The Timsort algorithm is a hybrid of insertion sort and merge sort designed for real-world data, which often contains already sorted runs. Tim Peters created it for Python in 2002, and Java uses it to sort objects. Step through a simplified version below, then read how it works. Try it: A hybrid of insertion sort…
The radix sort algorithm sorts numbers one digit at a time, starting from the ones digit, using a stable bucket pass for each digit. For fixed-length keys it runs in linear time without comparing elements. Step through it below, then read how it works. Try it: Sort numbers digit by digit, starting from the ones…
The counting sort algorithm sorts integers without comparing them: it counts how many times each value appears, then writes the values back in order. When the range of values is small, it runs in linear time. Step through it below, then read how it works and its limits. Try it: Works for small integers (here…
The shell sort algorithm speeds up insertion sort by first sorting elements that are far apart, then shrinking the gap until it is 1. Moving items long distances early leaves very little work for the final pass. Step through it below, then read how it works. Try it: Insertion sort applied to elements that are…
The heap sort algorithm turns the list into a max-heap, then repeatedly moves the largest element to the end and repairs the heap. It guarantees O(n log n) time with only O(1) extra memory. Step through it below, then read how it works. Try it: First rearrange the list into a max-heap (every parent is…
The insertion sort algorithm builds a sorted list one item at a time, sliding each new number left until it sits in the right place, much like sorting a hand of playing cards. It is the fastest simple sort on small or nearly sorted lists. Step through it below, then read how it works. Try…
The selection sort algorithm sorts a list by repeatedly finding the smallest remaining number and swapping it into place at the front. It is simple, uses no extra memory and makes very few swaps, but it always does O(n²) comparisons. Step through it below, then read how it works and when to use it. Try…
The merge sort algorithm is a divide-and-conquer sort: split the list in half, sort each half, then merge the two sorted halves. It guarantees O(n log n) time and keeps equal items in order, which is why it sits at the heart of many library sorts. Step through it below, then read how it works….
The quick sort algorithm picks a pivot, moves smaller numbers to its left and larger ones to its right, then sorts each side the same way. It is one of the fastest general-purpose sorts in practice, with an O(n log n) average case. Step through it below, then read how it works and where it…
The bubble sort algorithm is the simplest way to sort a list: walk through it, compare each pair of neighbours, and swap them when they are in the wrong order. Step through it yourself below, then read how it works, what it costs, and when (rarely) you should use it. Try it: click Next to…