Pattern Studioalgorithmic thinking
All patterns

Interval Processing

Greedy Algorithms & Mathematical Optimization
Intermediate
Interactive

Sort ranges and merge every overlap into the active span.

Time
O(n log n)
Space
O(n) output
ActiveComparingMatch / bestIn windowFrontierVisitedExcludedAnswer
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The idea

Interval problems become linear after sorting by start. Keep one active merged range: overlapping intervals extend its end, while a gap commits it and begins a new range.

Analogy

This visualization makes the state transitions behind interval processing explicit, one decision at a time.

When to reach for it

  • The problem exhibits this pattern's defining invariant.
  • A direct brute-force approach repeats work or explores unnecessary choices.
  • You need a standard interview-ready template.

Language-independent template

sort intervals by start
merged = []
for interval in intervals:
    if gap: append interval
    else: extend last interval

Complexity — time O(n log n), space O(n) output.

Common mistakes

  • Choosing the wrong state or invariant.
  • Updating state before preserving the value needed next.
  • Missing a boundary or base case.

Practice progression

Canonical interview problems, ordered from foundation to advanced application.

Easy
Summary RangesLC 228

Compress consecutive sorted values into disjoint ranges.

Medium
Merge IntervalsLC 56

Merge every overlapping pair of intervals.

Hard
Employee Free TimeLC 759

Find finite intervals when every employee is free.

Variations

Change the input to exercise another path.
Adapt the invariant to a related optimization or counting problem.