Concepts5

Double Counting

Double counting is the strategy of counting the same quantity in two different ways to derive an equality or an efficient algorithm.

#double counting#contribution technique#handshake lemma+12

∑MathIntermediate

Derangements

A derangement is a permutation with no element left in its original position, often written as !n or D(n).

#derangement#subfactorial#inclusion-exclusion+11

∑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

∑MathIntermediate

Stars and Bars

Stars and Bars counts the ways to distribute n identical items into k distinct bins using combinations.

#stars and bars#combinatorics#binomial coefficient+12

⚙️AlgorithmIntermediate

2D Prefix Sum

A 2D prefix sum (also called an integral image) lets you compute the sum of any axis-aligned sub-rectangle in constant time after O(nm) preprocessing.

#2d prefix sum#summed-area table#integral image+12