Choose a Shared Array Value with Minimum Weighted Unit Cost
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Other
### Problem
Changing `nums[i]` by one in either direction costs `cost[i]`. You may make any number of such changes. Return the minimum total cost needed to make every entry of `nums` equal. Both input arrays contain positive integers.
```cpp
class Solution {
public:
long long minCost(vector<int>& nums, vector<int>& cost);
};
```
### Examples
**Example 1:**
```text
Input: nums = [1,4], cost = [2,1]
Output: 3
Explanation: Move4 down to 1 for 3 units at unit cost 1; targeting4 would cost 6.
```
**Example 2:**
```text
Input: nums = [6,6], cost = [4,9]
Output: 0
Explanation: The values already agree.
```
### Constraints
- The arrays have equal length `n`, with `1 <= n <= 100000`.
- `1 <= nums[i], cost[i] <= 1000000`.
- The answer is guaranteed not to exceed `2^53 - 1`.
### Clarifying Questions
- Does an entry's unit cost change as its value changes? No.
- May changes increase or decrease a value? Either direction is allowed.
- Must the common target be returned? No; return only the minimum total cost.
- Are zero operations allowed? Yes, including when entries already agree.
```hint Check the boundary
Compare equal-size changes to entries whose unit costs differ.
```
Overview: Make all array values equal with minimum total cost when each entry has its own fixed cost per unit increase or decrease.
