Timsort is a fast sorting algorithm working at stable O(N log(N)) complexity
Timsort is a blend on Insertion Sort and Mergesort. This algorithm is implemented in Java’s Arrays.sort() as well as Python’s sorted() and sort()
The smaller part are sorted using Insertion Sort and is later merged together using Mergesort.
A quick implementation in Python:
def binary_search(the_array, item, start, end): if start == end: if the_array[start] > item: return start else: return start + 1 if start > end: return start mid = round((start + end)/ 2) if the_array[mid] < item: return binary_search(the_array, item, mid + 1, end) elif the_array[mid] > item: return binary_search(the_array, item, start, mid - 1) else: return mid """ Insertion sort that timsort uses if the array size is small or if the size of the "run" is small """ def insertion_sort(the_array): l = len(the_array) for index in range(1, l): value = the_array[index] pos = binary_search(the_array, value, 0, index - 1) the_array = the_array[:pos] + [value] + the_array[pos:index] + the_array[index+1:] return the_array def merge(left, right): """Takes two sorted lists and returns a single sorted list by comparing the elements one at a time. [1, 2, 3, 4, 5, 6] """ if not left: return right if not right: return left if left < right: return [left] + merge(left[1:], right) return [right] + merge(left, right[1:]) def timsort(the_array): runs, sorted_runs = ,  length = len(the_array) new_run = [the_array] # for every i in the range of 1 to length of array for i in range(1, length): # if i is at the end of the list if i == length - 1: new_run.append(the_array[i]) runs.append(new_run) break # if the i'th element of the array is less than the one before it if the_array[i] < the_array[i-1]: # if new_run is set to None (NULL) if not new_run: runs.append([the_array[i]]) new_run.append(the_array[i]) else: runs.append(new_run) new_run =  # else if its equal to or more than else: new_run.append(the_array[i]) # for every item in runs, append it using insertion sort for item in runs: sorted_runs.append(insertion_sort(item)) # for every run in sorted_runs, merge them sorted_array =  for run in sorted_runs: sorted_array = merge(sorted_array, run) print(sorted_array) timsort([2, 3, 1, 5, 6, 7])
Tim sort has a stable Complexity of O(N log(N)) and compares really well with Quicksort.
A comaprison of complexities can be found on this chart