Task Scheduling to Minimize Overall Completion Deadline (with Dependencies and Heap Optimization)

Problem: Task Scheduling (Incremental Constraints) You are given a set of tasks, each with a processing time. Your goal is to compute the minimum total time to finish all tasks (i.e., the time when the last task completes / overall deadline / makespan). The interview problem is split into three parts with increasing constraints. Note: The original post does not include the exact input schema and I/O format. The following is a faithful summary of the core requirements: minimize overall finishing time, add prerequisite constraints, and optimize using a heap. Part 1: Scheduling Without Constraints Input: a list of tasks with their durations. Constraints: no prerequisites or additional restrictions. Output: the minimum total time required to complete all tasks (the finishing time of the last task). Part 2: Add Subtask/Prerequisite Dependencies Input: tasks with durations. dependency relations: some tasks can only start after all their prerequisites are completed. Constraints: a task becomes "ready" only when all prerequisites are satisfied. Requirement: you may maintain a separate list/set of currently ready tasks and schedule from it. Output: the minimum total completion time under dependency constraints. Part 3: Data Structure / Time Optimization Based on Part 2: optimize the solution for performance. typical approach: use a heap/priority queue to maintain ready tasks and reduce selection overhead. Test Cases The original post contains no concrete I/O format or sample cases, so no runnable test cases are provided to avoid making incorrect assumptions.