Selection sort - Definition and Overview

Selection sort is a sort algorithm that works as follows:

• find the minimum value in the list
• swap it with the value in the first position
• find the minimum value amongst the remaining values
• swap it with the value in the second position
• repeat until the list is sorted

If you had to invent a sort algorithm on your own, you'd probably write an algorithm similar to selection sort because it is probably the most intuitive and immediate to invent.

An evolution of selection sort remembers the index of the minimum element that it finds in each pass. At the end of each pass it makes one exchange. This is more efficient because it reduces the total number of swaps, which cannot be bigger than the number n of elements to sort.

The naïve algorithm, iterating through a list of n unsorted items, has a worst-case, average-case, and best-case run-time of Θ(n²), assuming that comparisons can be done in constant time. Thus it is outperformed on almost-sorted lists by insertion sort.

Heapsort greatly improves the basic algorithm by using a heap data structure to speed up finding and removing the lowest datum.

Implementations of the basic Selection Sort

Implementation in C:

for(i=0 ; i<n-1 ; i++)
{
   for(j=i+1 ; j<n ; j++)
   {
      if(x[i] > x[j])
      {
         temp=x[j];
         x[j]=x[i];
         x[i]=temp;
      }
   }
}

Implementation in Basic:

For i = 1 To n - 1
   For j = i + 1 To n
      If x(i) > x(j) Then
         temp = x(i)
         x(i) = x(j)
         x(j) = temp
      End If
   Next j
Next i

Implementations of the evolved Selection Sort

Implementation in C:

void selection_sort (int arr[], int n){
  int i, j, min, min_i;

  for (i = 0; i < n-1; i++){
    min = arr[i];
    min_i = i;

    for (j = i+1; j < n; j++){
      if (arr[j] < min){
        min = arr[j];
        min_i = j;
      }
    }

    arr[i] ^= arr[min_i];
    arr[min_i] ^= arr[i];
    arr[i] ^= arr[min_i];
  }
} 

Implementation in Java (iterative):

   public static void selectionSort (int[] numbers)
   {
      int min, temp;

      for (int index = 0; index < numbers.length-1; index++)
      {
         min = index;
         for (int scan = index+1; scan < numbers.length; scan++)
            if (numbers[scan] < numbers[min])
               min = scan;

         // Swap the values
         temp = numbers[min];
         numbers[min] = numbers[index];
         numbers[index] = temp;
      }
   }

Implementation in Java (recursive):

	// Selection sort for an array of ints
        public static int findMin(int[] array, int index)
	{ 
		int min = index - 1;
		if(index < array.length - 1) min = findMin(array, index + 1);
		if(array[index] < array[min]) min = index;
		return min;
	}
	
	public static void selectionSort(int[] array)
	{ 
		for(int left = 0; left < array.length - 1; left++)
		{
			swap(array, left, findMin(array, left));
		}
	}

	public static void swap(int[] array, int index1, int index2)
	{//swap the two values
		int temp = array[index1];
		array[index1] = array[index2];
		array[index2] = temp;
	}