Coding Problems on Interval and Range Manipulation

Interval and Range Manipulation problems are common in algorithmic challenges, often requiring efficient handling of ranges or intervals to solve a specific problem. These problems deal with tasks like merging intervals, finding overlaps, or calculating sums and differences of intervals. The main challenge is to manage multiple intervals efficiently, sometimes requiring sorting, greedy approaches, or advanced data structures.

Common Techniques for Solving Interval and Range Manipulation Problems

1. Sorting: Often, problems require sorting intervals by their start or end points to simplify operations like merging or finding overlaps.
2. Greedy Approach: A greedy approach is frequently used to merge intervals or to find the maximum number of non-overlapping intervals.
3. Prefix Sum: The prefix sum technique can be useful for calculating the sum of distances or other metrics over ranges efficiently.
4. Sweep Line Algorithm: This approach involves moving a virtual line across intervals to track when they start or end, making it useful for problems like finding maximum overlap.
5. Segment Trees: For advanced problems involving range queries and updates, segment trees can efficiently handle operations on intervals.

Identifying Problems Involving Interval and Range Manipulation

Interval and range manipulation problems can vary in complexity and applications but generally involve the following key tasks:

1. Merging Intervals: When given multiple intervals, the problem might ask you to merge overlapping intervals and return the resulting set of intervals.
2. Finding Overlapping Intervals: These problems involve finding if two intervals overlap or computing the total number of overlapping intervals.
3. Interval Scheduling: This problem asks for scheduling tasks or events such that no two tasks overlap. It is often solved using a greedy approach to select the maximum number of non-overlapping intervals.
4. Interval Sum Calculations: Some problems ask you to compute the sum of values over a range or the distance between multiple intervals. This is commonly seen in problems involving time slots, process scheduling, or optimization.
5. Periodicity and Synchronization: These problems often deal with events or tasks that repeat at regular intervals, and LCM (Least Common Multiple) or GCD (Greatest Common Divisor) concepts might be applied to determine synchronization points.

Coding Problems on Interval and Range Manipulation

• Merge Intervals
• Insert Interval
• Interval Intersection
• Non-Overlapping Intervals
• Interval Coverage
• Count Overlapping Intervals
• Find Maximum Overlap
• Meeting Room
• Is There an Overlap?
• Interval to Points
• Free Time Interval
• Overlapping Range
• Weighted Job Scheduling
• Minimum Platforms
• Maximum Overlap
• Minimum Number of Rooms
• Non-overlapping intervals among given intervals
• Maximal Disjoint Intervals
• Job Sequencing Problem
• Add minimum sized interval such that all intervals merge into one

Also read:

• Top 50 Tree Coding Problems for Interviews
• Top 50 Queue Coding Problems for Interviews