Insertion Sort

     Insertion sort is a simple sorting algorithm: a comparison sort in which the sorted array (or list) is built one entry at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages:

• Simple implementation
• Efficient for (quite) small data sets
• Adaptive, i.e. efficient for data sets that are already substantially sorted: the time complexity is O(n + d), where d is the number of inversions
• More efficient in practice than most other simple quadratic, i.e. O(n²) algorithms such as selection sort or bubble sort; the best case (nearly sorted input) is O(n)
• Stable, i.e. does not change the relative order of elements with equal keys
• In-place, i.e. only requires a constant amount O(1) of additional memory space
• Online, i.e. can sort a list as it receives it

Algorithm

     Every repetition of insertion sort removes an element from the input data, inserting it into the correct position in the already-sorted list, until no input elements remain. The choice of which element to remove from the input is arbitrary, and can be made using almost any choice algorithm.

The most common variant of insertion sort, which operates on arrays, can be described as follows:

1. Suppose there exists a function called Insert designed to insert a value into a sorted sequence at the beginning of an array. It operates by beginning at the end of the sequence and shifting each element one place to the right until a suitable position is found for the new element. The function has the side effect of overwriting the value stored immediately after the sorted sequence in the array.
2. To perform an insertion sort, begin at the left-most element of the array and invoke Insert to insert each element encountered into its correct position. The ordered sequence into which the element is inserted is stored at the beginning of the array in the set of indices already examined. Each insertion overwrites a single value: the value being inserted.

Reference:

http://en.wikipedia.org/wiki/Insertion_sort