← Back to Index

Lecture 1 Sorting I

Selection Sort

Given an array of N integers, write a program to implement the Selection sorting algorithm.

Example 1:
Input: N = 6, array[] = {13,46,24,52,20,9}
Output: 9,13,20,24,46,52
Explanation: After sorting the array is: 9, 13, 20, 24, 46, 52

Example 2:
Input: N=5, array[] = {5,4,3,2,1}
Output: 1,2,3,4,5
Explanation: After sorting the array is: 1, 2, 3, 4, 5

Approach 1

• Take the smallest and replace with i

def selection_sort(nums):
    n = len(nums)

    for i in range(n-1):
        for j in range(i+1,n):
            if nums[j] < nums[i]:
                nums[i],nums[j] = nums[j],nums[i]

    return nums

print(selection_sort([13,46,24,52,20,9]))
print(selection_sort([5,4,3,2,1]))

[9, 13, 20, 24, 46, 52]
[1, 2, 3, 4, 5]

complexity analysus

• O(N^2) : N = len(nums)
• O(1)

Bubble Sort

Given an array of N integers, write a program to implement the Bubble sorting algorithm.

Example 1:
Input: N = 6, array[] = {13,46,24,52,20,9}
Output: 9,13,20,24,46,52
Explanation: After sorting the array is: 9, 13, 20, 24, 46, 52

Example 2:
Input: N=5, array[] = {5,4,3,2,1}
Output: 1,2,3,4,5
Explanation: After sorting the array is: 1, 2, 3, 4, 5

Approach 1

• just keep swapping left and right
• once there are not swaps , it means sorted

def bubble_sort(nums):
    n = len(nums)

    for i in range(n):
        swapped = False
        for j in range(n-1):
            if nums[j] > nums[j+1]:
                nums[j],nums[j+1] = nums[j+1],nums[j]
                swapped = True
        
        if not swapped:
            return nums

    return nums

print(bubble_sort([13,46,24,52,20,9]))
print(bubble_sort([5,4,3,2,1]))

[9, 13, 20, 24, 46, 52]
[1, 2, 3, 4, 5]

complexity analysus

• O(N^2) : N = len(nums)
• O(1)

Insertion Sort

Given an array of N integers, write a program to implement the Insertion sorting algorithm.

Example 1:
Input: N = 6, array[] = {13,46,24,52,20,9}
Output: 9,13,20,24,46,52
Explanation: After sorting the array is: 9, 13, 20, 24, 46, 52

Example 2:
Input: N=5, array[] = {5,4,3,2,1}
Output: 1,2,3,4,5
Explanation: After sorting the array is: 1, 2, 3, 4, 5

Approach 1

• assume first element is sorted
• not insert the elements from 1 to n to correct sorted position

def insertion_sort(nums):
    n = len(nums)

    for i in range(1,n):
        j = i-1
        while j>=0 and  nums[j+1] < nums[j]:
            nums[j+1],nums[j] = nums[j],nums[j+1]
            j-=1

    return nums

print(insertion_sort([13,46,24,52,20,9]))
print(insertion_sort([5,4,3,2,1]))

[9, 13, 20, 24, 46, 52]
[1, 2, 3, 4, 5]

complexity analysus

• O(N^2) : N = len(nums)
• O(1)