Reduce a Target by Removing Array Ends
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
In each operation, remove the current leftmost or rightmost element of `nums` and subtract that element from `x`. The removal changes which elements are available at the ends for later operations. Return the fewest operations that make x exactly zero, or `-1` when impossible.
```cpp
class Solution {
public:
int minOperations(vector<int>& nums, int x);
};
```
### Examples
**Example 1:**
```text
nums = [2,3,1,4], x = 6
Output: 2
Explanation: Remove 2 from the left and 4 from the right.
```
**Example 2:**
```text
nums = [3,2,2], x = 7
Output: 3
Explanation: Every element must be removed to subtract the full sum.
```
### Constraints
- `1 <= nums.length <= 10^5`.
- `1 <= nums[i] <= 10^4`.
- `1 <= x <= 10^9`.
### Clarifying Questions
The remaining elements form one contiguous middle block, possibly empty. Removing elements from arbitrary internal positions is not allowed.
```hint Inspect the structure
After several legal removals, which positions are still eligible for the next operation?
```
### Reasoning checkpoints
- Relate every proposed operation to a legal removal from a current end.
- Prove the smallest operation count and distinguish impossibility from removal of the whole array.
### Optional extensions
Why would negative array values invalidate this sliding-window argument?
Overview: Reduce a Target by Removing Array Ends. In each operation, remove the current leftmost or rightmost element of nums and subtract that element from x. The removal changes which elements are available at the ends for later operations.