Insertion sort

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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.[1]
  • 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
Quick facts: Class, Data structure, Worst-case performance...
Insertion sort
Animation of insertion sort
ClassSorting algorithm
Data structureArray
Worst-case performance comparisons and swaps
Best-case performance comparisons, swaps
Average performance comparisons and swaps
Worst-case space complexity total, auxiliary

When people manually sort cards in a bridge hand, most use a method that is similar to insertion sort.[2]