# What is Cycle Sort

**Cycle sort**is an in-place, unstable sorting algorithm that minimizes the number of writes to memory. It is particularly useful when the cost of writing to memory is high, such as in embedded systems or when dealing with non-volatile storage devices.

The basic idea behind cycle sort is to divide the input array into cycles, where each cycle contains all elements that belong to the same position in the sorted output. The algorithm then iterates over each cycle, moving each element to its correct position in the output array. This is done by swapping the element with the one that should occupy its current position, and repeating this process until the original element returns to its correct position in the cycle.

In Simple terms:

Cycle sort is a way to sort a list of numbers by moving each number to its correct position one at a time. Imagine you have a deck of cards that are shuffled randomly, and you want to sort them by suit and number. You could use cycle sort by looking at each card in the deck and figuring out where it should go in the sorted deck. Then, you would take that card and move it to its correct position, and repeat this process for each card in the deck.

The key idea behind cycle sort is that you don't need to move every card in the deck to sort it. Instead, you can divide the deck into groups called cycles, where each cycle represents a set of cards that need to be moved to their correct positions. Then, you can move the cards within each cycle until they are all in their correct positions. By doing this, you can sort the deck with fewer moves than other sorting methods.

Cycle sort is especially useful when you have limited memory or need to sort data on a slow device, because it minimizes the number of writes to memory. However, it is not always the fastest sorting method, and it may not be the best choice for all types of data.

## Who invented it?

The

Brown and Card were computer scientists who were interested in finding new ways to sort data efficiently in the early days of computing. Their algorithm was designed to minimize the number of writes to memory, which was a key consideration at the time due to the high cost of memory and slow processing speeds of early computers.

Since its invention, Cycle sort has been used in various applications, including in embedded systems and in situations where memory usage is a concern. While it may not be the fastest sorting algorithm in all cases, it remains a useful tool in many contexts.

**Cycle sort algorithm**was invented by W.N. Brown and L.R. Card in 1956. They published their algorithm in a paper titled "An efficient method of sorting in computer memory" in the Communications of the ACM (Association for Computing Machinery) journal.Brown and Card were computer scientists who were interested in finding new ways to sort data efficiently in the early days of computing. Their algorithm was designed to minimize the number of writes to memory, which was a key consideration at the time due to the high cost of memory and slow processing speeds of early computers.

Since its invention, Cycle sort has been used in various applications, including in embedded systems and in situations where memory usage is a concern. While it may not be the fastest sorting algorithm in all cases, it remains a useful tool in many contexts.

## Pseudocode

```
cycleSort(array)
n = length(array)
for i = 0 to n - 2 do
item = array[i]
pos = i
for j = i + 1 to n - 1 do
if array[j] < item then
pos++
end if
end for
if pos == i then
continue
end if
while item == array[pos] do
pos++
end while
temp = array[pos]
array[pos] = item
item = temp
while pos != i do
pos = i
for j = i + 1 to n - 1 do
if array[j] < item then
pos++
end if
end for
while item == array[pos] do
pos++
end while
temp = array[pos]
array[pos] = item
item = temp
end while
end for
end function
```

In this pseudocode, array is the input array to be sorted, n is the length of the array, item is the current item being sorted, and pos is the current position of item in the array.

The algorithm iterates over each item in the array, finding its correct position in the sorted array using the pos variable. It then swaps the current item with the item at pos, and continues to swap items until each item has been moved to its correct position.

The algorithm iterates over each item in the array, finding its correct position in the sorted array using the pos variable. It then swaps the current item with the item at pos, and continues to swap items until each item has been moved to its correct position.

## Sample Code

```
// C++ code snippet
void cycleSort(int arr[], int n) {
for (int i = 0; i < n - 1; i++) {
int item = arr[i];
int pos = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < item) {
pos++;
}
}
if (pos == i) {
continue;
}
while (item == arr[pos]) {
pos++;
}
int temp = arr[pos];
arr[pos] = item;
item = temp;
while (pos != i) {
pos = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < item) {
pos++;
}
}
while (item == arr[pos]) {
pos++;
}
temp = arr[pos];
arr[pos] = item;
item = temp;
}
}
}
int main() {
int arr[] = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
int n = sizeof(arr) / sizeof(arr[0]);
cycleSort(arr, n);
cout << "Sorted array: ";
for (int i = 0; i < n; i++) {
cout << arr[i] << " ";
}
return 0;
}
```

```
# Python code snippet
def cycle_sort(arr):
n = len(arr)
for i in range(n - 1):
item = arr[i]
pos = i
for j in range(i + 1, n):
if arr[j] < item:
pos += 1
if pos == i:
continue
while arr[pos] == item:
pos += 1
arr[pos], item = item, arr[pos]
while pos != i:
pos = i
for j in range(i + 1, n):
if arr[j] < item:
pos += 1
while arr[pos] == item:
pos += 1
arr[pos], item = item, arr[pos]
if __name__ == "__main__":
arr = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
cycle_sort(arr)
print("Sorted array:", arr)
```

```
import java.util.Arrays;
public class CycleSort {
public static void cycleSort(int[] arr) {
int n = arr.length;
for (int i = 0; i < n - 1; i++) {
int item = arr[i];
int pos = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < item) {
pos++;
}
}
if (pos == i) {
continue;
}
while (arr[pos] == item) {
pos++;
}
int temp = arr[pos];
arr[pos] = item;
item = temp;
while (pos != i) {
pos = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < item) {
pos++;
}
}
while (arr[pos] == item) {
pos++;
}
temp = arr[pos];
arr[pos] = item;
item = temp;
}
}
}
public static void main(String[] args) {
int[] arr = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
cycleSort(arr);
System.out.println("Sorted array: " + Arrays.toString(arr));
}
}
```

## Time and Space Complexity

The time and space complexity of the Cycle sort algorithm are as follows:

- Time complexity: O(n^2) in the worst case and O(n) in the best case and average case.

- In the worst case, Cycle sort performs n passes through the input array, each of which takes O(n) time to complete, resulting in a total time complexity of O(n^2).

- In the best and average cases, Cycle sort may complete in fewer passes because some elements are already in their correct positions, resulting in a total time complexity of O(n).

- Space complexity: O(1), as Cycle sort only requires a constant amount of additional memory to store temporary variables used during sorting. The algorithm sorts the input array in-place without requiring additional space.

In practice, the performance of the Cycle sort algorithm depends on the specific input data and its initial ordering. It may perform well on partially sorted or nearly sorted data, but may be less efficient on highly unsorted data due to the number of passes required to fully sort the array.

- Time complexity: O(n^2) in the worst case and O(n) in the best case and average case.

- In the worst case, Cycle sort performs n passes through the input array, each of which takes O(n) time to complete, resulting in a total time complexity of O(n^2).

- In the best and average cases, Cycle sort may complete in fewer passes because some elements are already in their correct positions, resulting in a total time complexity of O(n).

- Space complexity: O(1), as Cycle sort only requires a constant amount of additional memory to store temporary variables used during sorting. The algorithm sorts the input array in-place without requiring additional space.

In practice, the performance of the Cycle sort algorithm depends on the specific input data and its initial ordering. It may perform well on partially sorted or nearly sorted data, but may be less efficient on highly unsorted data due to the number of passes required to fully sort the array.

## Advantages

- Cycle sort is an in-place sorting algorithm, meaning that it does not require any additional memory to sort the input data.
- It is a stable sorting algorithm, meaning that the relative order of equal elements is preserved after sorting.
- Cycle sort is efficient on small input sizes and partially sorted or nearly sorted data, and can outperform other O(n^2) algorithms in these cases.
- It has a low number of writes to memory, making it suitable for use in applications with limited memory or where minimizing write operations is important.

## Disadvantages

- Cycle sort has a worst-case time complexity of O(n^2), making it less efficient than many other sorting algorithms on highly unsorted data.
- It is not well-suited for large input sizes, as the number of passes through the input array increases linearly with the size of the input.
- The algorithm has a higher computational overhead due to the need for multiple passes through the input array, which can impact performance on certain input types.
- It is not a widely-used or well-known algorithm, which may make it less accessible to developers or less supported in certain programming languages or libraries.
- Overall, Cycle sort is a useful algorithm for certain use cases, but its limitations mean that it may not always be the best choice for sorting large or highly unsorted data.