <code>arr[1]</code>. The array becomes <code>[7, -2, -7]</code>. The cost of this operation is 7.</li>
	<li>Add 2 to element <code>arr[2]</code>. The array becomes <code>[7, -2, -5]</code>. The cost of this operation is 2.</li>
</ul>

The total cost to make the arrays equal is <code>2 + 2 + 7 + 2 = 13</code>.
</div>

Example 2:

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

Output: 0

Explanation:

Since the arrays are already equal, no operations are needed, and the total cost is 0.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= arr.length == brr.length &lt;= 105</code></li>
	<li><code>0 &lt;= k &lt;= 2 * 1010</code></li>
	<li><code>-105 &lt;= arr[i] &lt;= 105</code></li>
	<li><code>-105 &lt;= brr[i] &lt;= 105</code></li>
</ul>