Cycle Sort
- Ω( n2 )
- Θ( n2 )
- O( n2 )
- space O( 1 )
Array
Comparator strip
Index down, time to the right
- Comparisons count only element-against-element checks; loop and index checks are never counted.
- Reads and writes include reads and writes to helper buffers (merge, counting, radix, bucket and tim sort).
- A swap counts once, as a swap. It is never also counted as a read or a write.
- Real time is the average time of the counted sort on this device over repeated runs, measured once before playback and independent of animation speed. Visual time is the time spent animating, excluding pauses.
How cycle sort works
Cycle sort works out where each element belongs by counting how many elements are smaller, then writes it straight into that position, picking up the element it displaced and repeating until the cycle closes.
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It does the theoretical minimum number of writes to the array, which matters for memory such as flash where writes wear the device out. The price is O(n²) comparisons.
| Best time | Ω( n2 ) | poor |
|---|---|---|
| Average time | Θ( n2 ) | poor |
| Worst time | O( n2 ) | poor |
| Worst space | O( 1 ) | good |
Big O notation gives the lower, average and upper bounds of an algorithm. Time complexity bounds the number of operations; space complexity bounds the extra memory it uses.