Optimal Interval Difference

Problem Overview

• Given an array of intervals [start, end], find the minimum gap between consecutive intervals after consolidating overlaps.
• Input: N followed by N pairs of integers (start, end). Output: a single integer, the smallest difference start(current) - end(previous) among the merged, sorted intervals.
• Context: useful for scheduling or timeline analysis where you need the tightest gap between events.
• This Amazon interviews problem is a common coding interview interview question.