Minimum Time to Complete All Tasks - Video Solutions

Problem Overview: Each task is represented as [start, end, duration]. You can run tasks at any integer time within their window, and multiple tasks can share the same time slot. The goal is to choose the minimum number of active time points so every task receives at least duration units of execution within its allowed interval.

Approach 1: Sweep Line Algorithm (O(n log n) time, O(n) space)

This approach treats the timeline like a sequence of events and processes tasks in sorted order by their end time. Sorting ensures you satisfy the most restrictive deadlines first. As you scan tasks, maintain a structure (often a stack or ordered list) that stores the time points already activated. For each task, count how many of those chosen time points already fall inside [start, end]. If the count is less than duration, activate additional time points starting from the task's end and moving backward. This greedy sweep ensures new time points are as late as possible so they can satisfy future tasks. The sweep-line idea combined with sorting avoids redundant allocations and keeps the active timeline minimal.

Core operations include sorting tasks (O(n log n)), checking existing active times inside an interval using binary search, and pushing new time slots when needed. The algorithm works well because later time points maximize reuse across overlapping intervals. Related concepts appear frequently in sorting and array scheduling problems.

Approach 2: Greedy Task Scheduling (O(n log n) time, O(n) space)

The most common interview solution uses a greedy scheduling strategy. First sort tasks by end. Maintain a boolean timeline or ordered structure that records which time slots are already used. For each task, iterate through the interval and count how many time points are already active. If the task still needs more execution time, add new active slots starting from end and moving backward until the required duration is met. Choosing the latest available slots preserves earlier ones for tasks with tighter windows.

This strategy is a classic greedy scheduling pattern: always satisfy the task with the earliest deadline while delaying work as much as possible. Implementations often combine sorting with binary search to quickly count existing slots in the interval. The technique mirrors interval scheduling problems commonly solved with greedy logic and occasionally binary search for efficient lookups.

Recommended for interviews: The greedy task scheduling approach is the expected solution. Interviewers want to see that you sort by end time and allocate execution slots from right to left. Explaining the sweep-line interpretation helps demonstrate deeper understanding of interval scheduling and timeline optimization.