Concepts2
∑MathIntermediate
Harmonic Lemma
The Harmonic Lemma says that the values of \lfloor n/i \rfloor only change about 2\sqrt{n} times, so you can iterate those value blocks in O(\sqrt{n}) instead of O(n).
#harmonic lemma#integer division trick#block decomposition+12
∑MathIntermediate
Inclusion-Exclusion Principle
The Inclusion-Exclusion Principle (IEP) corrects overcounting by alternately adding and subtracting sizes of intersections of sets.
#inclusion-exclusion#derangements#surjections+12