Tässä artikkelissa käsittelemme Quicksort-algoritmia. Quicksortin työskentelymenettely on myös yksinkertainen. Tämä artikkeli on erittäin hyödyllinen ja mielenkiintoinen opiskelijoille, koska he saattavat kohdata pikalajittelun kysymyksen kokeissaan. Joten on tärkeää keskustella aiheesta.
Lajittelu on tapa järjestää tavarat järjestelmällisesti. Quicksort on laajalti käytetty lajittelualgoritmi, joka tekee n log n vertailut keskimääräisessä tapauksessa n elementin taulukon lajittelemiseksi. Se on nopeampi ja erittäin tehokas lajittelualgoritmi. Tämä algoritmi noudattaa hajota ja hallitse -lähestymistapaa. Jaa ja hallitse on tekniikka, jossa algoritmit hajotetaan osaongelmiin, ratkaistaan sitten aliongelmat ja yhdistetään tulokset takaisin yhteen alkuperäisen ongelman ratkaisemiseksi.
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Jakaa: Valitse Divide-kohdassa ensin pivot-elementti. Tämän jälkeen osioita tai järjestä taulukko kahdeksi alitaulukoksi siten, että jokainen vasemman alitaulukon elementti on pienempi tai yhtä suuri kuin pivot-elementti ja jokainen oikean alitaulukon elementti on suurempi kuin pivot-elementti.
Valloittaa: Lajittele rekursiivisesti kaksi alitaulukkoa Quicksortilla.
Yhdistää: Yhdistä jo lajiteltu matriisi.
Quicksort poimii elementin pivotiksi ja jakaa sitten annetun taulukon valitun pivot-elementin ympärille. Pikalajittelussa suuri matriisi jaetaan kahteen taulukkoon, joista toisessa on määritettyä arvoa pienemmät arvot (Pivot) ja toisessa taulukossa pivotia suuremmat arvot.
Tämän jälkeen myös vasen ja oikea alitaulukko osioidaan samalla menetelmällä. Se jatkuu, kunnes yksittäinen elementti jää alitaulukkoon.
Pivotin valinta
Hyvän pivotin valitseminen on välttämätöntä pikalajittelun nopean toteuttamisen kannalta. On kuitenkin tyypillistä määrittää hyvä pivot. Joitakin tapoja valita pivot ovat seuraavat:
- Pivot voi olla satunnainen, eli valita satunnainen pivot annetusta taulukosta.
- Pivot voi olla joko annetun taulukon vasemmanpuoleisimman elementin oikeanpuoleisin elementti.
- Valitse mediaani pivot-elementiksi.
Algoritmi
Algoritmi:
QUICKSORT (array A, start, end) { 1 if (start <end) 2 3 4 5 6 { p="partition(A," start, end) quicksort (a, - 1) + 1, } < pre> <p> <strong>Partition Algorithm:</strong> </p> <p>The partition algorithm rearranges the sub-arrays in a place.</p> <pre> PARTITION (array A, start, end) { 1 pivot ? A[end] 2 i ? start-1 3 for j ? start to end -1 { 4 do if (A[j] <pivot) 1 5 6 7 8 9 { then i ? + swap a[i] with a[j] }} a[i+1] a[end] return i+1 } < pre> <h2>Working of Quick Sort Algorithm</h2> <p>Now, let's see the working of the Quicksort Algorithm.</p> <p>To understand the working of quick sort, let's take an unsorted array. It will make the concept more clear and understandable.</p> <p>Let the elements of array are -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-2.webp" alt="Quick Sort Algorithm"> <p>In the given array, we consider the leftmost element as pivot. So, in this case, a[left] = 24, a[right] = 27 and a[pivot] = 24.</p> <p>Since, pivot is at left, so algorithm starts from right and move towards left.</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-3.webp" alt="Quick Sort Algorithm"> <p>Now, a[pivot] <a[right], so algorithm moves forward one position towards left, i.e. -< p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-4.webp" alt="Quick Sort Algorithm"> <p>Now, a[left] = 24, a[right] = 19, and a[pivot] = 24.</p> <p>Because, a[pivot] > a[right], so, algorithm will swap a[pivot] with a[right], and pivot moves to right, as -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-5.webp" alt="Quick Sort Algorithm"> <p>Now, a[left] = 19, a[right] = 24, and a[pivot] = 24. Since, pivot is at right, so algorithm starts from left and moves to right.</p> <p>As a[pivot] > a[left], so algorithm moves one position to right as -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-6.webp" alt="Quick Sort Algorithm"> <p>Now, a[left] = 9, a[right] = 24, and a[pivot] = 24. As a[pivot] > a[left], so algorithm moves one position to right as -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-7.webp" alt="Quick Sort Algorithm"> <p>Now, a[left] = 29, a[right] = 24, and a[pivot] = 24. As a[pivot] <a[left], so, swap a[pivot] and a[left], now pivot is at left, i.e. -< p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-8.webp" alt="Quick Sort Algorithm"> <p>Since, pivot is at left, so algorithm starts from right, and move to left. Now, a[left] = 24, a[right] = 29, and a[pivot] = 24. As a[pivot] <a[right], so algorithm moves one position to left, as -< p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-9.webp" alt="Quick Sort Algorithm"> <p>Now, a[pivot] = 24, a[left] = 24, and a[right] = 14. As a[pivot] > a[right], so, swap a[pivot] and a[right], now pivot is at right, i.e. -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-10.webp" alt="Quick Sort Algorithm"> <p>Now, a[pivot] = 24, a[left] = 14, and a[right] = 24. Pivot is at right, so the algorithm starts from left and move to right.</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-11.webp" alt="Quick Sort Algorithm"> <p>Now, a[pivot] = 24, a[left] = 24, and a[right] = 24. So, pivot, left and right are pointing the same element. It represents the termination of procedure.</p> <p>Element 24, which is the pivot element is placed at its exact position.</p> <p>Elements that are right side of element 24 are greater than it, and the elements that are left side of element 24 are smaller than it.</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-12.webp" alt="Quick Sort Algorithm"> <p>Now, in a similar manner, quick sort algorithm is separately applied to the left and right sub-arrays. After sorting gets done, the array will be -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-13.webp" alt="Quick Sort Algorithm"> <h2>Quicksort complexity</h2> <p>Now, let's see the time complexity of quicksort in best case, average case, and in worst case. We will also see the space complexity of quicksort.</p> <h3>1. Time Complexity</h3> <table class="table"> <tr> <th>Case</th> <th>Time Complexity</th> </tr> <tr> <td> <strong>Best Case</strong> </td> <td>O(n*logn)</td> </tr> <tr> <td> <strong>Average Case</strong> </td> <td>O(n*logn)</td> </tr> <tr> <td> <strong>Worst Case</strong> </td> <td>O(n<sup>2</sup>)</td> </tr> </table> <ul> <tr><td>Best Case Complexity -</td> In Quicksort, the best-case occurs when the pivot element is the middle element or near to the middle element. The best-case time complexity of quicksort is <strong>O(n*logn)</strong> . </tr><tr><td>Average Case Complexity -</td> It occurs when the array elements are in jumbled order that is not properly ascending and not properly descending. The average case time complexity of quicksort is <strong>O(n*logn)</strong> . </tr><tr><td>Worst Case Complexity -</td> In quick sort, worst case occurs when the pivot element is either greatest or smallest element. Suppose, if the pivot element is always the last element of the array, the worst case would occur when the given array is sorted already in ascending or descending order. The worst-case time complexity of quicksort is <strong>O(n<sup>2</sup>)</strong> . </tr></ul> <p>Though the worst-case complexity of quicksort is more than other sorting algorithms such as <strong>Merge sort</strong> and <strong>Heap sort</strong> , still it is faster in practice. Worst case in quick sort rarely occurs because by changing the choice of pivot, it can be implemented in different ways. Worst case in quicksort can be avoided by choosing the right pivot element.</p> <h3>2. Space Complexity</h3> <table class="table"> <tr> <td> <strong>Space Complexity</strong> </td> <td>O(n*logn)</td> </tr> <tr> <td> <strong>Stable</strong> </td> <td>NO</td> </tr> </table> <ul> <li>The space complexity of quicksort is O(n*logn).</li> </ul> <h2>Implementation of quicksort</h2> <p>Now, let's see the programs of quicksort in different programming languages.</p> <p> <strong>Program:</strong> Write a program to implement quicksort in C language.</p> <pre> #include /* function that consider last element as pivot, place the pivot at its exact position, and place smaller elements to left of pivot and greater elements to right of pivot. */ int partition (int a[], int start, int end) { int pivot = a[end]; // pivot element int i = (start - 1); for (int j = start; j <= 27 end - 1; j++) { if current element is smaller than the pivot (a[j] < pivot) i++; increment index of int t="a[i];" a[i]="a[j];" a[j]="t;" } a[i+1]="a[end];" a[end]="t;" return (i + 1); * function to implement quick sort void quick(int a[], start, end) a[]="array" be sorted, start="Starting" index, (start p="partition(a," end); partitioning quick(a, 1, print an array printarr(int n) i; for i n; i++) printf('%d ', a[i]); main() 24, 9, 29, 14, 19, }; n="sizeof(a)" sizeof(a[0]); printf('before sorting elements are
'); printarr(a, n); 0, printf('
after 0; pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-14.webp" alt="Quick Sort Algorithm"> <p> <strong>Program:</strong> Write a program to implement quick sort in C++ language.</p> <pre> #include using namespace std; /* function that consider last element as pivot, place the pivot at its exact position, and place smaller elements to left of pivot and greater elements to right of pivot. */ int partition (int a[], int start, int end) { int pivot = a[end]; // pivot element int i = (start - 1); for (int j = start; j <= 26 end - 1; j++) { if current element is smaller than the pivot (a[j] < pivot) i++; increment index of int t="a[i];" a[i]="a[j];" a[j]="t;" } a[i+1]="a[end];" a[end]="t;" return (i + 1); * function to implement quick sort void quick(int a[], start, end) a[]="array" be sorted, start="Starting" index, (start p="partition(a," end); partitioning quick(a, 1, print an array printarr(int n) i; for i n; i++) cout< <a[i]<< ' '; main() 23, 8, 28, 13, 18, }; n="sizeof(a)" sizeof(a[0]); cout<<'before sorting elements are
'; printarr(a, n); 0, cout<<'
after 0; pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-15.webp" alt="Quick Sort Algorithm"> <p> <strong>Program:</strong> Write a program to implement quicksort in python.</p> <pre> #function that consider last element as pivot, #place the pivot at its exact position, and place #smaller elements to left of pivot and greater #elements to right of pivot. def partition (a, start, end): i = (start - 1) pivot = a[end] # pivot element for j in range(start, end): # If current element is smaller than or equal to the pivot if (a[j] <= 1 pivot): i="i" + a[i], a[j]="a[j]," a[i] a[i+1], a[end]="a[end]," a[i+1] return (i 1) # function to implement quick sort def quick(a, start, end): a[]="array" be sorted, start="Starting" index, end="Ending" index if (start < p="partition(a," end) is partitioning - 1, printarr(a): print the array for in range(len(a)): (a[i], ) a="[68," 13, 49, 58] print('before sorting elements are ') printarr(a) 0, len(a)-1) print('
after pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-16.webp" alt="Quick Sort Algorithm"> <p> <strong>Program:</strong> Write a program to implement quicksort in Java.</p> <pre> public class Quick { /* function that consider last element as pivot, place the pivot at its exact position, and place smaller elements to left of pivot and greater elements to right of pivot. */ int partition (int a[], int start, int end) { int pivot = a[end]; // pivot element int i = (start - 1); for (int j = start; j <= 25 end - 1; j++) { if current element is smaller than the pivot (a[j] < pivot) i++; increment index of int t="a[i];" a[i]="a[j];" a[j]="t;" } a[i+1]="a[end];" a[end]="t;" return (i + 1); * function to implement quick sort void quick(int a[], start, end) a[]="array" be sorted, start="Starting" index, (start p="partition(a," end); partitioning quick(a, 1, print an array printarr(int n) i; for i n; i++) system.out.print(a[i] ' '); public static main(string[] args) 13, 18, 27, 2, 19, }; n="a.length;" system.out.println('
before sorting elements are q1="new" quick(); q1.printarr(a, n); q1.quick(a, 0, system.out.println('
after system.out.println(); pre> <p> <strong>Output</strong> </p> <p>After the execution of above code, the output will be -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-17.webp" alt="Quick Sort Algorithm"> <p> <strong>Program:</strong> Write a program to implement quick sort in php.</p> <pre> <?php /* function that consider last element as pivot, place the pivot at its exact position, and place smaller elements to left of pivot and greater elements to right of pivot. */ function partition (&$a, $start, $end) { $pivot = $a[$end]; // pivot element $i = ($start - 1); for ($j = $start; $j <= $end - 1; $j++) { // If current element is smaller than the pivot if ($a[$j] < $pivot) { $i++; // increment index of smaller element $t = $a[$i]; $a[$i] = $a[$j]; $a[$j] = $t; } } $t = $a[$i+1]; $a[$i+1] = $a[$end]; $a[$end] = $t; return ($i + 1); } /* function to implement quick sort */ function quick(&$a, $start, $end) /* a[] = array to be sorted, start = Starting index, end = Ending index */ { if ($start < $end) { $p = partition($a, $start, $end); //p is partitioning index quick($a, $start, $p - 1); quick($a, $p + 1, $end); } } function printArray($a, $n) { for($i = 0; $i < $n; $i++) { print_r($a[$i]); echo ' '; } } $a = array( 89, 47, 2, 17, 8, 19 ); $n = count($a); echo 'Before sorting array elements are - <br>'; printArray($a, $n); quick($a, 0, $n - 1); echo ' <br> After sorting array elements are - <br>'; printArray($a, $n); ?> </pre> <p> <strong>Output</strong> </p> <p>After the execution of above code, the output will be -</p> <img src="//techcodeview.com/img/ds-tutorial/75/quick-sort-algorithm-18.webp" alt="Quick Sort Algorithm"> <p>So, that's all about the article. Hope the article will be helpful and informative to you.</p> <p>This article was not only limited to the algorithm. Along with the algorithm, we have also discussed the quick sort complexity, working, and implementation in different programming languages.</p> <hr></=></pre></=></pre></=></pre></=></pre></a[right],></p></a[left],></p></a[right],></p></pivot)></pre></end)> Lähtö
Yllä olevan koodin suorittamisen jälkeen tulos on -
Eli siinä kaikki artikkelista. Toivottavasti artikkeli on hyödyllinen ja informatiivinen sinulle.
Tämä artikkeli ei rajoittunut vain algoritmiin. Algoritmin ohella olemme keskustelleet myös pikalajittelun monimutkaisuudesta, toiminnasta ja toteutuksesta eri ohjelmointikielissä.
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