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| 1 | +# Cycle Sort |
| 2 | + |
| 3 | +#### Problem Statement |
| 4 | + |
| 5 | +Given an unsorted array of n elements, write a function to sort the array |
| 6 | + |
| 7 | +#### Approach |
| 8 | + |
| 9 | +- If the element is already at its correct position do nothing |
| 10 | +- Otherwise, find the correct position of a by counting the total number of elements that are less than current element |
| 11 | +- Insert current element into its correct position |
| 12 | +- Set replaced element as new current element and find its correct position |
| 13 | +- Continue process until array is sorted |
| 14 | + |
| 15 | +#### Time Complexity |
| 16 | + |
| 17 | +`O(n^2)` Worst case performance |
| 18 | + |
| 19 | +`O(n^2)` Best-case performance |
| 20 | + |
| 21 | +`O(n^2)` Average performance |
| 22 | + |
| 23 | +#### Space Complexity |
| 24 | + |
| 25 | +`O(n)` Worst case |
| 26 | + |
| 27 | +#### Application of algorithm |
| 28 | + |
| 29 | +- Cycle sort algorithm is useful for situations where memory write or element swap operations are costly. |
| 30 | + |
| 31 | +#### Example |
| 32 | + |
| 33 | +A single cycle of sorting array | b | d | e | a | c | |
| 34 | + |
| 35 | +``` |
| 36 | +1. Select element for which the cycle is run, i.e. "b". |
| 37 | + |
| 38 | +|b|d|e|a|c| |
| 39 | + |
| 40 | +b - current element |
| 41 | + |
| 42 | +2. Find correct location for current element and update current element. |
| 43 | + |
| 44 | +|b|b|e|a|c| |
| 45 | + |
| 46 | +d - current element |
| 47 | + |
| 48 | +3. One more time, find correct location for current element and update current element. |
| 49 | + |
| 50 | +|b|b|e|d|c| |
| 51 | + |
| 52 | +a - current element |
| 53 | + |
| 54 | +4. Current element is inserted into position of initial element "b" which ends the cycle. |
| 55 | + |
| 56 | +|a|b|e|d|c| |
| 57 | + |
| 58 | +a - current element |
| 59 | + |
| 60 | +5. New cycle should be started for next element. |
| 61 | +``` |
| 62 | + |
| 63 | +#### Video Explanation |
| 64 | + |
| 65 | +[A video explaining the Cycle Sort Algorithm](https://www.youtube.com/watch?v=gZNOM_yMdSQ) |
| 66 | + |
| 67 | +#### The Algorithms Page |
| 68 | + |
| 69 | +[Cycle Sort](https://the-algorithms.com/algorithm/cycle-sort) |
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