Löydä permutaatio, joka aiheuttaa sulautumisen pahimman tapauksen
Kun otetaan huomioon joukko elementtejä, selvittää, mikä näiden elementtien permutaatio johtaisi pahimpaan sulautumislajitteluun.
Asymptoottisesti sulautumislajittelu vie aina O (n log n) -ajan, mutta tapaukset, jotka vaativat enemmän vertailuja, vievät yleensä enemmän aikaa käytännössä. Meidän on periaatteessa löydettävä syöttöelementtien permutaatio, joka johtaisi maksimaaliseen vertailuihin lajiteltuna tyypillisen yhdistämislajittelun algoritmin avulla.
Esimerkki:
Consider the below set of elements
{1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16}
Below permutation of the set causes 153
comparisons.
{1 9 5 13 3 11 7 15 2 10 6
14 4 12 8 16}
And an already sorted permutation causes
30 comparisons.Nyt kuinka saada pahimman tapauksen syöttö sulautumisjoukkoon?
Antaa meidän yrittää rakentaa taulukko alhaalta ylöspäin
Olkoon lajiteltu taulukko {12345678}.Yhdistämisen pahimman tapauksen luomiseksi sulautumisoperaatio, joka johti edellä lajiteltuun taulukkoon, pitäisi johtaa maksimaalisiin vertailuihin. Yhdenmukaiseen toimintaan osallistuvan vasemman ja oikean alaryhmän tulisi tehdä niin lajitetun taulukon vaihtoehtoisia elementtejä. ts. Vasemman alajoukon tulisi olla {1357} ja oikean alaryhmän tulisi olla {2468}. Nyt jokaista taulukon elementtiä verrataan kerrankin pylväänä, ja se johtaa maksimaalisiin vertailuihin. Käytämme samaa logiikkaa myös vasemmalle ja oikealle alaryhmälle. Array {1357} Pahinta tapausta on, kun sen vasen ja oikea alajoukko ovat {15} ja {37} ja taulukossa {2468} Pahinta tapausta tapahtuu {24} ja {68}.
Täydellinen algoritmi -
GenerateworstCase (arr [])
- Luo kaksi apuryhmää vasemmalle ja oikealle ja säilytä niihin vaihtoehtoisia taulukkoelementtejä.
- Soita GenerateWorstCase vasemmalle alaryhmälle: GenerateWorstCase (vasen)
- Soita GenerateWorstCase oikealle alaryhmälle: GenerateWorstCase (oikea)
- Kopioi kaikki vasemman ja oikean alaryhmien elementit takaisin alkuperäiseen taulukkoon.
Alla on idean toteutus
C++C// C++ program to generate Worst Case // of Merge Sort #includeusing namespace std ; // Function to print an array void printArray ( int A [] int size ) { for ( int i = 0 ; i < size ; i ++ ) { cout < < A [ i ] < < ' ' ; } cout < < endl ; } // Function to join left and right subarray int join ( int arr [] int left [] int right [] int l int m int r ) { int i ; for ( i = 0 ; i <= m - l ; i ++ ) arr [ i ] = left [ i ]; for ( int j = 0 ; j < r - m ; j ++ ) { arr [ i + j ] = right [ j ]; } } // Function to store alternate elements in // left and right subarray int split ( int arr [] int left [] int right [] int l int m int r ) { for ( int i = 0 ; i <= m - l ; i ++ ) left [ i ] = arr [ i * 2 ]; for ( int i = 0 ; i < r - m ; i ++ ) right [ i ] = arr [ i * 2 + 1 ]; } // Function to generate Worst Case // of Merge Sort int generateWorstCase ( int arr [] int l int r ) { if ( l < r ) { int m = l + ( r - l ) / 2 ; // Create two auxiliary arrays int left [ m - l + 1 ]; int right [ r - m ]; // Store alternate array elements // in left and right subarray split ( arr left right l m r ); // Recurse first and second halves generateWorstCase ( left l m ); generateWorstCase ( right m + 1 r ); // Join left and right subarray join ( arr left right l m r ); } } // Driver code int main () { // Sorted array int arr [] = { 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 }; int n = sizeof ( arr ) / sizeof ( arr [ 0 ]); cout < < 'Sorted array is n ' ; printArray ( arr n ); // Generate Worst Case of Merge Sort generateWorstCase ( arr 0 n - 1 ); cout < < ' n Input array that will result ' < < 'in worst case of merge sort is n ' ; printArray ( arr n ); return 0 ; } // This code is contributed by Mayank Tyagi Java// C program to generate Worst Case of Merge Sort #include#include // Function to print an array void printArray ( int A [] int size ) { for ( int i = 0 ; i < size ; i ++ ) printf ( '%d ' A [ i ]); printf ( ' n ' ); } // Function to join left and right subarray int join ( int arr [] int left [] int right [] int l int m int r ) { int i ; // Used in second loop for ( i = 0 ; i <= m - l ; i ++ ) arr [ i ] = left [ i ]; for ( int j = 0 ; j < r - m ; j ++ ) arr [ i + j ] = right [ j ]; } // Function to store alternate elements in left // and right subarray int split ( int arr [] int left [] int right [] int l int m int r ) { for ( int i = 0 ; i <= m - l ; i ++ ) left [ i ] = arr [ i * 2 ]; for ( int i = 0 ; i < r - m ; i ++ ) right [ i ] = arr [ i * 2 + 1 ]; } // Function to generate Worst Case of Merge Sort int generateWorstCase ( int arr [] int l int r ) { if ( l < r ) { int m = l + ( r - l ) / 2 ; // create two auxiliary arrays int left [ m - l + 1 ]; int right [ r - m ]; // Store alternate array elements in left // and right subarray split ( arr left right l m r ); // Recurse first and second halves generateWorstCase ( left l m ); generateWorstCase ( right m + 1 r ); // join left and right subarray join ( arr left right l m r ); } } // Driver code int main () { // Sorted array int arr [] = { 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 }; int n = sizeof ( arr ) / sizeof ( arr [ 0 ]); printf ( 'Sorted array is n ' ); printArray ( arr n ); // generate Worst Case of Merge Sort generateWorstCase ( arr 0 n - 1 ); printf ( ' n Input array that will result in ' 'worst case of merge sort is n ' ); printArray ( arr n ); return 0 ; } Python// Java program to generate Worst Case of Merge Sort import java.util.Arrays ; class GFG { // Function to join left and right subarray static void join ( int arr [] int left [] int right [] int l int m int r ) { int i ; for ( i = 0 ; i <= m - l ; i ++ ) arr [ i ] = left [ i ] ; for ( int j = 0 ; j < r - m ; j ++ ) arr [ i + j ] = right [ j ] ; } // Function to store alternate elements in left // and right subarray static void split ( int arr [] int left [] int right [] int l int m int r ) { for ( int i = 0 ; i <= m - l ; i ++ ) left [ i ] = arr [ i * 2 ] ; for ( int i = 0 ; i < r - m ; i ++ ) right [ i ] = arr [ i * 2 + 1 ] ; } // Function to generate Worst Case of Merge Sort static void generateWorstCase ( int arr [] int l int r ) { if ( l < r ) { int m = l + ( r - l ) / 2 ; // create two auxiliary arrays int [] left = new int [ m - l + 1 ] ; int [] right = new int [ r - m ] ; // Store alternate array elements in left // and right subarray split ( arr left right l m r ); // Recurse first and second halves generateWorstCase ( left l m ); generateWorstCase ( right m + 1 r ); // join left and right subarray join ( arr left right l m r ); } } // driver program public static void main ( String [] args ) { // sorted array int arr [] = { 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 }; int n = arr . length ; System . out . println ( 'Sorted array is' ); System . out . println ( Arrays . toString ( arr )); // generate Worst Case of Merge Sort generateWorstCase ( arr 0 n - 1 ); System . out . println ( 'nInput array that will result in n' + 'worst case of merge sort is n' ); System . out . println ( Arrays . toString ( arr )); } } // Contributed by Pramod KumarC## Python program to generate Worst Case of Merge Sort # Function to join left and right subarray def join ( arr left right l m r ): i = 0 ; for i in range ( m - l + 1 ): arr [ i ] = left [ i ]; i += 1 ; for j in range ( r - m ): arr [ i + j ] = right [ j ]; # Function to store alternate elements in left # and right subarray def split ( arr left right l m r ): for i in range ( m - l + 1 ): left [ i ] = arr [ i * 2 ]; for i in range ( r - m ): right [ i ] = arr [ i * 2 + 1 ]; # Function to generate Worst Case of Merge Sort def generateWorstCase ( arr l r ): if ( l < r ): m = l + ( r - l ) // 2 ; # create two auxiliary arrays left = [ 0 for i in range ( m - l + 1 )]; right = [ 0 for i in range ( r - m )]; # Store alternate array elements in left # and right subarray split ( arr left right l m r ); # Recurse first and second halves generateWorstCase ( left l m ); generateWorstCase ( right m + 1 r ); # join left and right subarray join ( arr left right l m r ); # driver program if __name__ == '__main__' : # sorted array arr = [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ]; n = len ( arr ); print ( 'Sorted array is' ); print ( arr ); # generate Worst Case of Merge Sort generateWorstCase ( arr 0 n - 1 ); print ( ' n Input array that will result in n ' + 'worst case of merge sort is ' ); print ( arr ); # This code contributed by shikhasingrajputJavaScript// C# program to generate Worst Case of // Merge Sort using System ; class GFG { // Function to join left and right subarray static void join ( int [] arr int [] left int [] right int l int m int r ) { int i ; for ( i = 0 ; i <= m - l ; i ++ ) arr [ i ] = left [ i ]; for ( int j = 0 ; j < r - m ; j ++ ) arr [ i + j ] = right [ j ]; } // Function to store alternate elements in // left and right subarray static void split ( int [] arr int [] left int [] right int l int m int r ) { for ( int i = 0 ; i <= m - l ; i ++ ) left [ i ] = arr [ i * 2 ]; for ( int i = 0 ; i < r - m ; i ++ ) right [ i ] = arr [ i * 2 + 1 ]; } // Function to generate Worst Case of // Merge Sort static void generateWorstCase ( int [] arr int l int r ) { if ( l < r ) { int m = l + ( r - l ) / 2 ; // create two auxiliary arrays int [] left = new int [ m - l + 1 ]; int [] right = new int [ r - m ]; // Store alternate array elements // in left and right subarray split ( arr left right l m r ); // Recurse first and second halves generateWorstCase ( left l m ); generateWorstCase ( right m + 1 r ); // join left and right subarray join ( arr left right l m r ); } } // driver program public static void Main () { // sorted array int [] arr = { 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 }; int n = arr . Length ; Console . Write ( 'Sorted array isn' ); for ( int i = 0 ; i < n ; i ++ ) Console . Write ( arr [ i ] + ' ' ); // generate Worst Case of Merge Sort generateWorstCase ( arr 0 n - 1 ); Console . Write ( 'nInput array that will ' + 'result in n worst case of' + ' merge sort is n' ); for ( int i = 0 ; i < n ; i ++ ) Console . Write ( arr [ i ] + ' ' ); } } // This code is contributed by SmithaLähtö:
Sorted array is
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Input array that will result in worst
case of merge sort is
1 9 5 13 3 11 7 15 2 10 6 14 4 12 8 16Ajan monimutkaisuus: o (n logn)
Aputila: O (n)
Viitteet - Pinon ylivuoto
