The "median of medians" is an algorithm used in computer science to select an approximate median from a list of numbers. It serves as a method to perform a good pivot selection in selection algorithms like Quickselect, which can be used to find the k-th smallest (or largest) element in an unordered list. ### How the Median of Medians Algorithm Works 1. **Divide the List**: Split the list into groups of a fixed size, typically 5.
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For deterministic linear-time selection, group keys into fives, compute the median of each group, and recursively select the median of those medians as a pivot. Apart from bounded end effects, at least keys lie on either side. Thus the selection cost satisfies , since the fractions sum to . A strong induction with sufficiently large linear coefficient absorbs the lower-order terms.