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Concept
Insertion sort
Summary
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. 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: Jon Bentley shows a three-line C/C++ version that is five lines when optimized.
Efficient for (quite) small data sets, much like other quadratic (i.e., O(n2)) sorting algorithms
More efficient in practice than most other simple quadratic algorithms such as selection sort or bubble sort
Adaptive, i.e., efficient for data sets that are already substantially sorted: the time complexity is O(kn) when each element in the input is no more than k places away from its sorted position
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
When people manually sort cards in a bridge hand, most use a method that is similar to insertion sort.
Insertion sort iterates, consuming one input element each repetition, and grows a sorted output list. At each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.
Sorting is typically done in-place, by iterating up the array, growing the sorted list behind it. At each array-position, it checks the value there against the largest value in the sorted list (which happens to be next to it, in the previous array-position checked). If larger, it leaves the element in place and moves to the next. If smaller, it finds the correct position within the sorted list, shifts all the larger values up to make a space, and inserts into that correct position.
The resulting array after k iterations has the property where the first k + 1 entries are sorted ("+1" because the first entry is skipped).
Official source
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