Maximize the Smallest Separation

### Problem There are baskets at the distinct coordinates in `position`. Place exactly `m` balls, at most one in each basket. The separation of two balls is the absolute difference of their coordinates. Return the greatest achievable minimum pairwise separation. ```cpp class Solution { public: int maxDistance(vector<int>& position, int m); }; ``` ### Examples **Example 1:** ```text position = [2,5,8,11], m = 3 Output: 3 Explanation: Baskets 2, 5, 11 give a minimum gap of 3. A gap greater than 3 allows at most two balls. ``` **Example 2:** ```text position = [10,3,7], m = 2 Output: 7 Explanation: Use the extreme coordinates 3 and 10. ``` ### Constraints - `n == position.length`, with `2 <= n <= 10^5`. - Coordinates are distinct integers in `[1, 10^9]`. - `2 <= m <= n`. ### Clarifying Questions Each selected basket holds one ball. Only the maximum separation value is returned, so several optimal placements do not create multiple answers. ```hint Inspect the structure What must remain true about every selected pair when exactly `m` baskets are occupied? ``` ### Reasoning checkpoints - Show that the reported minimum separation can be achieved with exactly `m` distinct baskets. - Rule out every larger minimum separation and explain resource use at the stated coordinate and input-size limits. ### Optional extensions If the ball coordinates themselves were also requested, how would you recover one placement after finding the optimum?