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g3101_3200.s3139_minimum_cost_to_equalize_array.readme.md Maven / Gradle / Ivy

3139\. Minimum Cost to Equalize Array

Hard

You are given an integer array `nums` and two integers `cost1` and `cost2`. You are allowed to perform **either** of the following operations **any** number of times:

*   Choose an index `i` from `nums` and **increase** `nums[i]` by `1` for a cost of `cost1`.
*   Choose two **different** indices `i`, `j`, from `nums` and **increase** `nums[i]` and `nums[j]` by `1` for a cost of `cost2`.

Return the **minimum** **cost** required to make all elements in the array **equal**_._

Since the answer may be very large, return it **modulo** 109 + 7.

**Example 1:**

**Input:** nums = [4,1], cost1 = 5, cost2 = 2

**Output:** 15

**Explanation:**

The following operations can be performed to make the values equal:

*   Increase `nums[1]` by 1 for a cost of 5. `nums` becomes `[4,2]`.
*   Increase `nums[1]` by 1 for a cost of 5. `nums` becomes `[4,3]`.
*   Increase `nums[1]` by 1 for a cost of 5. `nums` becomes `[4,4]`.

The total cost is 15.

**Example 2:**

**Input:** nums = [2,3,3,3,5], cost1 = 2, cost2 = 1

**Output:** 6

**Explanation:**

The following operations can be performed to make the values equal:

*   Increase `nums[0]` and `nums[1]` by 1 for a cost of 1. `nums` becomes `[3,4,3,3,5]`.
*   Increase `nums[0]` and `nums[2]` by 1 for a cost of 1. `nums` becomes `[4,4,4,3,5]`.
*   Increase `nums[0]` and `nums[3]` by 1 for a cost of 1. `nums` becomes `[5,4,4,4,5]`.
*   Increase `nums[1]` and `nums[2]` by 1 for a cost of 1. `nums` becomes `[5,5,5,4,5]`.
*   Increase `nums[3]` by 1 for a cost of 2. `nums` becomes `[5,5,5,5,5]`.

The total cost is 6.

**Example 3:**

**Input:** nums = [3,5,3], cost1 = 1, cost2 = 3

**Output:** 4

**Explanation:**

The following operations can be performed to make the values equal:

*   Increase `nums[0]` by 1 for a cost of 1. `nums` becomes `[4,5,3]`.
*   Increase `nums[0]` by 1 for a cost of 1. `nums` becomes `[5,5,3]`.
*   Increase `nums[2]` by 1 for a cost of 1. `nums` becomes `[5,5,4]`.
*   Increase `nums[2]` by 1 for a cost of 1. `nums` becomes `[5,5,5]`.

The total cost is 4.

**Constraints:**

*   1 <= nums.length <= 105
*   1 <= nums[i] <= 106
*   1 <= cost1 <= 106
*   1 <= cost2 <= 106