Cocktail shaker sort

Like most variants of bubble sort, cocktail shaker sort is used primarily as an educational tool. More efficient algorithms such as quicksort, merge sort, or timsort are used by the sorting libraries built into popular programming languages such as Python and Java.

Pseudocode

The simplest form goes through the whole list each time:

<b id="mwLA">procedure</b> cocktailShakerSort(A <b id="mwLQ">:</b> list of sortable items) <b id="mwLg">is</b> <b id="mwLw">do</b> swapped := false <b id="mwMA">for each</b> i <b id="mwMQ">in</b> 0 <b id="mwMg">to</b> length(A) − 2 <b id="mwMw">do:</b> <b id="mwNA">if</b> A[i] > A[i + 1] <b id="mwNQ">then</b> <span style="color:green" id="mwNg">// test whether the two elements are in the wrong order</span> swap(A[i], A[i + 1]) <span style="color:green" id="mwNw">// let the two elements change places</span> swapped := true <b id="mwOA">end if</b> <b id="mwOQ">end for</b> <b id="mwOg">if not</b> swapped <b id="mwOw">then</b> <span style="color:green" id="mwPA">// we can exit the outer loop here if no swaps occurred.</span> <b id="mwPQ">break do-while loop</b> <b id="mwPg">end if</b> swapped := false <b id="mwPw">for each</b> i <b id="mwQA">in</b> length(A) − 2 <b id="mwQQ">to</b> 0 <b id="mwQg">do:</b> <b id="mwQw">if</b> A[i] > A[i + 1] <b id="mwRA">then</b> swap(A[i], A[i + 1]) swapped := true <b id="mwRQ">end if</b> <b id="mwRg">end for</b> <b id="mwRw">while</b> swapped <span style="color:green" id="mwSA">// if no elements have been swapped, then the list is sorted</span> <b id="mwSQ">end procedure</b>

The first rightward pass will shift the largest element to its correct place at the end, and the following leftward pass will shift the smallest element to its correct place at the beginning. The second complete pass will shift the second largest and second smallest elements to their correct places, and so on. After i passes, the first i and the last i elements in the list are in their correct positions, and do not need to be checked. By shortening the part of the list that is sorted each time, the number of operations can be halved (see bubble sort).

This is an example of the algorithm in MATLAB/OCTAVE with the optimization of remembering the last swap index and updating the bounds.

<span id="mwUg"></span><span class="k" id="mwUw">function</span><span class="w" id="mwVA"> </span>A<span class="w" id="mwVQ"> </span><span class="p" id="mwVg">=</span><span class="w" id="mwVw"> </span><span class="nf" id="mwWA">cocktailShakerSort</span><span class="p" id="mwWQ">(</span>A<span class="p" id="mwWg">)</span> <span class="c" id="mwWw">% `beginIdx` and `endIdx` marks the first and last index to check</span> <span class="n" id="mwXA">beginIdx</span><span class="w" id="mwXQ"> </span><span class="p" id="mwXg">=</span><span class="w" id="mwXw"> </span><span class="mi" id="mwYA">1</span><span class="p" id="mwYQ">;</span> <span class="n" id="mwYg">endIdx</span><span class="w" id="mwYw"> </span><span class="p" id="mwZA">=</span><span class="w" id="mwZQ"> </span><span class="nb" id="mwZg">length</span><span class="p" id="mwZw">(</span><span class="n" id="mwaA">A</span><span class="p" id="mwaQ">)</span><span class="w" id="mwag"> </span><span class="o" id="mwaw">-</span><span class="w" id="mwbA"> </span><span class="mi" id="mwbQ">1</span><span class="p" id="mwbg">;</span> <span class="k" id="mwbw">while</span><span class="w" id="mwcA"> </span><span class="n" id="mwcQ">beginIdx</span><span class="w" id="mwcg"> </span><span class="o" id="mwcw"><=</span><span class="w" id="mwdA"> </span><span class="n" id="mwdQ">endIdx</span> <span class="w" id="mwdg"> </span><span class="n" id="mwdw">newBeginIdx</span><span class="w" id="mweA"> </span><span class="p" id="mweQ">=</span><span class="w" id="mweg"> </span><span class="n" id="mwew">endIdx</span><span class="p" id="mwfA">;</span> <span class="w" id="mwfQ"> </span><span class="n" id="mwfg">newEndIdx</span><span class="w" id="mwfw"> </span><span class="p" id="mwgA">=</span><span class="w" id="mwgQ"> </span><span class="n" id="mwgg">beginIdx</span><span class="p" id="mwgw">;</span> <span class="w" id="mwhA"> </span><span class="k" id="mwhQ">for</span><span class="w" id="mwhg"> </span><span class="n" id="mwhw">ii</span><span class="w" id="mwiA"> </span><span class="p" id="mwiQ">=</span><span class="w" id="mwig"> </span><span class="n" id="mwiw">beginIdx</span><span class="p" id="mwjA">:</span><span class="n" id="mwjQ">endIdx</span> <span class="w" id="mwjg"> </span><span class="k" id="mwjw">if</span><span class="w" id="mwkA"> </span><span class="n" id="mwkQ">A</span><span class="p" id="mwkg">(</span><span class="n" id="mwkw">ii</span><span class="p" id="mwlA">)</span><span class="w" id="mwlQ"> </span><span class="o" id="mwlg">></span><span class="w" id="mwlw"> </span><span class="n" id="mwmA">A</span><span class="p" id="mwmQ">(</span><span class="n" id="mwmg">ii</span><span class="w" id="mwmw"> </span><span class="o" id="mwnA">+</span><span class="w" id="mwnQ"> </span><span class="mi" id="mwng">1</span><span class="p" id="mwnw">)</span> <span class="w" id="mwoA"> </span><span class="p" id="mwoQ">[</span><span class="n" id="mwog">A</span><span class="p" id="mwow">(</span><span class="n" id="mwpA">ii</span><span class="o" id="mwpQ">+</span><span class="mi" id="mwpg">1</span><span class="p" id="mwpw">),</span><span class="w" id="mwqA"> </span><span class="n" id="mwqQ">A</span><span class="p" id="mwqg">(</span><span class="n" id="mwqw">ii</span><span class="p" id="mwrA">)]</span><span class="w" id="mwrQ"> </span><span class="p" id="mwrg">=</span><span class="w" id="mwrw"> </span><span class="n" id="mwsA">deal</span><span class="p" id="mwsQ">(</span><span class="n" id="mwsg">A</span><span class="p" id="mwsw">(</span><span class="n" id="mwtA">ii</span><span class="p" id="mwtQ">),</span><span class="w" id="mwtg"> </span><span class="n" id="mwtw">A</span><span class="p" id="mwuA">(</span><span class="n" id="mwuQ">ii</span><span class="o" id="mwug">+</span><span class="mi" id="mwuw">1</span><span class="p" id="mwvA">));</span> <span class="w" id="mwvQ"> </span><span class="n" id="mwvg">newEndIdx</span><span class="w" id="mwvw"> </span><span class="p" id="mwwA">=</span><span class="w" id="mwwQ"> </span><span class="n" id="mwwg">ii</span><span class="p" id="mwww">;</span> <span class="w" id="mwxA"> </span><span class="k" id="mwxQ">end</span> <span class="w" id="mwxg"> </span><span class="k" id="mwxw">end</span> <span class="w" id="mwyA"> </span><span class="c" id="mwyQ">% decreases `endIdx` because the elements after `newEndIdx` are in correct order</span> <span class="w" id="mwyg"> </span><span class="n" id="mwyw">endIdx</span><span class="w" id="mwzA"> </span><span class="p" id="mwzQ">=</span><span class="w" id="mwzg"> </span><span class="n" id="mwzw">newEndIdx</span><span class="w" id="mw0A"> </span><span class="o" id="mw0Q">-</span><span class="w" id="mw0g"> </span><span class="mi" id="mw0w">1</span><span class="p" id="mw1A">;</span> <span class="w" id="mw1Q"> </span><span class="k" id="mw1g">for</span><span class="w" id="mw1w"> </span><span class="n" id="mw2A">ii</span><span class="w" id="mw2Q"> </span><span class="p" id="mw2g">=</span><span class="w" id="mw2w"> </span><span class="n" id="mw3A">endIdx</span><span class="p" id="mw3Q">:</span><span class="o" id="mw3g">-</span><span class="mi" id="mw3w">1</span><span class="p" id="mw4A">:</span><span class="n" id="mw4Q">beginIdx</span> <span class="w" id="mw4g"> </span><span class="k" id="mw4w">if</span><span class="w" id="mw5A"> </span><span class="n" id="mw5Q">A</span><span class="p" id="mw5g">(</span><span class="n" id="mw5w">ii</span><span class="p" id="mw6A">)</span><span class="w" id="mw6Q"> </span><span class="o" id="mw6g">></span><span class="w" id="mw6w"> </span><span class="n" id="mw7A">A</span><span class="p" id="mw7Q">(</span><span class="n" id="mw7g">ii</span><span class="w" id="mw7w"> </span><span class="o" id="mw8A">+</span><span class="w" id="mw8Q"> </span><span class="mi" id="mw8g">1</span><span class="p" id="mw8w">)</span> <span class="w" id="mw9A"> </span><span class="p" id="mw9Q">[</span><span class="n" id="mw9g">A</span><span class="p" id="mw9w">(</span><span class="n" id="mw-A">ii</span><span class="o" id="mw-Q">+</span><span class="mi" id="mw-g">1</span><span class="p" id="mw-w">),</span><span class="w" id="mw_A"> </span><span class="n" id="mw_Q">A</span><span class="p" id="mw_g">(</span><span class="n" id="mw_w">ii</span><span class="p" id="mwAQA">)]</span><span class="w" id="mwAQE"> </span><span class="p" id="mwAQI">=</span><span class="w" id="mwAQM"> </span><span class="n" id="mwAQQ">deal</span><span class="p" id="mwAQU">(</span><span class="n" id="mwAQY">A</span><span class="p" id="mwAQc">(</span><span class="n" id="mwAQg">ii</span><span class="p" id="mwAQk">),</span><span class="w" id="mwAQo"> </span><span class="n" id="mwAQs">A</span><span class="p" id="mwAQw">(</span><span class="n" id="mwAQ0">ii</span><span class="o" id="mwAQ4">+</span><span class="mi" id="mwAQ8">1</span><span class="p" id="mwARA">));</span> <span class="w" id="mwARE"> </span><span class="n" id="mwARI">newBeginIdx</span><span class="w" id="mwARM"> </span><span class="p" id="mwARQ">=</span><span class="w" id="mwARU"> </span><span class="n" id="mwARY">ii</span><span class="p" id="mwARc">;</span> <span class="w" id="mwARg"> </span><span class="k" id="mwARk">end</span> <span class="w" id="mwARo"> </span><span class="k" id="mwARs">end</span> <span class="w" id="mwARw"> </span><span class="c" id="mwAR0">% increases `beginIdx` because the elements before `newBeginIdx` are in correct order</span> <span class="w" id="mwAR4"> </span><span class="n" id="mwAR8">beginIdx</span><span class="w" id="mwASA"> </span><span class="p" id="mwASE">=</span><span class="w" id="mwASI"> </span><span class="n" id="mwASM">newBeginIdx</span><span class="w" id="mwASQ"> </span><span class="o" id="mwASU">+</span><span class="w" id="mwASY"> </span><span class="mi" id="mwASc">1</span><span class="p" id="mwASg">;</span> <span class="k" id="mwASk">end</span> <span class="k" id="mwASo">end</span>