# Insertion Sort

**Topics:**Sorting algorithm, Insertion sort, Big O notation

**Pages:**3 (690 words)

**Published:**January 30, 2012

Insertion sort belongs to the O(n2) sorting algorithms. Unlike many sorting algorithms with quadratic complexity, it is actually applied in practice for sorting small arrays of data. For instance, it is used to improve quicksort routine. Some sources notice, that people use same algorithm ordering items, for example, hand of cards. Algorithm

Insertion sort algorithm somewhat resembles selection sort. Array is imaginary divided into two parts - sorted one and unsorted one. At the beginning, sorted part contains first element of the array and unsorted one contains the rest. At every step, algorithm takes first element in the unsorted part and inserts it to the right place of the sorted one. When unsorted part becomes empty, algorithm stops. Sketchy, insertion sort algorithm step looks like this: [pic]

becomes

[pic]

The idea of the sketch was originaly posted here.

Let us see an example of insertion sort routine to make the idea of algorithm clearer. Example. Sort {7, -5, 2, 16, 4} using insertion sort.

[pic]

The ideas of insertion

The main operation of the algorithm is insertion. The task is to insert a value into the sorted part of the array. Let us see the variants of how we can do it. "Sifting down" using swaps

The simplest way to insert next element into the sorted part is to sift it down, until it occupies correct position. Initially the element stays right after the sorted part. At each step algorithm compares the element with one before it and, if they stay in reversed order, swap them. Let us see an illustration. [pic]

This approach writes sifted element to temporary position many times. Next implementation eliminates those unnecessary writes. Shifting instead of swapping

We can modify previous algorithm, so it will write sifted element only to the final correct position. Let us see an illustration. [pic]

It is the most commonly used modification of the insertion sort. Using binary search

It is reasonable to use binary search...

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