- Oorsig
- Algemene algoritme
- Pseudokode
- Illustrasie
- C++ Voorbeeld
- Java Example
- Complexity Analysis Of The Insertion Sort Algorithm
- Conclusion
'n In-diepte blik op invoegingssortering met klassieke voorbeelde.
Invoegingssortering is 'n sorteertegniek wat gesien kan word op 'n manier wat ons kaarte byderhand speel. Die manier waarop ons enige kaart in 'n dek insit of dit verwyder, invoegsorteer werk op 'n soortgelyke manier.
Invoegingssorteeralgoritmetegniek is meer doeltreffend as die borrelsorteer- en seleksie-sorteertegnieke, maar is minder doeltreffend as die ander tegnieke soos Quicksort en Merge sort.
Oorsig
In die invoegingssorteertegniek begin ons van die tweede element en vergelyk dit met die eerste element en plaas dit op 'n regte plek. Dan voer ons hierdie proses uit vir die daaropvolgende elemente.
Ons vergelyk elke element met al sy vorige elemente en plaas of plaas die element in sy regte posisie. Invoegingssorteertegniek is meer haalbaar vir skikkings met 'n kleiner aantal elemente. Dit is ook nuttig om gekoppelde lyste te sorteer.
Gekoppelde lyste het 'n wyser na die volgende element (in die geval van 'n enkelgeskakelde lys) en 'n wyser na die vorige element ook (in die geval van 'n dubbelgeskakelde lys) ). Daarom word dit makliker om invoegingssorteer vir 'n gekoppelde lys te implementeer.
Kom ons verken alles oor invoegingssortering in hierdie tutoriaal.
Algemene algoritme
Stap 1 : Herhaal Stap 2 tot 5 vir K = 1 tot N-1
Stap 2 : stel temp = A[K]
Stap 3 : stel J = K– 1
Stap 4 : Herhaal terwyl temp =A[J]
stel A[J + 1] = A[J]
stel J = J – 1
[einde van binnelus]
Stap 5 : stel A[J + 1] = temp
[ einde van lus]
Stap 6 : uitgang
In die invoegingssorteertegniek begin ons dus vanaf die tweede element aangesien ons aanneem dat die eerste element altyd gesorteer is . Dan van die tweede element tot die laaste element, vergelyk ons elke element met al sy vorige elemente en plaas daardie element in die regte posisie.
Pseudokode
Die pseudokode vir invoegingssorteer word hieronder gegee.
procedure insertionSort(array,N ) array – array to be sorted N- number of elements begin int freePosition int insert_val for i = 1 to N -1 do: insert_val = array[i] freePosition = i //locate free position to insert the element whilefreePosition> 0 and array[freePosition -1] >insert_val do: array [freePosition] = array [freePosition -1] freePosition = freePosition -1 end while //insert the number at free position array [freePosition] = insert_val end for end procedure
Gegewe hierbo is die pseudokode vir Invoegingssortering, volgende, ons sal hierdie tegniek in die volgende voorbeeld illustreer.
Illustrasie
Die skikking wat gesorteer moet word, is soos volg:
Nou vir elke pas, vergelyk ons die huidige element met al sy vorige elemente. So in die eerste pas, begin ons met die tweede element.
Daarom benodig ons N aantal deure om 'n skikking wat N aantal elemente bevat, heeltemal te sorteer.
Bogenoemde illustrasie kan in 'n tabelvorm opgesom word:
Slaag | Ongesorteerde lys | vergelyking | Gesorteerlys |
---|---|---|---|
1 | {12,3,5,10,8,1} | {12,3} | {3,12,5,10,8,1} |
2 | {3,12,5,10,8,1} | {3,12,5} | {3,5,12,10,8,1} |
3 | { 3,5,12,10,8,1} | {3,5,12,10} | {3,5,10,12,8,1} |
4 | {3,5,10,12,8,1} | {3,5,10,12,8} | {3,5,8,10,12,1} |
5 | {3,5,8,10,12,1} | {3,5,8,10,12,1} | {1,3,5,8,10,12} |
6 | {} | {} | {1,3,5,8,10,12} |
Soos getoon in die illustrasie hierbo, begin ons met die 2de element aangesien ons aanneem dat die eerste element altyd gesorteer is. Ons begin dus met die vergelyking van die tweede element met die eerste een en ruil die posisie om as die tweede element minder as die eerste is.
Hierdie vergelyking en omruilproses plaas twee elemente op hul regte plekke. Vervolgens vergelyk ons die derde element met sy vorige (eerste en tweede) elemente en voer dieselfde prosedure uit om die derde element op die regte plek te plaas.
Op hierdie manier, vir elke pas, plaas ons een element in sy plek. Vir die eerste pas plaas ons die tweede element in sy plek. Dus, oor die algemeen, om N elemente op hul regte plek te plaas, benodig ons N-1 slaag.
Volgende, sal ons die Invoeging sorteer tegniek implementering in C++ taal demonstreer.
C++ Voorbeeld
#include using namespace std; int main () { int myarray[10] = { 12,4,3,1,15,45,33,21,10,2}; cout"\nInput list is \n"; for(int i=0;i10;i++) { cout="" Output:
Input list is
12 4 3 1 15 45 33 21 10 2
Sorted list is
1 2 3 4 10 12 15 21 33 45
Next, we will see the Java implementation of the Insertion sort technique.
Java Example
public class Main { public static void main(String[] args) { int[] myarray = {12,4,3,1,15,45,33,21,10,2}; System.out.println("Input list of elements ..."); for(int i=0;i10;i++) { System.out.print(myarray[i] + " "); } for(int k=1; k=0 && temp = myarray[j]) { myarray[j+1] = myarray[j]; j = j-1; } myarray[j+1] = temp; } System.out.println("\nsorted list of elements ..."); for(int i=0;i10;i++) { System.out.print(myarray[i] + " "); } } }Output:
Input list of elements …
12 4 3 1 15 45 33 21 10 2
sorted list of elements …
1 2 3 4 10 12 15 21 33 45
In both the implementations, we can see that we begin sorting from the 2nd element of the array (loop variable j = 1) and repeatedly compare the current element to all its previous elements and then sort the element to place it in its correct position if the current element is not in order with all its previous elements.
Insertion sort works the best and can be completed in fewer passes if the array is partially sorted. But as the list grows bigger, its performance decreases. Another advantage of Insertion sort is that it is a Stable sort which means it maintains the order of equal elements in the list.
Complexity Analysis Of The Insertion Sort Algorithm
From the pseudo code and the illustration above, insertion sort is the efficient algorithm when compared to bubble sort or selection sort. Instead of using for loop and present conditions, it uses a while loop that does not perform any more extra steps when the array is sorted.
However, even if we pass the sorted array to the Insertion sort technique, it will still execute the outer for loop thereby requiring n number of steps to sort an already sorted array. This makes the best time complexity of insertion sort a linear function of N where N is the number of elements in the array.
Thus the various complexities for Insertion sort technique are given below:
Worst case time complexity O(n 2 ) Best case time complexity O(n) Average time complexity O(n 2 ) Space complexity O(1) In spite of these complexities, we can still conclude that Insertion sort is the most efficient algorithm when compared with the other sorting techniques like Bubble sort and Selection sort.
Conclusion
Insertion sort is the most efficient of all the three techniques discussed so far. Here, we assume that the first element is sorted and then repeatedly compare every element to all its previous elements and then place the current element in its correct position in the array.
In this tutorial, while discussing Insertion sort we have noticed that we compare the elements using an increment of 1 and also they are contiguous. This feature results in requiring more passes to get the sorted list.
In our upcoming tutorial, we will discuss “Shell sort” which is an improvement over the Selection sort.
In shell sort, we introduce a variable known as “increment” or a “gap” using which we divide the list into sublists containing non-contiguous elements that “gap” apart. Shell sort requires fewer passes when compared to Insertion sort and is also faster.
In our future tutorials, we will learn about two sorting techniques, “Quicksort” and “Mergesort” which use “Divide and conquer” strategy for sorting data lists.