didactics (14)

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 and you may cover these at university. However, insertion sort provides several advantages:

·         simple implementation

·         efficient on small data sets

·         uses a fixed amount of memory when running

Insertion sort requires the use of two arrays, one ordered, and one unordered. Each repetition of the algorithm moves an item from the unordered list, into a sorted position in the ordered list, until there are no elements left in the unordered list.

Sorting is typically done in-place without needing extra memory. The resulting array after k iterations has the property where the first k + 1 entries are sorted. In each iteration the first remaining entry of the input is removed, inserted into the result at the correct position, thus extending the result:

becomes

with each element greater than x copied to the right as it is compared against x.

Animation of the insertion sort sorting a 30 element array. Notice how the ordered array (left hand side) slowly consumes the unordered array (right hand side), until the entire data set is ordered

 for i ← 1 to i ← length(A)-1

   {

     // A[ i ] is added in the sorted sequence A[0, .. i-1]

     // save A[i] to make a hole at index iHole

     item ← A[i]

     iHole ← i

     // keep moving the hole to next smaller index until A[iHole - 1] is <= item

     while iHole > 0 and A[iHole - 1] > item

       {

         // move hole to next smaller index

         A[iHole] ← A[iHole - 1]

         iHole ← iHole - 1

       }

     // put item in the hole

     A[iHole] ← item

   }

' a procedure to sort an array of integers

From

https://en.wikibooks.org/wiki/A-level_Computing/AQA/Paper_1/Fundamentals_of_algorithms/Sorting_algorithms

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