Increase Values Just Enough for Strict Order

### Problem One operation increments one entry of `nums` by one. Without rearranging or decreasing entries, make the array strictly increasing and return the smallest number of operations required. ```cpp class Solution { public: int minOperations(vector<int>& nums); }; ``` ### Examples **Example 1:** ```text nums = [3,3,2] Output: 4 Explanation: The minimal final values are [3,4,5], costing 0+1+3. ``` **Example 2:** ```text nums = [2,5,7] Output: 0 Explanation: The array already strictly increases. ``` ### Constraints - `1 <= nums.length <= 5000`. - Original values are in `[1,10^4]`. ### Clarifying Questions The output is an operation count. Final values may exceed the original input bound because increments are unrestricted. ```hint Inspect the structure Which changes are allowed, and must the result be strictly increasing rather than merely nondecreasing? ``` ### Reasoning checkpoints - Use only increments and keep the original entry order. - Prove that the returned total is the minimum cost of making every adjacent pair strictly increasing. ### Optional extensions How would allowing decrements as well change the optimization?