 # Selection Sort Algorithm

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.

## Working of Selection Sort

1. Set the first element as `minimum`. Select first element as minimum
2. 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
3. After each iteration, `minimum` is placed in the front of the unsorted list. Swap the first with minimum

## 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 < currentMinimum
set element as new minimum
swap minimum with first unsorted position
end selectionSort``````

## Selection Sort Code in Python, Java, and C/C++

``````# 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)``````
``````// 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));
}
}``````
``````// 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);
selectionSort(data, size);
printf("Sorted array in Acsending Order:\n");
printArray(data, size);
}``````
``````// 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);
selectionSort(data, size);
cout << "Sorted array in Acsending Order:\n";
printArray(data, size);
}``````

## Selection Sort Complexity

Time Complexity Space Complexity Best O(n2) Worst O(n2) Average O(n2) O(1) 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.

## 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)