During my last experiments I tried to optimize my code at every line and dig into sort algorithms to find the fastest solution. As you may know Flash itself is using one of Quick Sort implementations. It is one of the fastest algorithms.
But I’ve tried different implementations and found some better solutions.
I tried 3 different ideas: Quick Sort + Insertion Sort, 3 Way Quick Sort and Quick Sort + Bubble Sort.
Here is my results:
- Quick Sort + Insertion Sort | 65 – 84 Ms.
- 3 Way Quick Sort | 74 – 91 Ms.
- Built in Array Sort | 87 – 103 Ms.
- Quick Sort + Bubble Sort | 117 – 124 Ms.
Below you will find simple test class. I used this algorithms to sort indexes of another array, sorry but I’m too lazy to adopt it to sort provided array (I suppose it is not hard to adopt it if you need)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 | package { import flash.display.Sprite; import flash.events.Event; import flash.utils.getTimer; /** * Simple test for sorting algorithms * @author Eugene Zatepyakin */ public class SortTest extends Sprite { private var centzs:Vector.<Number>; private var ord:Vector.<int>; private var arr:Array; public function SortTest() { if (stage) { init(); } else { addEventListener(Event.ADDED_TO_STAGE, init); } } private function init(e:Event = null):void { removeEventListener(Event.ADDED_TO_STAGE, init); var t:int = 100; centzs = new Vector.<Number>(); ord = new Vector.<int>(); arr = new Array(); for (var i:int = 0; i < t; i++) { centzs[i] = 1000 - Math.random() * 2000; ord[i] = i; arr[i] = centzs[i]; } var tt:int = getTimer(); // Quick Sort + Insertion Sort //qsort(0, int(t - 1)); //InsertionSort(0, int(t - 1)); // 3 Way Quick Sort //qsort3(0, int(t - 1)); // Quick Sort + Bubble Sort //qsort2(0, int(t - 1)); // Built in Array sort //arr.sort(Array.NUMERIC); //arr = arr.sort(Array.NUMERIC | Array.RETURNINDEXEDARRAY); // qsort + ins // 65 - 84 // qsort 3way // 74 - 91 // array // 87 - 103 // qsort + bubble // 117 - 124 trace(getTimer() - tt); } private function InsertionSort(min:int, max:int):void { var i:int, j:int, k:int, vi:int, v:Number; for ( i = int(min + 1); i <= max; i++) { v = centzs[ (vi = ord[i]) ]; j = i; while ( (j > min) && (centzs[ ord[ (k = int(j - 1)) ] ] > v) ) { ord[j] = ord[k]; j--; } ord[j] = vi; } } private function qsort(l:int, r:int):void { const M:int = 4; var i:int, j:int, k:int, vi:int, v:Number; //var loop:int = 0; if (int(r - l) > M) { i = int(r + l) >> 1; if (centzs[ ord[l] ] > centzs[ ord[i] ]) { //swap(l, i); vi = ord[l]; ord[l] = ord[i]; ord[i] = vi; } if (centzs[ ord[l] ] > centzs[ ord[r] ]) { //swap(l, r); vi = ord[l]; ord[l] = ord[r]; ord[r] = vi; } if (centzs[ ord[l] ] > centzs[ ord[r] ]) { //swap(i, r); vi = ord[i]; ord[i] = ord[r]; ord[r] = vi; } j = int(r - 1); //swap(i, j); vi = ord[i]; ord[i] = ord[j]; ord[j] = vi; i = l; v = centzs[ ord[j] ]; while (true) { while (centzs[ ord[++i] ] < v); while (centzs[ ord[--j] ] > v); if (j < i) break; //swap(i, j); vi = ord[i]; ord[i] = ord[j]; ord[j] = vi; //if (++loop > 100) { return; } } //swap(i, r - 1); vi = ord[i]; ord[i] = ord[ (k = int(r - 1)) ]; ord[k] = vi; qsort(l, j); qsort(int(i + 1), r); } } private function qsort3(l:int, r:int):void { var i:int = int(l - 1), j:int = r, p:int = int(l - 1), q:int = r, vi:int; if (r <= l) return; var v:Number = centzs[ ord[r] ]; while (true) { while (centzs[ ord[++i] ] < v); while (v < centzs[ ord[--j] ]) { if (j == l) break; } if (i >= j) break; vi = ord[i]; ord[i] = ord[j]; ord[j] = vi; if (centzs[ ord[i] ] == v) { p++; vi = ord[p]; ord[p] = ord[i]; ord[i] = vi; } if (v == centzs[ ord[j] ]) { q--; vi = ord[j]; ord[j] = ord[q]; ord[q] = vi; } } vi = ord[i]; ord[i] = ord[r]; ord[r] = vi; j = int(i - 1); i = int(i + 1); for (var k:int = l; k < p; k++, j--) { vi = ord[k]; ord[k] = ord[j]; ord[j] = vi; } for (k = int(r - 1); k > q; k--, i++) { vi = ord[i]; ord[i] = ord[k]; ord[k] = vi; } qsort3(l, j); qsort3(i, r); } private function qsort2(lo0:int, hi0:int):void { var lo:int = lo0; var hi:int = hi0; if ((hi-lo) <= 6) { bsort(lo, hi); return; } var t:int; var mid:int = int(lo + hi) >> 1; var vi:int = ord[ mid ]; var pivot:int = centzs[ vi ]; ord[mid] = ord[hi]; ord[hi] = vi; while( lo < hi ) { /* * Search forward from a[lo] until an element is found that * is greater than the pivot or lo >= hi */ while (centzs[ ord[lo] ] <= pivot && lo < hi) lo++; /* * Search backward from a[hi] until element is found that * is less than the pivot, or hi <= lo */ while (pivot <= centzs[ ord[hi] ] && lo < hi ) hi--; /* * Swap elements a[lo] and a[hi] */ if( lo < hi ) { t = ord[lo]; ord[lo] = ord[hi]; ord[hi] = t; } } /* * Put the median in the "center" of the list */ ord[hi0] = ord[hi]; ord[hi] = vi; /* * Recursive calls, elements a[lo0] to a[lo-1] are less than or * equal to pivot, elements a[hi+1] to a[hi0] are greater than * pivot. */ qsort2(lo0,int(lo-1)); qsort2(int(hi+1), hi0); } private function bsort(lo:int, hi:int):void { var t:int; var k:int; var flipped:Boolean; for (var j:int = hi; j > lo; j--) { flipped = false; for (var i:int = lo; i < j; i++) { if ( centzs[ ord[i] ] > centzs[ ord[ (k = int(i+1)) ] ] ) { t = ord[i]; ord[i] = ord[ k ]; ord[k] = t; flipped = true; } } if(!flipped) return; } } } } |


I’d love to have some fast alternative sorting options, but I think you first have to adjust your testing conditions a bit, so the comparison is real life. The way you built your test the initial conditions are different for the internal sort and your sort algorithms. You make heavy use of the ord[] array that contains the array indices, but you create that array outside your timing look. In a real world situation I would send an unsorted array to the sort algorithm and there would not be any prebuilt index array.
So for an honest comparison you have to recreate that index before every sort and include the time it takes to do that in your timings. Of course you are free to prebuild one big index table and just concat() or slice() it.
Nevertheless – you have a great blog! I wonder why it took me until today to discover it.
@Mario I know my test conditions isn’t good at all but this test class was a very quick extract from my main application where it was implemented as it is. I just wanted to note that for me it was faster to use custom sort algo. Thanx for pointing this out. I’ll try to create a real test conditions and see the results.
And thanx for the good words about my blog/experiments here and in twitter
I just discovered your blog today. liked it. About the quicksort + insertion sort combination, it has been proved mathematically that this combination is the fastest way to sort until today.