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Problem · Array

Get Minimal Cost

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Howdy, amazing user friends! This problem was identified as a duplicate of Selling Shoes. However, after serious consideration, I decided not to merge duplicates for now as both of them have received code submissions. I will figure an approach to handle a situation like this in the future. Thank you for your understanding! All your hard working will eventually be rewarded in a way you expect! 🧡

An online retailer offers products in n different dimensions as specified in the array dimensions. The category supervisor notices that several dimensions are redundant and do not offer a favorable customer experience. To optimize the available stock, the product should be offered in unique dimensions. The dimension of the i-th product, dimensions[i], can be augmented by one unit for a fee given in the adjustmentCosts array, adjustmentCosts[i].

Determine the minimal total fee required to ensure that all product dimensions are unique.

dimensions === size, cost === adjustmentCosts

Examples

01 · Example 1

dimensions = [3, 7, 9, 7, 8]
adjustmentCosts = [5, 2, 5, 7, 5]
return = 6

Increase the second value in size from 7 to 10 at a cost of 3 * 2 = 6.

02 · Example 2

dimensions = [3, 3, 4, 5]
adjustmentCosts = [5, 2, 2, 1]
return = 5

• Increase the second 3 to 5 at a cost of 2 * 2 = 4. • Increase 5 to 6 at a cost of 1. • Total cost = 5.

03 · Example 3

dimensions = [2, 3, 3, 2]
adjustmentCosts = [2, 4, 5, 1]
return = 7

Process: The array size contains duplicate values. Adjust size[3] from 2 to 3 at a cost of 1 × 1 = 1. Adjust size[2] from 3 to 4 at a cost of 1 × 4 = 4. The total cost is 7. Alternatively, • Adjust size[1] to 5, which costs cost[1] * (5 - size[1]) = 8, and • Adjust size[3] to 4, which costs cost[3] * (4 - size[3]) = 2. • Therefore, the total cost = 8 + 2 = 10. Thus, 7 is the minimum cost required to make all sizes distinct.

Constraints

1 ≤ n ≤ 2 * 10^5
1 ≤ size[i] ≤ 10^9
1 ≤ cost[i] ≤ 10^4