Minimum Number of Work Sessions to Finish the Tasks

Minimum Number of Work Sessions to Finish the Tasks

1. What is this problem about?

You have a set of tasks, each taking a certain amount of time, and a fixed sessionTime (the maximum time you can work in one session). You must finish all tasks using the minimum number of work sessions. The tasks can be completed in any order, but a single task cannot be split across sessions.

2. Why is this asked in interviews?

This "Minimum Number of Work Sessions to Finish the Tasks interview question" is a variation of the Bin Packing problem, which is NP-hard. Amazon and Swiggy ask it to see if a candidate can implement an efficient backtracking solution or use Bitmask Dynamic Programming for small constraints. It tests your ability to handle combinatorial optimization and state-space pruning.

3. Algorithmic pattern used

The optimal pattern for the small constraints typical of this problem is Dynamic Programming with Bitmasking. A state can be represented as (mask, current_time), where mask is a bitmask of tasks already completed, and current_time is the time used in the current session. Alternatively, you can use backtracking with memoization to explore different task assignments while pruning branches that exceed the current best session count.

4. Example explanation

Tasks: [1, 2, 3], Session Time: 3.

• Session 1: Task with time 1 and Task with time 2. Total 3.
• Session 2: Task with time 3. Total 3. Total sessions = 2.
• Another way: Session 1: Task 3. Session 2: Task 1 and 2. Still 2. The algorithm tries all combinations to ensure no other grouping (like putting each task in its own session) is better, though here 2 is clearly the minimum.

5. Common mistakes candidates make

A common error is trying a greedy approach, such as always picking the largest task first. Greedy does not work for bin packing! For example, if session time is 10 and tasks are [6, 5, 5, 4], greedy might take [6, 4] and [5, 5] (2 sessions), but in other cases, it might fail to find the optimal packing. Another mistake is not using memoization in backtracking, leading to redundant work and exponential time complexity.

6. Interview preparation tip

When you see a problem where you need to group items into "buckets" of fixed capacity and the number of items is small (usually less than 15-20), think Bitmask DP. It's the standard way to solve small-scale NP-hard optimization problems in coding interviews.