Why is Insertion sort better than Quick sort for small list of elements?

Question

Isn\'t Insertion sort O(n^2) > Quicksort O(n log n)...so for a small n, won\'t the relation be the same?

Answer 1

Good real-world example when insertion sort can be used in conjunction with quicksort is the implementation of qsort function from glibc.

The first thing to point is qsort implements quicksort algorithm with a stack because it consumes less memory, stack implemented through macros directives.

Summary of current implementation from the source code (you'll find a lot of useful information through comments if you take a look at it):

1. Non-recursive

2. Chose the pivot element using a median-of-three decision tree

3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving insertion sort to order the MAX_THRESH items within each partition. This is a big win, since insertion sort is faster for small, mostly sorted array segments.

4. The larger of the two sub-partitions is always pushed onto the stack first

What is MAX_THRESH value stands for? Well, just a small constant magic value which

was chosen to work best on a Sun 4/260.