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Insertion Sort Algorithm

If the first few objects are already sorted, an unsorted object can be inserted in the sorted set in proper place. This is called insertion sort. An algorithm consider the elements one at a time, inserting each in its suitable place among those already considered (keeping them sorted). Insertion sort is an example of an incremental algorithm; it builds the sorted sequence one number at a time. This is perhaps the simplest example of the incremental insertion technique, where we build up a complicated structure on n items by first building it on n − 1 items and then making the necessary changes to fix things in adding the last item. The given sequences are typically stored in arrays. We also refer the numbers as keys. Along with each key may be additional information, known as satellite data. [Note that "satellite data" does not necessarily come from satellite!]

Algorithm: Insertion Sort

It works the way you might sort a hand of playing cards:

1. We start with an empty left hand [sorted array] and the cards face down on the table [unsorted array].

2. Then remove one card [key] at a time from the table [unsorted array], and insert it into the correct position in the left hand [sorted array].

3. To find the correct position for the card, we compare it with each of the cards already in the hand, from right to left.

Note that at all times, the cards held in the left hand are sorted, and these cards were originally the top cards of the pile on the table.

Pseudocode

We use a procedure INSERTION_SORT. It takes as parameters an array A[1.. n] and the length n of the array. The array A is sorted in place: the numbers are rearranged within the array, with at most a constant number outside the array at any time.

INSERTION_SORT (A)

Example: Following figure (from CLRS) shows the operation of INSERTION-SORT on the array A = (5, 2, 4, 6, 1, 3). Each part shows what happens for a particular iteration with the value of j indicated. j indexes the "current card" being inserted into the hand.

Read the figure row by row. Elements to the left of A[j] that are greater than A[j] move one position to the right, and A[j] moves into the evacuated position.