Selection Sort Algorithm

Table of Contents

1. Working of Selection Sort
2. Selection Sort Algorithm
3. Selection Sort Code in Python, Java, and C/C++
4. Selection Sort Complexity
5. Selection Sort Applications
6. Similar Sorting Algorithms

In this tutorial, you will learn about the selection sort algorithm and its implementation in Python, Java, C, and C++.

Selection sort is a sorting algorithm that selects the smallest element from an unsorted list in each iteration and places that element at the beginning of the unsorted list.

1. Working of Selection Sort

Set the first element as minimum.

Select first element as minimum

Compare minimum with the second element. If the second element is smaller than minimum, assign the second element as minimum.

Compare minimum with the third element. Again, if the third element is smaller, then assign minimum to the third element otherwise do nothing. The process goes on until the last element.

Compare minimum with the remaining elements

After each iteration, minimum is placed in the front of the unsorted list.

Swap the first with minimum

For each iteration, indexing starts from the first unsorted element. Step 1 to 3 are repeated until all the elements are placed at their correct positions.

The first iteration

The second iteration

The third iteration

The fourth iteration

2. Selection Sort Algorithm

selectionSort(array, size)
  repeat (size - 1) times
  set the first unsorted element as the minimum
  for each of the unsorted elements
    if element &lt; currentMinimum
      set element as new minimum
  swap minimum with first unsorted position
end selectionSort

3. Selection Sort Code in Python, Java, and C/C++

Source code by Python Language:

# Selection sort in Python
 
 
def selectionSort(array, size):
    
    for step in range(size):
        min_idx = step
 
        for i in range(step + 1, size):
          
            # to sort in descending order, change > to < in this line
            # select the minimum element in each loop
            if array[i] < array[min_idx]:
                min_idx = i
          
        # put min at the correct position
        (array[step], array[min_idx]) = (array[min_idx], array[step])
 
 
data = [-2, 45, 0, 11, -9]
size = len(data)
selectionSort(data, size)
print('Sorted Array in Ascending Order:')
print(data)

Source code by Java Language:

// Selection sort in Java
 
import java.util.Arrays;
 
class SelectionSort {
  void selectionSort(int array[]) {
    int size = array.length;
 
    for (int step = 0; step < size - 1; step++) {
      int min_idx = step;
 
      for (int i = step + 1; i < size; i++) {
 
        // To sort in descending order, change > to < in this line.
        // Select the minimum element in each loop.
        if (array[i] < array[min_idx]) {
          min_idx = i;
        }
      }
 
      // put min at the correct position
      int temp = array[step];
      array[step] = array[min_idx];
      array[min_idx] = temp;
    }
  }
 
  // driver code
  public static void main(String args[]) {
    int[] data = { 20, 12, 10, 15, 2 };
    SelectionSort ss = new SelectionSort();
    ss.selectionSort(data);
    System.out.println("Sorted Array in Ascending Order: ");
    System.out.println(Arrays.toString(data));
  }
}

Source code by C Language:

// Selection sort in C
 
#include <stdio.h>
 
// function to swap the the position of two elements
void swap(int *a, int *b) {
  int temp = *a;
  *a = *b;
  *b = temp;
}
 
void selectionSort(int array[], int size) {
  for (int step = 0; step < size - 1; step++) {
    int min_idx = step;
    for (int i = step + 1; i < size; i++) {
 
      // To sort in descending order, change > to < in this line.
      // Select the minimum element in each loop.
      if (array[i] < array[min_idx])
        min_idx = i;
    }
 
    // put min at the correct position
    swap(&array[min_idx], &array[step]);
  }
}
 
// function to print an array
void printArray(int array[], int size) {
  for (int i = 0; i < size; ++i) {
    printf("%d  ", array[i]);
  }
  printf("\n");
}
 
// driver code
int main() {
  int data[] = {20, 12, 10, 15, 2};
  int size = sizeof(data) / sizeof(data[0]);
  selectionSort(data, size);
  printf("Sorted array in Acsending Order:\n");
  printArray(data, size);
}

Source code by C++ Language:

// Selection sort in C++
 
#include <iostream>
using namespace std;
 
// function to swap the the position of two elements
void swap(int *a, int *b) {
  int temp = *a;
  *a = *b;
  *b = temp;
}
 
// function to print an array
void printArray(int array[], int size) {
  for (int i = 0; i < size; i++) {
    cout << array[i] << " ";
  }
  cout << endl;
}
 
void selectionSort(int array[], int size) {
  for (int step = 0; step < size - 1; step++) {
    int min_idx = step;
    for (int i = step + 1; i < size; i++) {
 
      // To sort in descending order, change > to < in this line.
      // Select the minimum element in each loop.
      if (array[i] < array[min_idx])
        min_idx = i;
    }
 
    // put min at the correct position
    swap(&array[min_idx], &array[step]);
  }
}
 
// driver code
int main() {
  int data[] = {20, 12, 10, 15, 2};
  int size = sizeof(data) / sizeof(data[0]);
  selectionSort(data, size);
  cout << "Sorted array in Acsending Order:\n";
  printArray(data, size);
}

4. Selection Sort Complexity

Time Complexity
Best	O(n²)
Worst	O(n²)
Average	O(n²)
Space Complexity	O(1)
Stability	No

Cycle	Number of Comparison
1st	(n-1)
2nd	(n-2)
3rd	(n-3)
…	…
last	1

Number of comparisons: (n - 1) + (n - 2) + (n - 3) + ..... + 1 = n(n - 1) / 2 nearly equals to n².

Complexity = O(n²)

Also, we can analyze the complexity by simply observing the number of loops. There are 2 loops so the complexity is n*n = n².

Time Complexities:

Worst Case Complexity: O(n²)
If we want to sort in ascending order and the array is in descending order then, the worst case occurs.
Best Case Complexity: O(n²)
It occurs when the array is already sorted
Average Case Complexity: O(n²)
It occurs when the elements of the array are in jumbled order (neither ascending nor descending).

The time complexity of the selection sort is the same in all cases. At every step, you have to find the minimum element and put it in the right place. The minimum element is not known until the end of the array is not reached.

Space Complexity:

Space complexity is O(1) because an extra variable temp is used.

5. Selection Sort Applications

The selection sort is used when

a small list is to be sorted
cost of swapping does not matter
checking of all the elements is compulsory
cost of writing to a memory matters like in flash memory (number of writes/swaps is O(n) as compared to O(n²) of bubble sort)