Cycle sort is an in-place, unstable sorting algorithm that minimizes the number of writes performed during the sorting process. It was developed by Ralph E. Bryant in 1969 and is particularly efficient when the input array contains a large number of duplicate elements.
The algorithm divides the input array into cycles and performs a series of swaps within each cycle until all elements are in their correct positions. A cycle is formed by moving an element to its correct position, which in turn displaces the element previously at that position, continuing this process until a cycle is completed.
Here's a step-by-step explanation of the cycle sort algorithm −
Start with an unsorted input array of size n.
Initialize the current index, i, as 0.
Iterate through the array elements using a loop.
For each element at index i, perform the following steps:
a. Set the element's value, val, as the current element at index i.
b. Find the correct position, pos, for val in the array.
pos is the index where val should be placed if the array were sorted.
Iterate through the array elements from index i+1 to n-1 and count the number of elements smaller than val. pos should be equal to i + count.
c. If pos is equal to i, it means the element is already in its correct position, so move to the next element.
d. Otherwise, swap the element at pos with val, which places val in its correct position and displaces the element previously at pos.
e. Increment a variable, writes, to keep track of the number of writes (swaps) performed.
f. Repeat steps b-d until val is in its correct position.
Increment i by 1 and repeat steps 4-5 until i reaches n-1.
The array is now sorted, and the number of writes performed is stored in the writes variable.
Cycle sort has a time complexity of O(n^2) in the worst case, which occurs when the input array is completely reversed. However, it performs better when there are fewer unique elements in the array, as it reduces the number of writes. The algorithm's space complexity is O(1) since it performs sorting in-place.
Cycle sort is often used in scenarios where the cost of writing to memory is high, such as embedded systems or when sorting data with expensive swap operations.
Characteristics
In-place sorting: Cycle sort sorts the array in-place, meaning it does not require any additional memory beyond the input array.
Unstable sorting: Cycle sort is an unstable sorting algorithm, which means it does not necessarily preserve the relative order of elements with equal values. If the order of equal elements is important, an additional step or data structure is needed to maintain it.
Minimal writes: One of the key advantages of cycle sort is its ability to minimize the number of writes (swaps) performed during the sorting process. This makes it efficient when writing to memory is costly or time-consuming.
Advantages
Efficiency with duplicate elements: Cycle sort performs particularly well when there are a large number of duplicate elements in the input array. It minimizes redundant swaps by finding the correct position for each element and avoids unnecessary operations.
In-place sorting: Since cycle sort operates in-place, it does not require additional memory allocation for sorting, making it memory-efficient.
Limitations
Time complexity: The worst-case time complexity of cycle sort is O(n^2), which occurs when the input array is already sorted in reverse order. This time complexity can be a disadvantage when dealing with large or partially sorted arrays.
Not suitable for large arrays: Due to its time complexity, cycle sort is not considered suitable for large arrays. Other sorting algorithms, such as merge sort or quicksort, are more efficient in such cases.
Not a general-purpose sorting algorithm: Cycle sort's efficiency stems from its ability to minimize writes, but it may not perform as well in scenarios where the cost of writing is relatively low. Other sorting algorithms, like insertion sort or merge sort, may be more suitable for general-purpose sorting tasks.
Use cases
Embedded systems: Cycle sort is often used in embedded systems or scenarios where memory resources are limited, and the cost of writes is high. It optimizes the number of writes and reduces memory overhead.
Expensive swap operations: If the cost of swapping elements is high compared to other operations, cycle sort can be beneficial as it minimizes the number of swaps required.
Overall, cycle sort is a specialized sorting algorithm that excels in scenarios with duplicate elements and high write costs. While it may not be the go-to choice for general-purpose sorting tasks, it provides a valuable solution in specific contexts where minimizing writes is crucial.