Cycle sort is an in-place, unstable sorting algorithm that sorts an array by repeatedly swapping elements until all elements are positioned correctly.

The cycle sort algorithm can be visualized as a cyclic graph, where each node represents an element of the array and the edges indicate their desired positions in the sorted array. The algorithm begins by detecting cycles within this graph and rearranging the elements along these cycles until every element is in its correct position.

To identify a cycle, the algorithm starts with the first element of the array and calculates its correct position in the sorted order. If the element is already in the correct position, the algorithm proceeds to the next element. However, if the element is not in its proper place, the algorithm swaps it with the element that is currently occupying its correct position. This process continues until the first element returns to its correct position, thereby completing one cycle.

Once a cycle is completed, the algorithm moves on to the next unprocessed element in the array to identify the next cycle. This procedure is repeated until all elements have been processed and are correctly positioned.

A notable feature of cycle sort is its ability to minimize the number of memory writes, making it particularly advantageous in scenarios where write operations are expensive. However, it is important to note that cycle sort is not a stable sorting algorithm, which means that equal elements may lose their original relative order in the sorted array.

In terms of time complexity, cycle sort is less efficient compared to other sorting algorithms. Both the worst-case and average time complexity is $O(n^2)$, which can lead to inefficiencies when handling large data sets. On the other hand, its space complexity is $O(1)$, indicating that it requires a constant amount of additional space, regardless of the size of the input array.

In summary, cycle sort is a distinctive sorting algorithm that organizes elements by identifying cycles within the array. While it is not the most time-efficient sorting method, it stands out for its ability to minimize memory writes and maintain a constant space usage.