Cyclic Sort Pattern: Efficient Range-Based Sorting

In the realm of algorithmic problem-solving, the “Cyclic Sort” pattern is a powerful technique used to sort an array containing numbers within a specified range efficiently. This method is particularly valuable when dealing with problems that involve sorting elements within a known range or sequence. In this comprehensive guide, we will explore the Cyclic Sort pattern, understand its applications, delve into problem-solving strategies, and provide real-world examples to illustrate its practical relevance. The Cyclic Sort pattern is a valuable technique for sorting elements within a known range or sequence efficiently. By understanding its applications and employing appropriate strategies, you can efficiently tackle a wide range of algorithmic challenges. Whether you’re sorting elements within a specific range, detecting duplicates, transforming values, or counting frequencies, the Cyclic Sort pattern empowers you to navigate and manipulate array elements effectively, making it an essential tool in the world of algorithmic problem-solving.

The Cyclic Sort pattern is an algorithmic approach that focuses on sorting elements within a given range or sequence. It leverages the property that the elements are within a known range, which enables the algorithm to sort them in O(N) time complexity. The core idea is to place each element in its correct position within the range, achieving a sorted order.

Key Applications of the Cyclic Sort Pattern

1. Range-Based Sorting: Sorting elements within a known range or sequence, such as integers or characters.
2. Duplicate Detection: Identifying and handling duplicates efficiently within the range.
3. Value Transformation: Transforming values within the range to a specific order or format.
4. Frequency Counting: Counting the frequency of elements within the range.

Strategies for Cyclic Sort Problem Solving

1. Index-Based Sorting: Map each element to its correct index within the range, effectively placing it in its sorted position.
2. Loop-Based Sorting: Iterate through the array, swapping elements until each element is in its correct position.
3. Value Transformation: When sorting is accompanied by value transformations, map elements to their transformed values based on the desired order.

Real-World Examples

Let’s illustrate the Cyclic Sort pattern with real-world scenarios:

Example 1: Sorting Elements in a Known Range

Given an array containing distinct integers from 1 to N, sort the elements in-place.

def cyclicSort(nums):
    i = 0
    while i < len(nums):
        if nums[i] != i + 1:
            correct_index = nums[i] - 1
            nums[i], nums[correct_index] = nums[correct_index], nums[i]
        else:
            i += 1

def findDuplicate(nums):
    i = 0
    while i < len(nums):
        if nums[i] != i + 1:
            correct_index = nums[i] - 1
            if nums[i] == nums[correct_index]:
                return nums[i]
            nums[i], nums[correct_index] = nums[correct_index], nums[i]
        else:
            i += 1