Minimum Segments

Problem Overview

• Given n intervals (a[i], b[i]) and an integer k, add exactly one segment (a, b) with b − a ≤ k to minimize the number of connected sets.
• Return the minimum number of sets after adding this segment.
• A set is connected if every point from the minimum start to the maximum end is covered by some segment.
• Inputs: arrays a, b, and k; n ≤ 2e5, values ≤ 1e9.
• Snowflake coding interview problem and interview question; context: timeline coverage and range merging.