The Cyclic Sort pattern is used when dealing with an array containing numbers in a given range. It involves iterating through the array and placing each number at its correct index by swapping elements. Here's an example to help you understand the pattern better:

Problem: Given an unsorted array containing numbers from 1 to n with one number missing, find the missing number.

Example:

Input: [4, 2, 3, 1, 6] Output: 5

In this problem, the array should contain numbers from 1 to n, but the number 5 is missing. We can solve this problem using the Cyclic Sort pattern as follows:

def find_missing_number(nums):
    i = 0
    while i < len(nums):
        correct_index = nums[i] - 1  # Calculate the index where the current number should be
        if nums[i] != nums[correct_index]:  # If the number is not at its correct index, swap
            nums[i], nums[correct_index] = nums[correct_index], nums[i]
        else:
            i += 1

    # Find the missing number
    for i in range(len(nums)):
        if nums[i] != i + 1:
            return i + 1

    # If no missing number found, return n + 1
    return len(nums) + 1

Let's analyze the code:

1. We start by initializing the i pointer to 0 and iterate through the array.
2. For each number nums[i], we calculate the correct index where it should be placed (nums[i] - 1).
3. If the number is not already at its correct index, we swap it with the number at its correct index.
4. If the number at the current index is already in its correct position, we move to the next index.
5. After the cyclic sort is complete, we iterate through the sorted array and find the missing number (the first number that is not at its correct index).
6. If no missing number is found, we return len(nums) + 1 as the missing number (since all numbers from 1 to n are present).

Now, let's test the function using the example input:

nums = [4, 2, 3, 1, 6]
missing_number = find_missing_number(nums)
print(missing_number)  # Output: 5

The missing number is correctly identified as 5 using the Cyclic Sort pattern.

The Cyclic Sort pattern can be applied to solve various other problems, such as finding the smallest missing positive number, finding all missing numbers, or finding duplicate numbers. The underlying idea remains the same - placing each number at its correct index using swaps.