Cyclic Sort is a specialized sorting algorithm that is particularly useful for sorting arrays where each element is in the range from 1 to n (or 0 to n-1), and each element appears exactly once or is missing at most one element. The algorithm works by placing each element in its correct position in the array.

Process

1. Initialization: Start by iterating through the array.

2. Placement: For each element, check if it is already in its correct position (i.e., the element at index i should be i+1 for 1-based indexing or i for 0-based indexing). Swap it with the element at its correct index if incorrectly positioned.

3. Cyclic Swap: Continue swapping the element with the element at its correct index until the current index is in its correct position.

4. Iteration: Move to the next element in the array and repeat the process until all elements are in their correct positions.

5. Termination: The process terminates when all elements have been processed and are in their correct positions.

When to Use

1. Finding Missing Numbers: To find missing numbers in an array where each number from 1 to n should appear exactly once.

2. Finding Duplicates: To identify duplicate numbers in an array where each number from 1 to n should appear exactly once.

3. Sorting Permutations: To sort arrays that are permutations of the numbers from 1 to n.

How Does It Reduce Time Complexity?

1. Linear Time Complexity: The cyclic sort algorithm has a time complexity of O(n), where n is the number of elements in the array. This is because each element is constantly moved into its correct position and is processed at most once.

2. In-Place Sorting: The algorithm sorts the array in place without requiring additional space, making it space-efficient.

Example problem for better understanding

Missing Number

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