-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathquick-sort.html
More file actions
1113 lines (782 loc) · 52.7 KB
/
quick-sort.html
File metadata and controls
1113 lines (782 loc) · 52.7 KB
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
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<html lang="en">
<head>
<title>Quick Sort</title>
<!-- Google tag (gtag.js) -->
<script async="" src="https://www.googletagmanager.com/gtag/js?id=G-HCERBDV76D"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag() { dataLayer.push(arguments); }
gtag('js', new Date());
gtag('config', 'G-HCERBDV76D');
</script>
<meta content="B0487B46A104E90209E8A3BEA24ECA0E" name="msvalidate.01"/>
<meta content="f044b3a12c7918f1" name="yandex-verification"/>
<!--end-->
<meta content="learn about data types, variables, lists, tuples, dictionaries,if else,DSA,loops,user-defined functions, oop, threading and scripting." name="description"/>
<meta content="learnPython" name="author"/>
<meta content="Learn Python for free,learn python for beginners,Core Python,Web frameworks,Multiprocess architecture,Serverside templating language,python tutorials,python4" name="keywords"/>
<meta content="website" property="og:type"/>
<meta content="US-CA" name="”geo.region”"/>
<meta content="353 Jane Stanford Way, Stanford, CA 94305, United States" name="”geo.placename”"/>
<meta content="37.430089898615456;-122.17332683124829" name="”geo.position”"/>
<meta content="37.430089898615456, -122.17332683124829" name="”ICBM”"/>
<link href="https://pythonread.github.io/?m=1" rel="alternate"/>
<link href="/favicon.png" rel="icon"/>
<meta charset="utf-8"/>
<meta content="IE=edge" http-equiv="X-UA-Compatible"/>
<meta content="width=device-width, initial-scale=1.0" name="viewport"/>
<link href="/style1.css" media="all" rel="stylesheet" type="text/css"/>
<link href="/style2.css" media="all" rel="stylesheet" type="text/css"/>
<link href="/style0.css" media="all" rel="stylesheet" type="text/css"/>
<!--<![endif]-->
</head>
<body>
<div class="nav-wrapper">
<div class="container">
<nav>
<div class="logo wave">
<a href="/" id="logo">
Python Tutorial
</a>
</div>
<div class="nav-toggle-icon" id="nav-toggle-icon" onclick="mobileMenu()">
<div class="material-hamburger">
<span>
</span>
<span>
</span>
<span>
</span>
</div>
</div>
<div class="menu-wrapper" id="menu-wrapper">
<div class="nav-indicator">
</div>
<ul class="menus">
<li>
<a class="wave" href="/">
Home
</a>
</li>
<li>
<a class="wave" href="/projects.html">
Projects
</a>
</li>
<li>
<a class="wave" href="/free-course.html" target="_blank">
Free Course
</a>
</li>
<li>
<a class="wave" href="/dsa.html">
DSA
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
<div class="contents contents--neg" style="margin-top: 60px">
<div class="container">
<div class="row">
<div class="col-sm-12">
<div class="d-flex">
<div class="left-bar d-none d-lg-block">
<div class="card-alt mb-10x">
<h3>Page Index</h3>
<div class="list">
<ul>
<li><a href="/dsa.html#data-structure-1" title="Data Structures (I)">Data Structures
(I)</a></li>
<li><a href="/dsa.html#data-structure-2" title="Data Structures (II)">Data Structures
(II)</a></li>
<li><a href="/dsa.html#tree-1" title="Tree based DSA (I)">Tree based DSA (I)</a></li>
<li><a href="/dsa.html#tree-2" title="Tree based DSA (II)">Tree based DSA (II)</a></li>
<li><a href="/dsa.html#graph" title="Graph Data Structures and Algorithm">Graph based
DSA</a></li>
<li><a href="/dsa.html#sorting-searching" title="Sorting and Searching">Sorting and
Searching</a></li>
<li><a href="/dsa.html#greedy-algorithm" title="Greedy Algorithms">Greedy Algorithms</a>
</li>
<li><a href="/dsa.html#dynamic-programming" title="Dynamic Programming">Dynamic
Programming</a></li>
<li><a href="/dsa.html#other-algorithms" title="Other Algorithms">Other Algorithms</a>
</li>
</ul>
</div>
</div>
</div>
<div class="right-bar">
<!--first part end-------------------------------------------->
<iframe width="560" height="315" src="https://www.youtube.com/embed/MuiyN7THiO4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
<div class="editor-contents">
<h1>Quicksort Algorithm</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn about the quick sort algorithm and its implementation in Python, Java, C, and C++.</p>
<div id="node-1501" class="node node-algorithm clearfix" about="/dsa/quick-sort" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Quicksort Algorithm" class="rdf-meta element-hidden"></span>
<div class="content">
<p id="definition">Quicksort is <a href="/dsa.html">a sorting algorithm</a> based on the <strong>divide and conquer approach</strong> where</p>
<ol><li>An array is divided into subarrays by selecting a <strong>pivot element</strong> (element selected from the array).<br><br>
While dividing the array, the pivot element should be positioned in such a way that elements less than pivot are kept on the left side and elements greater than pivot are on the right side of the pivot.</li>
<li>The left and right subarrays are also divided using the same approach. This process continues until each subarray contains a single element.</li>
<li>At this point, elements are already sorted. Finally, elements are combined to form a sorted array.</li>
</ol><hr><h2 id="working">Working of Quicksort Algorithm</h2>
<p><strong>1. Select the Pivot Element</strong></p>
<p>There are different variations of quicksort where the pivot element is selected from different positions. Here, we will be selecting the rightmost element of the array as the pivot element.</p>
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-0.1_0.png" title="Selection of rightmost element" width="460" height="88.4"><figcaption>Select a pivot element</figcaption></figure><p><strong>2. Rearrange the Array</strong></p>
<p>Now the elements of the array are rearranged so that elements that are smaller than the pivot are put on the left and the elements greater than the pivot are put on the right.</p>
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-0.2_0.png" title="pivoting" width="460" height="88.4"><figcaption>Put all the smaller elements on the left and greater on the right of pivot element</figcaption></figure><p>Here's how we rearrange the array:</p>
<ol type="a"><li>A pointer is fixed at the pivot element. The pivot element is compared with the elements beginning from the first index.
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-partition-first-step.png" title="Quick Sort Steps" width="460" height="134.2"><figcaption>Comparison of pivot element with element beginning from the first index</figcaption></figure></li>
<li>If the element is greater than the pivot element, a second pointer is set for that element.
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-partition-second-step.png" title="Quick Sort Steps" width="460" height="134.2"><figcaption>If the element is greater than the pivot element, a second pointer is set for that element.</figcaption></figure></li>
<li>Now, pivot is compared with other elements. If an element smaller than the pivot element is reached, the smaller element is swapped with the greater element found earlier.
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-partition-third-step.png" title="Quick Sort Steps" width="450" height="290"><figcaption>Pivot is compared with other elements.</figcaption></figure></li>
<li>Again, the process is repeated to set the next greater element as the second pointer. And, swap it with another smaller element.
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-partition-fourth-step.png" title="Quick Sort Steps" width="450" height="206"><figcaption>The process is repeated to set the next greater element as the second pointer.</figcaption></figure></li>
<li>The process goes on until the second last element is reached.
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-partition-fifth-step.png" title="Quick Sort Steps" width="450" height="125"><figcaption>The process goes on until the second last element is reached.</figcaption></figure></li>
<li>Finally, the pivot element is swapped with the second pointer.
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-partition-sixth-step.png" title="Quick Sort Steps" width="450" height="257"><figcaption>Finally, the pivot element is swapped with the second pointer.</figcaption></figure></li>
</ol><p><strong>3. Divide Subarrays</strong></p>
<p>Pivot elements are again chosen for the left and the right sub-parts separately. And, <strong>step 2</strong> is repeated.</p>
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort_1.png" title="Quick Sort Steps" width="450" height="257"><figcaption>Select pivot element of in each half and put at correct place using recursion</figcaption></figure><p></p><div class="clearfix"></div><p> </p>
<p>The subarrays are divided until each subarray is formed of a single element. At this point, the array is already sorted.</p>
<hr><h2 id="algorithm">Quick Sort Algorithm</h2>
<pre style="max-height: 600px;"><code class="dsa hljs swift">
<span class="hljs-built_in">quickSort</span>(array, leftmostIndex, rightmostIndex)
<span class="hljs-keyword">if</span> (leftmostIndex < rightmostIndex)
pivotIndex <- <span class="hljs-built_in">partition</span>(array,leftmostIndex, rightmostIndex)
<span class="hljs-built_in">quickSort</span>(array, leftmostIndex, pivotIndex - <span class="hljs-number">1</span>)
<span class="hljs-built_in">quickSort</span>(array, pivotIndex, rightmostIndex)
<span class="hljs-built_in">partition</span>(array, leftmostIndex, rightmostIndex)
<span class="hljs-keyword">set</span> rightmostIndex <span class="hljs-keyword">as</span> pivotIndex
storeIndex <- leftmostIndex - <span class="hljs-number">1</span>
<span class="hljs-keyword">for</span> i <- leftmostIndex + <span class="hljs-number">1</span> to rightmostIndex
<span class="hljs-keyword">if</span> element[i] < pivotElement
<span class="hljs-built_in">swap</span> element[i] and element[storeIndex]
storeIndex++
<span class="hljs-built_in">swap</span> pivotElement and element[storeIndex+<span class="hljs-number">1</span>]
<span class="hljs-keyword">return</span> storeIndex + <span class="hljs-number">1</span></code></pre>
<h3>Visual Illustration of Quicksort Algorithm</h3>
<p>You can understand the working of quicksort algorithm with the help of the illustrations below.</p>
<figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-working.png" title="Quick Sort first half" width="1200" height="317"><figcaption>Sorting the elements on the left of pivot using recursion</figcaption></figure><figure><img alt="Quick Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/quick-sort-1.png" title="Quick Sort second half" width="1200" height="403"><figcaption>Sorting the elements on the right of pivot using recursion</figcaption></figure><hr><hr><h2 id="code">Quicksort Code in Python, Java, and C/C++</h2>
<div class="tabbed-editor">
<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>
<div id="java1" onclick="changejava()" class="tabbed-editor__node"><a href="#java-code">Java</a></div>
<div id="c1" onclick="changec()" class="tabbed-editor__node"><a href="#c-code">C</a></div>
<div id="cpp1" onclick="changecpp()" class="tabbed-editor__node"><a href="#cpp-code">C++</a></div>
</div>
<div class="code-editor code-editor--tabbed">
<div class="code-editor__area code-editor__area--active" id="python-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Quick sort in Python</span>
<span class="hljs-comment"># function to find the partition position</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">partition</span><span class="hljs-params">(array, low, high)</span>:</span>
<span class="hljs-comment"># choose the rightmost element as pivot</span>
pivot = array[high]
<span class="hljs-comment"># pointer for greater element</span>
i = low - <span class="hljs-number">1</span>
<span class="hljs-comment"># traverse through all elements</span>
<span class="hljs-comment"># compare each element with pivot</span>
<span class="hljs-keyword">for</span> j <span class="hljs-keyword">in</span> range(low, high):
<span class="hljs-keyword">if</span> array[j] <= pivot:
<span class="hljs-comment"># if element smaller than pivot is found</span>
<span class="hljs-comment"># swap it with the greater element pointed by i</span>
i = i + <span class="hljs-number">1</span>
<span class="hljs-comment"># swapping element at i with element at j</span>
(array[i], array[j]) = (array[j], array[i])
<span class="hljs-comment"># swap the pivot element with the greater element specified by i</span>
(array[i + <span class="hljs-number">1</span>], array[high]) = (array[high], array[i + <span class="hljs-number">1</span>])
<span class="hljs-comment"># return the position from where partition is done</span>
<span class="hljs-keyword">return</span> i + <span class="hljs-number">1</span>
<span class="hljs-comment"># function to perform quicksort</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">quickSort</span><span class="hljs-params">(array, low, high)</span>:</span>
<span class="hljs-keyword">if</span> low < high:
<span class="hljs-comment"># find pivot element such that</span>
<span class="hljs-comment"># element smaller than pivot are on the left</span>
<span class="hljs-comment"># element greater than pivot are on the right</span>
pi = partition(array, low, high)
<span class="hljs-comment"># recursive call on the left of pivot</span>
quickSort(array, low, pi - <span class="hljs-number">1</span>)
<span class="hljs-comment"># recursive call on the right of pivot</span>
quickSort(array, pi + <span class="hljs-number">1</span>, high)
data = [<span class="hljs-number">8</span>, <span class="hljs-number">7</span>, <span class="hljs-number">2</span>, <span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">6</span>]
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Unsorted Array"</span>)
<span class="hljs-keyword">print</span>(data)
size = len(data)
quickSort(data, <span class="hljs-number">0</span>, size - <span class="hljs-number">1</span>)
<span class="hljs-keyword">print</span>(<span class="hljs-string">'Sorted Array in Ascending Order:'</span>)
<span class="hljs-keyword">print</span>(data)</code></pre></div>
</div>
<div class="code-editor__area" id="java-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Quick sort in Java</span>
<span class="hljs-keyword">import</span> java.util.Arrays;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Quicksort</span> </span>{
<span class="hljs-comment">// method to find the partition position</span>
<span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-keyword">int</span> <span class="hljs-title">partition</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-comment">// choose the rightmost element as pivot</span>
<span class="hljs-keyword">int</span> pivot = array[high];
<span class="hljs-comment">// pointer for greater element</span>
<span class="hljs-keyword">int</span> i = (low - <span class="hljs-number">1</span>);
<span class="hljs-comment">// traverse through all elements</span>
<span class="hljs-comment">// compare each element with pivot</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = low; j < high; j++) {
<span class="hljs-keyword">if</span> (array[j] <= pivot) {
<span class="hljs-comment">// if element smaller than pivot is found</span>
<span class="hljs-comment">// swap it with the greatr element pointed by i</span>
i++;
<span class="hljs-comment">// swapping element at i with element at j</span>
<span class="hljs-keyword">int</span> temp = array[i];
array[i] = array[j];
array[j] = temp;
}
}
<span class="hljs-comment">// swapt the pivot element with the greater element specified by i</span>
<span class="hljs-keyword">int</span> temp = array[i + <span class="hljs-number">1</span>];
array[i + <span class="hljs-number">1</span>] = array[high];
array[high] = temp;
<span class="hljs-comment">// return the position from where partition is done</span>
<span class="hljs-keyword">return</span> (i + <span class="hljs-number">1</span>);
}
<span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">quickSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-keyword">if</span> (low < high) {
<span class="hljs-comment">// find pivot element such that</span>
<span class="hljs-comment">// elements smaller than pivot are on the left</span>
<span class="hljs-comment">// elements greater than pivot are on the right</span>
<span class="hljs-keyword">int</span> pi = partition(array, low, high);
<span class="hljs-comment">// recursive call on the left of pivot</span>
quickSort(array, low, pi - <span class="hljs-number">1</span>);
<span class="hljs-comment">// recursive call on the right of pivot</span>
quickSort(array, pi + <span class="hljs-number">1</span>, high);
}
}
}
<span class="hljs-comment">// Main class</span>
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Main</span> </span>{
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span> </span>{
<span class="hljs-keyword">int</span>[] data = { <span class="hljs-number">8</span>, <span class="hljs-number">7</span>, <span class="hljs-number">2</span>, <span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">6</span> };
System.out.println(<span class="hljs-string">"Unsorted Array"</span>);
System.out.println(Arrays.toString(data));
<span class="hljs-keyword">int</span> size = data.length;
<span class="hljs-comment">// call quicksort() on array data</span>
Quicksort.quickSort(data, <span class="hljs-number">0</span>, size - <span class="hljs-number">1</span>);
System.out.println(<span class="hljs-string">"Sorted Array in Ascending Order: "</span>);
System.out.println(Arrays.toString(data));
}
}</code></pre></div>
</div>
<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Quick sort in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-comment">// function to swap elements</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">swap</span><span class="hljs-params">(<span class="hljs-keyword">int</span> *a, <span class="hljs-keyword">int</span> *b)</span> </span>{
<span class="hljs-keyword">int</span> t = *a;
*a = *b;
*b = t;
}
<span class="hljs-comment">// function to find the partition position</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">partition</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-comment">// select the rightmost element as pivot</span>
<span class="hljs-keyword">int</span> pivot = <span class="hljs-built_in">array</span>[high];
<span class="hljs-comment">// pointer for greater element</span>
<span class="hljs-keyword">int</span> i = (low - <span class="hljs-number">1</span>);
<span class="hljs-comment">// traverse each element of the array</span>
<span class="hljs-comment">// compare them with the pivot</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = low; j < high; j++) {
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[j] <= pivot) {
<span class="hljs-comment">// if element smaller than pivot is found</span>
<span class="hljs-comment">// swap it with the greater element pointed by i</span>
i++;
<span class="hljs-comment">// swap element at i with element at j</span>
swap(&<span class="hljs-built_in">array</span>[i], &<span class="hljs-built_in">array</span>[j]);
}
}
<span class="hljs-comment">// swap the pivot element with the greater element at i</span>
swap(&<span class="hljs-built_in">array</span>[i + <span class="hljs-number">1</span>], &<span class="hljs-built_in">array</span>[high]);
<span class="hljs-comment">// return the partition point</span>
<span class="hljs-keyword">return</span> (i + <span class="hljs-number">1</span>);
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">quickSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-keyword">if</span> (low < high) {
<span class="hljs-comment">// find the pivot element such that</span>
<span class="hljs-comment">// elements smaller than pivot are on left of pivot</span>
<span class="hljs-comment">// elements greater than pivot are on right of pivot</span>
<span class="hljs-keyword">int</span> pi = partition(<span class="hljs-built_in">array</span>, low, high);
<span class="hljs-comment">// recursive call on the left of pivot</span>
quickSort(<span class="hljs-built_in">array</span>, low, pi - <span class="hljs-number">1</span>);
<span class="hljs-comment">// recursive call on the right of pivot</span>
quickSort(<span class="hljs-built_in">array</span>, pi + <span class="hljs-number">1</span>, high);
}
}
<span class="hljs-comment">// function to print array elements</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; ++i) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, <span class="hljs-built_in">array</span>[i]);
}
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);
}
<span class="hljs-comment">// main function</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> data[] = {<span class="hljs-number">8</span>, <span class="hljs-number">7</span>, <span class="hljs-number">2</span>, <span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">6</span>};
<span class="hljs-keyword">int</span> n = <span class="hljs-keyword">sizeof</span>(data) / <span class="hljs-keyword">sizeof</span>(data[<span class="hljs-number">0</span>]);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Unsorted Array\n"</span>);
printArray(data, n);
<span class="hljs-comment">// perform quicksort on data</span>
quickSort(data, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Sorted array in ascending order: \n"</span>);
printArray(data, n);
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Quick sort in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-comment">// function to swap elements</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">swap</span><span class="hljs-params">(<span class="hljs-keyword">int</span> *a, <span class="hljs-keyword">int</span> *b)</span> </span>{
<span class="hljs-keyword">int</span> t = *a;
*a = *b;
*b = t;
}
<span class="hljs-comment">// function to print the array</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < size; i++)
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">array</span>[i] << <span class="hljs-string">" "</span>;
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;
}
<span class="hljs-comment">// function to rearrange array (find the partition point)</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">partition</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-comment">// select the rightmost element as pivot</span>
<span class="hljs-keyword">int</span> pivot = <span class="hljs-built_in">array</span>[high];
<span class="hljs-comment">// pointer for greater element</span>
<span class="hljs-keyword">int</span> i = (low - <span class="hljs-number">1</span>);
<span class="hljs-comment">// traverse each element of the array</span>
<span class="hljs-comment">// compare them with the pivot</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = low; j < high; j++) {
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[j] <= pivot) {
<span class="hljs-comment">// if element smaller than pivot is found</span>
<span class="hljs-comment">// swap it with the greater element pointed by i</span>
i++;
<span class="hljs-comment">// swap element at i with element at j</span>
swap(&<span class="hljs-built_in">array</span>[i], &<span class="hljs-built_in">array</span>[j]);
}
}
<span class="hljs-comment">// swap pivot with the greater element at i</span>
swap(&<span class="hljs-built_in">array</span>[i + <span class="hljs-number">1</span>], &<span class="hljs-built_in">array</span>[high]);
<span class="hljs-comment">// return the partition point</span>
<span class="hljs-keyword">return</span> (i + <span class="hljs-number">1</span>);
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">quickSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-keyword">if</span> (low < high) {
<span class="hljs-comment">// find the pivot element such that</span>
<span class="hljs-comment">// elements smaller than pivot are on left of pivot</span>
<span class="hljs-comment">// elements greater than pivot are on righ of pivot</span>
<span class="hljs-keyword">int</span> pi = partition(<span class="hljs-built_in">array</span>, low, high);
<span class="hljs-comment">// recursive call on the left of pivot</span>
quickSort(<span class="hljs-built_in">array</span>, low, pi - <span class="hljs-number">1</span>);
<span class="hljs-comment">// recursive call on the right of pivot</span>
quickSort(<span class="hljs-built_in">array</span>, pi + <span class="hljs-number">1</span>, high);
}
}
<span class="hljs-comment">// Driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> data[] = {<span class="hljs-number">8</span>, <span class="hljs-number">7</span>, <span class="hljs-number">6</span>, <span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">2</span>};
<span class="hljs-keyword">int</span> n = <span class="hljs-keyword">sizeof</span>(data) / <span class="hljs-keyword">sizeof</span>(data[<span class="hljs-number">0</span>]);
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Unsorted Array: \n"</span>;
printArray(data, n);
<span class="hljs-comment">// perform quicksort on data</span>
quickSort(data, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Sorted array in ascending order: \n"</span>;
printArray(data, n);
}</code></pre></div>
</div>
</div>
<hr><h2 id="complexity">Quicksort Complexity</h2>
<div class="table-responsive">
<table border="0"><tbody><tr><th><strong>Time Complexity</strong></th>
<td> </td>
</tr><tr><td>Best</td>
<td>O(n*log n)</td>
</tr><tr><td>Worst</td>
<td>O(n<sup>2</sup>)</td>
</tr><tr><td>Average</td>
<td>O(n*log n)</td>
</tr><tr><th><strong>Space Complexity</strong></th>
<td>O(log n)</td>
</tr><tr><th><strong>Stability</strong></th>
<td>No</td>
</tr></tbody></table></div>
<hr><h3>1. Time Complexities</h3>
<ul><li><strong>Worst Case Complexity [Big-O]</strong>: <code>O(n<sup>2</sup>)</code><br>
It occurs when the pivot element picked is either the greatest or the smallest element.<br><br>
This condition leads to the case in which the pivot element lies in an extreme end of the sorted array. One sub-array is always empty and another sub-array contains <code>n - 1</code> elements. Thus, quicksort is called only on this sub-array.<br><br>
However, the quicksort algorithm has better performance for scattered pivots.</li>
</ul><ul><li><strong>Best Case Complexity [Big-omega]</strong>: <code>O(n*log n)</code><br>
It occurs when the pivot element is always the middle element or near to the middle element.</li>
<li><strong>Average Case Complexity [Big-theta]</strong>: <code>O(n*log n)</code><br>
It occurs when the above conditions do not occur.</li>
</ul><h3>2. Space Complexity</h3>
<p>The space complexity for quicksort is <code>O(log n)</code>.</p>
<hr><h2 id="application">Quicksort Applications</h2>
<p>Quicksort algorithm is used when</p>
<ul><li>the programming language is good for recursion</li>
<li>time complexity matters</li>
<li>space complexity matters</li>
</ul><hr><h3>Similar Sorting Algorithms</h3>
<ul><li><a href="/dsa/insertion-sort.html">Insertion Sort</a></li>
<li><a href="/dsa/merge-sort.html">Merge Sort</a></li>
<li><a href="/dsa/selection-sort.html">Selection Sort</a></li>
<li><a href="/dsa/bucket-sort.html">Bucket Sort</a></li>
</ul></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#definition">Definition</a></li>
<li><a href="#working">Working of Quicksort Algorithm</a></li>
<li><a href="#algorithm">Quick Sort Algorithm</a></li>
<li><a href="#code">Quicksort Code in Python, Java, and C/C++ </a></li>
<li><a href="#complexity">Complexity</a></li>
<li><a href="#application">Applications</a></li>
</ul></div></div></div> </div>
<!--second------------------------------------------->
<div>
<ul>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/stack.html">
Stack</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/queue.html">
Queue</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/types-of-queue.html">
Types of Queue</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/circular-queue.html">
Circular Queue</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/priority-queue.html">
Priority Queue</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/deque.html">
Deque</a></button>
<br/>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/linked-list.html">
Linked List</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/linked-list-operations.html">
Linked List Operations</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/linked-list-types.html">
Types of Linked List</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/hash-table.html">
Hash Table</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/heap-data-structure.html">
Heap Data Structure</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/fibonacci-heap.html">
Fibonacci Heap</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/decrease-key-and-delete-node-from-a-fibonacci-heap.html">
Decrease Key and Delete node from Fibonacci Heap</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/trees.html">
Tree Data Structure</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/tree-traversal.html">
Tree Traversal</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/binary-tree.html">
Binary Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/full-binary-tree.html">
Full Binary Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/perfect-binary-tree.html">
Perfect Binary Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/complete-binary-tree.html">
Complete Binary Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/balanced-binary-tree.html">
Balanced Binary Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/binary-search-tree.html">
Binary Search Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/avl-tree.html">
AVL Tree</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/b-tree.html">
B Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/insertion-into-a-b-tree.html">
Insertion into B-tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/deletion-from-a-b-tree.html">
Deletion from B-tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/b-plus-tree.html">
B+ Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/insertion-on-a-b-plus-tree.html">
Insertion on a B+ Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/deletion-from-a-b-plus-tree.html">
Deletion from a B+ Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/red-black-tree.html">
Red Black Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/insertion-in-a-red-black-tree.html">
Insertion in Red Black Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/deletion-from-a-red-black-tree.html">
Deletion from Red Black Tree</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/graph.html">
Graph Data Structure</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/spanning-tree-and-minimum-spanning-tree.html">
Spanning Tree</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/strongly-connected-components.html">
Strongly Connected Components</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/graph-adjacency-matrix.html">
Adjacency Matrix</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/graph-adjacency-list.html">
Adjacency List</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/graph-dfs.html">
DFS Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/graph-bfs.html">
Breadth-first Search</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/bellman-ford-algorithm.html">
Bellman Ford's Algorithm</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/bubble-sort.html">
Bubble Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/selection-sort.html">
Selection Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/insertion-sort.html">
Insertion Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/merge-sort.html">
Merge Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/quick-sort.html">
Quick Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/counting-sort.html">
Counting Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/radix-sort.html">
Radix Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/bucket-sort.html">
Bucket Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/heap-sort.html">
Heap Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/shell-sort.html">
Shell Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/linear-search.html">
Linear Search</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/binary-search.html">
Binary Search</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/greedy-algorithm.html">
Greedy Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/ford-fulkerson-algorithm.html">
Ford-Fulkerson Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/dijkstra-algorithm.html">
Dijkstra's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/kruskal-algorithm.html">
Kruskal's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/prim-algorithm.html">
Prim's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/huffman-coding.html">
Huffman Code</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/dynamic-programming.html">
Dynamic Programming</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/floyd-warshall-algorithm.html">
Floyd Warshall Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/longest-common-subsequence.html">
Longest Common Subsequence</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/backtracking-algorithm.html">
Backtracking Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/rabin-karp-algorithm.html">
Rabin-Karp Algorithm</a></button>
<br>
<br/>
<h2>Free Courses on YouTube</h2>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="
https://www.youtube.com/watch?v=IbSXF7eT-AU&list=PLR_5PTwg_uAQw40OhdvAwN4NvzWv0xOZ2">
Python Full Course Playlist</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://www.youtube.com/watch?v=UEl6wB90Gs8">
105 STL Algorithms in Less Than an Hour</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://www.youtube.com/watch?v=zZXTgN7L1UU&list=PLR_5PTwg_uAS6C1cSMjU6oVhOcCX8Zu_4">
C++ STL Playlist</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://youtu.be/ty9756v3kc8">
Learn Node.js </a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://youtu.be/exrIpdS3Crc">
Learn Data Science Full course</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://youtu.be/Q8tDO2uSk5U">
Learn Computer Networking Full course</a></button>
<br/>
</br></br></br></br></br></br></br></br></ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<footer class="afooter" style="margin-left:20px">
<p>
<a href="/cookie-policy.html">Cookie policy</a> |
<a href="/privacy-policy.html">Privacy policy</a> |
<a href="/terms-of-use.html">Terms of use</a> |
<a href="/disclaimer.html">Disclaimer</a> |
<a href="/about-us.html">About Us</a>
</p>
<p>
© 2023 <a href="https://pythonread.github.io">https://pythonread.github.io</a>
</p>
</footer>
<script type="text/javascript">
document.addEventListener('DOMContentLoaded', function () { htmlTableOfContents() }); function htmlTableOfContents(documentRef) { var documentRef = documentRef || document; var toc = documentRef.getElementById("toc"); var headings = [].slice.call(documentRef.body.querySelectorAll('h2, h3')); headings.forEach(function (heading, index) { var ref = "toc" + index; if (heading.hasAttribute("id")) { ref = heading.getAttribute("id") } else { heading.setAttribute("id", ref) } var link = documentRef.createElement("a"); link.setAttribute("href", "#" + ref); link.textContent = heading.textContent; var div = documentRef.createElement("div"); div.setAttribute("class", heading.tagName.toLowerCase()); div.appendChild(link); toc.appendChild(div) }) } try { module.exports = htmlTableOfContents } catch (e) { } function isScrolledIntoView(el) { var rect = el.getBoundingClientRect(); var elemTop = rect.top; var elemBottom = rect.bottom; var isVisible = (elemTop >= -10) && (elemBottom <= (window.innerHeight)); return isVisible } function highlightMenu() { var headers = document.querySelectorAll("h2, h3"); for (var i = 0; i < headers.length; i += 1) { if (isScrolledIntoView(headers[i])) { var childDivs = document.getElementById('toc').getElementsByTagName('div'); var c = childDivs[i].classList; c.add("active"); for (var j = 0; j < i; j += 1) { var c = childDivs[j].classList; c.remove("active") } for (var j = i + 1; j < childDivs.length; j += 1) { var c = childDivs[j].classList; c.remove("active") } break } } } function highlightMenuLastItem() { var childDivs = document.getElementById('toc').getElementsByTagName('div'); for (var j = 0; j < childDivs.length - 1; j += 1) { var c = childDivs[j].classList; c.remove("active") } var c = childDivs[childDivs.length - 1].classList; c.add("active") } window.addEventListener("click", function (event) { highlightMenu() }); window.onscroll = function (e) { highlightMenu(); if ((window.innerHeight + window.scrollY) >= document.body.offsetHeight) { highlightMenuLastItem() } }; function mobileMenu() { var classes = document.getElementById('nav-toggle-icon').classList; if (classes.contains("active")) { classes.remove("active") } else { classes.add("active") } var classes = document.getElementById('menu-wrapper').classList; if (classes.contains("active")) { classes.remove("active") } else { classes.add("active") } }
</script>
<script type="text/javascript">
function changepy(){
document.getElementById('py1').className = 'tabbed-editor__node tabbed-editor__node--active';
document.getElementById('java1').className = 'tabbed-editor__node';
document.getElementById('c1').className = 'tabbed-editor__node';
document.getElementById('cpp1').className = 'tabbed-editor__node';
document.getElementById('python-code').className = 'code-editor__area code-editor__area--active';