Schedule Tasks with the Least Starting Energy

### Problem Each pair in `tasks` is `[actual, minimum]`: a task requires at least minimum energy before starting and consumes actual energy on completion. Finish every task, choosing their order freely. Return the least initial energy that permits completion of them all. ```cpp class Solution { public: int minimumEffort(vector<vector<int>>& tasks); }; ``` ### Examples **Example 1:** ```text tasks = [[2,5],[3,4]] Output: 6 Explanation: With 6, do [2,5] then [3,4], leaving 4 then 1. Starting at 5 fails in either order. ``` **Example 2:** ```text tasks = [[1,4],[2,6],[2,2]] Output: 6 Explanation: Do [2,6], then [1,4], then [2,2], leaving 4, 3, and 1. ``` ### Constraints - `1 <= tasks.length <= 10^5`. - Every task has `1 <= actual <= minimum <= 10^4`. ### Clarifying Questions Minimum is a starting threshold, not an amount consumed. Energy is never replenished during the real schedule. ```hint Inspect the structure How do a task's starting threshold and its actual energy consumption constrain a complete schedule? ``` ### Reasoning checkpoints - Keep each task's starting threshold separate from the energy it consumes. - Prove that the reported initial energy is sufficient and no smaller amount can complete all tasks in any order. ### Optional extensions How would allowing energy-producing tasks change the exchange argument?