Selection sort

Selection sort is a simple sorting algorithm. This sorting algorithm is an in-place comparison-based algorithm in which the list is divided into two parts, the sorted part at the left end and the unsorted part at the right end. Initially, the sorted part is empty and the unsorted part is the entire list.

The smallest element is selected from the unsorted array and swapped with the leftmost element, and that element becomes a part of the sorted array. This process continues moving unsorted array boundary by one element to the right.

How Selection Sort Works?

Consider the following elements are to be sorted in ascending order using selection sort-

6, 2, 11, 7, 5

Selection sort works as-

  • It finds the first smallest element (2).
  • It swaps it with the first element of the unordered list.
  • It finds the second smallest element (5).
  • It swaps it with the second element of the unordered list.
  • Similarly, it continues to sort the given elements.

As a result, sorted elements in ascending order are-

2, 5, 6, 7, 11

Algorithm of the Selection Sort Algorithm

The selection sort algorithm is as follows:

Step 1: Set Min to location 0 in Step 1.

Step 2: Look for the smallest element on the list.

Step 3: Replace the value at location Min with a different value.

Step 4: Increase Min to point to the next element

Step 5: Continue until the list is sorted.

 Example

Time Complexity Analysis-

  • Selection sort algorithm consists of two nested loops.
  • Owing to the two nested loops, it has O(n2) time complexity.

  • Best Case Complexity - It occurs when there is no sorting required, i.e. the array is already sorted. The best-case time complexity of selection sort is O(n2).
  • Average Case Complexity - It occurs when the array elements are in jumbled order that is not properly ascending and not properly descending. The average case time complexity of selection sort is O(n2).
  • Worst Case Complexity - It occurs when the array elements are required to be sorted in reverse order. That means suppose you have to sort the array elements in ascending order, but its elements are in descending order. The worst-case time complexity of selection sort is O(n2).

Space Complexity Analysis-

  • Selection sort is an in-place algorithm.
  • It performs all computation in the original array and no other array is used.
  • Hence, the space complexity works out to be O(1).

Important Notes-

  • Selection sort is not a very efficient algorithm when data sets are large.
  • This is indicated by the average and worst case complexities.
  • Selection sort uses minimum number of swap operations O(n) among all the sorting algorithms.

Applications of Selection Sort:

The selection sort technique has the following applications:

  • Applicable for smaller datasets.
  • Used in those algorithms where the cost of swapping does not matter.
  • It cannot work for online data. It needs to have all the array elements for each iteration.
  • Best suitable when the cost of writing in flash memory matters.

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