From d14ef693953bafcf65baf95fa69b373baf2d6d83 Mon Sep 17 00:00:00 2001
From: Mohit Chakraverty <79406819+mohitchakraverty@users.noreply.github.com>
Date: Sat, 13 Aug 2022 00:50:58 +0530
Subject: [PATCH] docs(en): add cycle sort (#799)

---
 docs/en/README.md             |  1 +
 docs/en/Sorting/Cycle-Sort.md | 91 +++++++++++++++++++++++++++++++++++
 2 files changed, 92 insertions(+)
 create mode 100644 docs/en/Sorting/Cycle-Sort.md

diff --git a/docs/en/README.md b/docs/en/README.md
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--- a/docs/en/README.md
+++ b/docs/en/README.md
@@ -8,6 +8,7 @@
 - [Insertion Sort](./Sorting/Insertion-Sort.md)
 - [Heap Sort](./Sorting/Heap-Sort.md)
 - [Quick Sort](./Sorting/Quick-Sort.md)
+- [Cycle Sort](./Sorting/Cycle-Sort.md)
 
 ## Strings
 
diff --git a/docs/en/Sorting/Cycle-Sort.md b/docs/en/Sorting/Cycle-Sort.md
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+# 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)
\ No newline at end of file