91 lines
2.3 KiB
Markdown
91 lines
2.3 KiB
Markdown
|
# Cycle Sort
|
||
|
|
|
||
|
|
Cycle sort is a comparison sorting algorithm that forces array to be factored into the number of cycles where each of them can be rotated to produce a sorted array. It is theoretically optimal in the sense that it reduces the number of writes to the original array.
|
||
|
|
It is an in-place and unstable sorting algorithm.
|
||
|
|
|
||
|
|
Time Complexity : O(n^2)
|
||
|
|
- Worst Case : O(n^2)
|
||
|
|
- Average Case: O(n^2)
|
||
|
|
- Best Case : O(n^2)
|
||
|
|
|
||
|
|
Space complexity :
|
||
|
|
The space complexity is constant cause this algorithm is in place so it does not use any extra memory to sort.
|
||
|
|
Auxiliary space: O(1)
|
||
|
|
|
||
|
|
## Steps
|
||
|
|
|
||
|
|
Suppose there is an array **arr** with **n** distinct elements. Given an element **A**, we can find its index by counting the number of elements smaller than **A**.
|
||
|
|
|
||
|
|
1. If the element is at its correct position, simply leave it as it is.
|
||
|
|
2. Else, we have to find the correct position of **A** by counting the number of elements smaller than it. Another element **B** is replaced to be moved to its correct position. This process continues until we get an element at the original position of **A**.
|
||
|
|
|
||
|
|
The above-illustrated process constitutes a cycle. Repeat this cycle for every element of the list until the list is sorted.
|
||
|
|
|
||
|
|
## Example
|
||
|
|
|
||
|
|
arr[] = {10, 5, 2, 3}
|
||
|
|
|
||
|
|
index = 0 1 2 3
|
||
|
|
|
||
|
|
cycle_start = 0
|
||
|
|
|
||
|
|
item = 10 = arr[0]
|
||
|
|
|
||
|
|
Find position where we put the item
|
||
|
|
|
||
|
|
pos = cycle_start
|
||
|
|
|
||
|
|
i=pos+1
|
||
|
|
|
||
|
|
while(i < n)
|
||
|
|
|
||
|
|
if (arr[i] < item)
|
||
|
|
|
||
|
|
pos++;
|
||
|
|
|
||
|
|
We put 10 at arr[3] and change item to
|
||
|
|
old value of arr[3].
|
||
|
|
|
||
|
|
arr[] = {10, 5, 2, 10}
|
||
|
|
|
||
|
|
item = 3
|
||
|
|
|
||
|
|
Again rotate rest cycle that start with index '0'
|
||
|
|
|
||
|
|
Find position where we put the item = 3
|
||
|
|
|
||
|
|
we swap item with element at arr[1] now
|
||
|
|
|
||
|
|
arr[] = {10, 3, 2, 10}
|
||
|
|
|
||
|
|
item = 5
|
||
|
|
|
||
|
|
Again rotate rest cycle that start with index '0' and item = 5
|
||
|
|
|
||
|
|
we swap item with element at arr[2].
|
||
|
|
|
||
|
|
arr[] = {10, 3, 5, 10 }
|
||
|
|
|
||
|
|
item = 2
|
||
|
|
|
||
|
|
Again rotate rest cycle that start with index '0' and item = 2
|
||
|
|
|
||
|
|
arr[] = {2, 3, 5, 10}
|
||
|
|
|
||
|
|
Above is one iteration for cycle_stat = 0.
|
||
|
|
|
||
|
|
Repeat above steps for cycle_start = 1, 2, ..n-2
|
||
|
|
|
||
|
|
## Implementation
|
||
|
|
|
||
|
|
- [C++](../../../algorithms/CPlusPlus/Sorting/cycle-sort.cpp)
|
||
|
|
- [Java](../../../algorithms/Java/sorting/cyclic-sort.java)
|
||
|
|
- [Python](../../../algorithms/Python/sorting/count-sort.py)
|
||
|
|
|
||
|
|
## Video URL
|
||
|
|
|
||
|
|
[Youtube Video about Cycle Sort](https://youtu.be/gZNOM_yMdSQ)
|
||
|
|
|
||
|
|
## Other
|
||
|
|
|
||
|
|
[Wikipedia](https://en.wikipedia.org/wiki/Cycle_sort)
|