PROBLEM 65 OF 75

Non-overlapping Intervals

Remove the fewest intervals so the rest do not overlap.

PATTERNIntervals & sweep lineAfter sorting, only the active frontier can conflict.
SPOT THE SIGNAL

Why does this pattern fit?

FRAME · 1 OF 4

Restate the exact job

Remove the fewest intervals so the rest do not overlap.

WHY THIS FITS

Keeping the interval that ends earliest leaves the most room for future intervals.

COMPLEXITY

O(n log n) time · O(1) extra after sort

COMMON FAILURE

Keeping the earlier-starting interval can block more future choices.

THE REASONING, IN ONE PLACE

How to solve Non-overlapping Intervals

The goal is to solve this problem from the pattern, not to memorize a finished answer. Use this as a check after your own attempt.

What the question asks

Remove the fewest intervals so the rest do not overlap.

Why Intervals & sweep line fits

Keeping the interval that ends earliest leaves the most room for future intervals.

State to maintain

Last kept end and removal count.

Transition

Sort by end; keep compatible intervals and count the others as removals.

Time and space

O(n log n) time · O(1) extra after sort

Counterexample to the tempting mistake

Keeping the earlier-starting interval can block more future choices.

Prove it again tomorrow

Close this page. Rebuild the state and transition from memory, write a test that exposes the mistake above, then solve a fresh input without looking back. A same-day reread is practice, not proof of retention.

Open blank recall ↗