# Selection Sort

In computer science, **selection sort** is a sorting algorithm, specifically an in-place comparison sort. It has O(*n*^{2}) time complexity, making it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity, and it has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited.

The algorithm divides the input list into two parts: the sublist of items already sorted, which is built up from left to right at the front (left) of the list, and the sublist of items remaining to be sorted that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right.

Here is an example of this sort algorithm sorting five elements:

64 25 12 22 11 // this is the initial, starting state of the array 11 25 12 22 64 // sorted sublist = {11} 11 12 25 22 64 // sorted sublist = {11, 12} 11 12 22 25 64 // sorted sublist = {11, 12, 22} 11 12 22 25 64 // sorted sublist = {11, 12, 22, 25} 11 12 22 25 64 // sorted sublist = {11, 12, 22, 25, 64}

(Nothing appears changed on this last two lines because the last two numbers were already in order)

Selection sort can also be used on list structures that make add and remove efficient, such as a linked list. In this case it is more common to *remove* the minimum element from the remainder of the list, and then *insert* it at the end of the values sorted so far. For example:

64 25 12 22 11 11 64 25 12 22 11 12 64 25 22 11 12 22 64 25 11 12 22 25 64

/* a[0] to a[n-1] is the array to sort */ int i,j; int iMin; /* advance the position through the entire array */ /* (could do j < n-1 because single element is also min element) */ for (j = 0; j < n-1; j++) { /* find the min element in the unsorted a[j .. n-1] */ /* assume the min is the first element */ iMin = j; /* test against elements after j to find the smallest */ for ( i = j+1; i < n; i++) { /* if this element is less, then it is the new minimum */ if (a[i] < a[iMin]) { /* found new minimum; remember its index */ iMin = i; } } if(iMin != j) { swap(a[j], a[iMin]); } }