Problem Description
You have n tasks represented as an integer array tasks, where tasks[i] indicates the hours needed to complete the i-th task. A work session allows you to work for at most sessionTime consecutive hours. You need to determine the minimum number of work sessions required to finish all tasks, given the constraints that tasks must be completed within the same session and can be done in any order.
Key Insights
- Each task must be completed in the same work session in which it is started.
- You can arrange tasks in any order to optimize the number of sessions.
- The challenge is to fit tasks into sessions without exceeding the
sessionTime. - Given the constraints (maximum of 14 tasks and task times between 1 and 10), a backtracking approach can be effectively utilized.
Space and Time Complexity
Time Complexity: O(2^n * n) - where n is the number of tasks, as we may explore all subsets of tasks. Space Complexity: O(n) - for the recursion stack in the backtracking approach.
Solution
The solution employs a backtracking algorithm to explore all possible combinations of tasks that can fit within the sessionTime. A bitmask can be used to represent the state of completed tasks. By iterating through all possible combinations, we can keep track of the number of sessions required to finish all tasks. The optimal solution is determined by minimizing the number of sessions.