Split Values into the Fewest Pieces for Nondecreasing Order
Company: Salesforce
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Other
### Problem
One operation replaces a single array element by two integer elements whose sum equals that element, retaining their position in the sequence. Return the smallest number of operations needed to make the resulting array nondecreasing.
```cpp
class Solution {
public:
long long minimumReplacement(vector<int>& nums);
};
```
### Examples
**Example 1:**
```text
Input: nums = [10,4]
Output: 2
Explanation: Replace 10 by 3 and 7, then replace 7 by 3 and 4, giving [3,3,4,4]. At least three pieces are needed for a total of 10 when every piece is at most 4.
```
**Example 2:**
```text
Input: nums = [2,2,3]
Output: 0
Explanation: The input is already nondecreasing, so no operation is needed.
```
### Constraints
- `1 <= nums.length <= 100000`.
- `1 <= nums[i] <= 10^9`.
### Clarifying Questions
- May the original entries be reordered? No; a replacement occupies the replaced element's position in the sequence.
- Must the final order be strictly increasing? No; equal neighboring values are allowed.
- Does making three pieces count as one operation? No; each operation replaces one element by exactly two.
- Is the final array returned? No, return only the minimum number of operations.
```hint Check the boundary
Compare the number of operations with the number of pieces produced from one original entry.
```
Overview: Find the fewest binary splits of array entries needed to obtain nondecreasing order while preserving each entry’s total value.