# Understanding the Cyclic Sort algorithm

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

**Initialization**: Start by iterating through the array.**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.**Cyclic Swap**: Continue swapping the element with the element at its correct index until the current index is in its correct position.**Iteration**: Move to the next element in the array and repeat the process until all elements are in their correct positions.**Termination**: The process terminates when all elements have been processed and are in their correct positions.

### When to Use

**Finding Missing Numbers**: To find missing numbers in an array where each number from 1 to n should appear exactly once.**Finding Duplicates**: To identify duplicate numbers in an array where each number from 1 to n should appear exactly once.**Sorting Permutations**: To sort arrays that are permutations of the numbers from 1 to n.

### How Does It Reduce Time Complexity?

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

### Example problem for better understanding

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