divide_and_conquer.kth_order_statistic

Find the kth smallest element in linear time using divide and conquer. Recall we can do this trivially in O(nlogn) time. Sort the list and access kth element in constant time.

This is a divide and conquer algorithm that can find a solution in O(n) time.

For more information of this algorithm: https://web.stanford.edu/class/archive/cs/cs161/cs161.1138/lectures/08/Small08.pdf

Functions

kth_number(→ int)	Return the kth smallest number in lst.
random_pivot(lst)	Choose a random pivot for the list.

Module Contents

divide_and_conquer.kth_order_statistic.kth_number(lst: list[int], k: int) → int

Return the kth smallest number in lst. >>> kth_number([2, 1, 3, 4, 5], 3) 3 >>> kth_number([2, 1, 3, 4, 5], 1) 1 >>> kth_number([2, 1, 3, 4, 5], 5) 5 >>> kth_number([3, 2, 5, 6, 7, 8], 2) 3 >>> kth_number([25, 21, 98, 100, 76, 22, 43, 60, 89, 87], 4) 43

divide_and_conquer.kth_order_statistic.random_pivot(lst)

Choose a random pivot for the list. We can use a more sophisticated algorithm here, such as the median-of-medians algorithm.