Sorting Unique Integers Without Built-in Functions in Python

Introduction:
Sorting a list of unique integers is a common task in programming, often requiring efficient algorithms to achieve the desired result. In this tutorial, we’ll explore how to implement a Python function to sort unique integers in ascending order without using any built-in sort functions. We’ll delve into the insertion sort algorithm and demonstrate its application in sorting unique integers efficiently.

Understanding the Problem:
Given a list of integers, our task is to sort the unique integers in ascending order. We need to remove any duplicates while preserving the original order of elements in the list.

Efficient Solution Approach:
To efficiently sort unique integers without using built-in sort functions, we’ll employ the following approach:

1. Remove duplicates from the list while preserving the original order.
2. Implement the insertion sort algorithm to sort the unique integers in ascending order.

Insertion Sort Algorithm:
Insertion sort is a simple sorting algorithm that builds the final sorted list one item at a time. It iterates through the input list, shifting elements as necessary to insert each element into its correct position.

Implementation in Python:

def unique_sort(nums):
    # Remove duplicates while preserving original order
    unique_nums = list(dict.fromkeys(nums))

    # Implement insertion sort algorithm
    for i in range(1, len(unique_nums)):
        key = unique_nums[i]
        j = i - 1
        while j >= 0 and unique_nums[j] > key:
            unique_nums[j + 1] = unique_nums[j]
            j -= 1
        unique_nums[j + 1] = key

    return unique_nums

# Example usage:
nums = [4, 2, 6, 2, 4, 7, 8, 9, 1, 3, 5, 9]
print(unique_sort(nums))  # Output: [1, 2, 3, 4, 5, 6, 7, 8, 9]

Explanation:

• We first remove duplicates from the input list nums while preserving the original order using the dict.fromkeys() method.
• Then, we implement the insertion sort algorithm to sort the unique numbers in ascending order.
• Finally, we return the sorted list of unique integers.

Conclusion:
By leveraging the insertion sort algorithm and efficient techniques for removing duplicates, we’ve successfully implemented a Python function to sort unique integers without using any built-in sort functions. Understanding these algorithms and techniques is essential for mastering sorting operations and enhancing your programming skills. Happy coding!