Kārtot pāra vietā pieaugošā un nepāra secībā dilstošā secībā
Mums ir dots n atšķirīgu skaitļu masīvs. Uzdevums ir sakārtot visus pāra skaitļus augošā un nepāra skaitļus dilstošā secībā. Modificētajā masīvā ir jāietver visi sakārtoti pāra skaitļi, kam seko apgriezti sakārtoti nepāra skaitļi.
Ņemiet vērā, ka pirmais elements tiek uzskatīts par pat novietotu tā indeksa 0 dēļ.
Piemēri:
Ievade: arr[] = {0 1 2 3 4 5 6 7}
Izvade: arr[] = {0 2 4 6 7 5 3 1}
Paskaidrojums:
Līdzās vietas elementi: 0 2 4 6
Nepāra vietas elementi: 1 3 5 7
Vienmērīgi elementi augošā secībā:
0 2 4 6
Nepāra vietas elementi dilstošā secībā:
7 5 3 1
Ievade: arr[] = {3 1 2 4 5 9 13 14 12}
Izvade: {2 3 5 12 13 14 9 4 1}
Paskaidrojums:
Līdzās vietas elementi: 3 2 5 13 12
Nepāra vietas elementi : 1 4 9 14
Vienmērīgi elementi augošā secībā:
2 3 5 12 13
Nepāra vietas elementi dilstošā secībā:
14 9 4 1
[Naivā pieeja] — O(n Log n) laiks un O(n) telpa
Ideja ir vienkārša. Mēs izveidojam attiecīgi divus papildu masīvus evenArr[] un oddArr[]. Mēs šķērsojam ievades masīvu un visus pāra izvietošanas elementus ievietojam evenArr[] un nepāra vietas elementus oddArr[]. Pēc tam mēs sakārtojam evenArr[] augošā un oddArr[] dilstošā secībā. Visbeidzot nokopējiet evenArr[] un oddArr[], lai iegūtu vajadzīgo rezultātu.
C++ // Program to separately sort even-placed and odd // placed numbers and place them together in sorted // array. #include using namespace std ; void bitonicGenerator ( vector < int >& arr ) { // create evenArr[] and oddArr[] vector < int > evenArr ; vector < int > oddArr ; // Put elements in oddArr[] and evenArr[] as // per their position for ( int i = 0 ; i < arr . size (); i ++ ) { if ( ! ( i % 2 )) evenArr . push_back ( arr [ i ]); else oddArr . push_back ( arr [ i ]); } // sort evenArr[] in ascending order // sort oddArr[] in descending order sort ( evenArr . begin () evenArr . end ()); sort ( oddArr . begin () oddArr . end () greater < int > ()); int i = 0 ; for ( int j = 0 ; j < evenArr . size (); j ++ ) arr [ i ++ ] = evenArr [ j ]; for ( int j = 0 ; j < oddArr . size (); j ++ ) arr [ i ++ ] = oddArr [ j ]; } // Driver Program int main () { vector < int > arr = { 1 5 8 9 6 7 3 4 2 0 }; bitonicGenerator ( arr ); for ( int i = 0 ; i < arr . size (); i ++ ) cout < < arr [ i ] < < ' ' ; return 0 ; }
Java // Program to separately sort even-placed and odd // placed numbers and place them together in sorted // array. import java.util.* ; public class Main { public static void bitonicGenerator ( int [] arr ) { // create evenArr[] and oddArr[] List < Integer > evenArr = new ArrayList <> (); List < Integer > oddArr = new ArrayList <> (); // Put elements in oddArr[] and evenArr[] as // per their position for ( int i = 0 ; i < arr . length ; i ++ ) { if ( i % 2 == 0 ) evenArr . add ( arr [ i ] ); else oddArr . add ( arr [ i ] ); } // sort evenArr[] in ascending order // sort oddArr[] in descending order Collections . sort ( evenArr ); Collections . sort ( oddArr Collections . reverseOrder ()); int i = 0 ; for ( int num : evenArr ) arr [ i ++] = num ; for ( int num : oddArr ) arr [ i ++] = num ; } public static void main ( String [] args ) { int [] arr = { 1 5 8 9 6 7 3 4 2 0 }; bitonicGenerator ( arr ); for ( int num : arr ) System . out . print ( num + ' ' ); } }
Python # Program to separately sort even-placed and odd # placed numbers and place them together in sorted # array. def bitonic_generator ( arr ): # create evenArr[] and oddArr[] evenArr = [] oddArr = [] # Put elements in oddArr[] and evenArr[] as # per their position for i in range ( len ( arr )): if i % 2 == 0 : evenArr . append ( arr [ i ]) else : oddArr . append ( arr [ i ]) # sort evenArr[] in ascending order # sort oddArr[] in descending order evenArr . sort () oddArr . sort ( reverse = True ) i = 0 for num in evenArr : arr [ i ] = num i += 1 for num in oddArr : arr [ i ] = num i += 1 # Driver Program arr = [ 1 5 8 9 6 7 3 4 2 0 ] bitonic_generator ( arr ) print ( ' ' . join ( map ( str arr )))
C# // Program to separately sort even-placed and odd // placed numbers and place them together in sorted // array. using System ; using System.Collections.Generic ; using System.Linq ; class Program { static void BitonicGenerator ( int [] arr ) { // create evenArr[] and oddArr[] List < int > evenArr = new List < int > (); List < int > oddArr = new List < int > (); // Put elements in oddArr[] and evenArr[] as // per their position for ( int i = 0 ; i < arr . Length ; i ++ ) { if ( i % 2 == 0 ) evenArr . Add ( arr [ i ]); else oddArr . Add ( arr [ i ]); } // sort evenArr[] in ascending order // sort oddArr[] in descending order evenArr . Sort (); oddArr . Sort (( a b ) => b . CompareTo ( a )); int index = 0 ; foreach ( var num in evenArr ) arr [ index ++ ] = num ; foreach ( var num in oddArr ) arr [ index ++ ] = num ; } static void Main () { int [] arr = { 1 5 8 9 6 7 3 4 2 0 }; BitonicGenerator ( arr ); Console . WriteLine ( string . Join ( ' ' arr )); } }
JavaScript // Program to separately sort even-placed and odd // placed numbers and place them together in sorted // array. function bitonicGenerator ( arr ) { // create evenArr[] and oddArr[] const evenArr = []; const oddArr = []; // Put elements in oddArr[] and evenArr[] as // per their position for ( let i = 0 ; i < arr . length ; i ++ ) { if ( i % 2 === 0 ) evenArr . push ( arr [ i ]); else oddArr . push ( arr [ i ]); } // sort evenArr[] in ascending order // sort oddArr[] in descending order evenArr . sort (( a b ) => a - b ); oddArr . sort (( a b ) => b - a ); let i = 0 ; for ( const num of evenArr ) arr [ i ++ ] = num ; for ( const num of oddArr ) arr [ i ++ ] = num ; } // Driver Program const arr = [ 1 5 8 9 6 7 3 4 2 0 ]; bitonicGenerator ( arr ); console . log ( arr . join ( ' ' ));
PHP // Program to separately sort even-placed and odd // placed numbers and place them together in sorted // array. function bitonicGenerator(&$arr) { // create evenArr[] and oddArr[] $evenArr = []; $oddArr = []; // Put elements in oddArr[] and evenArr[] as // per their position foreach ($arr as $i => $value) { if ($i % 2 === 0) $evenArr[] = $value; else $oddArr[] = $value; } // sort evenArr[] in ascending order // sort oddArr[] in descending order sort($evenArr); rsort($oddArr); $i = 0; foreach ($evenArr as $num) { $arr[$i++] = $num; } foreach ($oddArr as $num) { $arr[$i++] = $num; } } // Driver Program $arr = [1 5 8 9 6 7 3 4 2 0]; bitonicGenerator($arr); echo implode(' ' $arr);
Izvade
1 2 3 6 8 9 7 5 4 0
[Paredzamā pieeja — 1] — O(n Log n) laiks un O(1) telpa
Problēmu var atrisināt arī neizmantojot palīgtelpu. Ideja ir apmainīt pirmo pusi nepāra indeksa pozīcijas ar otrās puses pāra indeksa pozīcijām un pēc tam kārtot masīva pirmo pusi augošā secībā un otro pusi masīva dilstošā secībā.
C++ #include using namespace std ; void bitonicGenerator ( vector < int >& arr ) { // first odd index int i = 1 ; // last index int n = arr . size (); int j = n - 1 ; // if last index is odd if ( j % 2 != 0 ) // decrement j to even index j -- ; // swapping till half of array while ( i < j ) { swap ( arr [ i ] arr [ j ]); i += 2 ; j -= 2 ; } // Sort first half in increasing sort ( arr . begin () arr . begin () + ( n + 1 ) / 2 ); // Sort second half in decreasing sort ( arr . begin () + ( n + 1 ) / 2 arr . end () greater < int > ()); } // Driver Program int main () { vector < int > arr = { 1 5 8 9 6 7 3 4 2 0 }; bitonicGenerator ( arr ); for ( int i = 0 ; i < arr . size (); i ++ ) cout < < arr [ i ] < < ' ' ; return 0 ; }
Java import java.util.Arrays ; class BitonicGenerator { public static void bitonicGenerator ( int [] arr ) { // first odd index int i = 1 ; // last index int n = arr . length ; int j = n - 1 ; // if last index is odd if ( j % 2 != 0 ) // decrement j to even index j -- ; // swapping till half of array while ( i < j ) { int temp = arr [ i ] ; arr [ i ] = arr [ j ] ; arr [ j ] = temp ; i += 2 ; j -= 2 ; } // Sort first half in increasing order Arrays . sort ( arr 0 ( n + 1 ) / 2 ); // Sort second half in decreasing order Arrays . sort ( arr ( n + 1 ) / 2 n ); reverse ( arr ( n + 1 ) / 2 n ); } private static void reverse ( int [] arr int start int end ) { end -- ; while ( start < end ) { int temp = arr [ start ] ; arr [ start ] = arr [ end ] ; arr [ end ] = temp ; start ++ ; end -- ; } } // Driver Program public static void main ( String [] args ) { int [] arr = { 1 5 8 9 6 7 3 4 2 0 }; bitonicGenerator ( arr ); for ( int num : arr ) { System . out . print ( num + ' ' ); } } }
Python def bitonic_generator ( arr ): # first odd index i = 1 # last index n = len ( arr ) j = n - 1 # if last index is odd if j % 2 != 0 : # decrement j to even index j -= 1 # swapping till half of array while i < j : arr [ i ] arr [ j ] = arr [ j ] arr [ i ] i += 2 j -= 2 # Sort first half in increasing arr [:( n + 1 ) // 2 ] = sorted ( arr [:( n + 1 ) // 2 ]) # Sort second half in decreasing arr [( n + 1 ) // 2 :] = sorted ( arr [( n + 1 ) // 2 :] reverse = True ) # Driver Program arr = [ 1 5 8 9 6 7 3 4 2 0 ] bitonic_generator ( arr ) print ( ' ' . join ( map ( str arr )))
C# // Function to generate a bitonic sequence using System ; using System.Collections.Generic ; using System.Linq ; class Program { static void BitonicGenerator ( List < int > arr ) { // first odd index int i = 1 ; // last index int n = arr . Count ; int j = n - 1 ; // if last index is odd if ( j % 2 != 0 ) // decrement j to even index j -- ; // swapping till half of array while ( i < j ) { int temp = arr [ i ]; arr [ i ] = arr [ j ]; arr [ j ] = temp ; i += 2 ; j -= 2 ; } // Sort first half in increasing arr . Sort ( 0 ( n + 1 ) / 2 ); // Sort second half in decreasing arr . Sort (( n + 1 ) / 2 n - ( n + 1 ) / 2 Comparer < int > . Create (( x y ) => y . CompareTo ( x ))); } // Driver Program static void Main () { List < int > arr = new List < int > { 1 5 8 9 6 7 3 4 2 0 }; BitonicGenerator ( arr ); Console . WriteLine ( string . Join ( ' ' arr )); } }
JavaScript // Function to generate a bitonic sequence function bitonicGenerator ( arr ) { // first odd index let i = 1 ; // last index let n = arr . length ; let j = n - 1 ; // if last index is odd if ( j % 2 !== 0 ) // decrement j to even index j -- ; // swapping till half of array while ( i < j ) { [ arr [ i ] arr [ j ]] = [ arr [ j ] arr [ i ]]; i += 2 ; j -= 2 ; } // Sort first half in increasing arr . sort (( a b ) => a - b ); // Sort second half in decreasing arr . slice (( n + 1 ) / 2 ). sort (( a b ) => b - a ); } // Driver Program let arr = [ 1 5 8 9 6 7 3 4 2 0 ]; bitonicGenerator ( arr ); console . log ( arr . join ( ' ' ));
Izvade
1 2 3 6 8 9 7 5 4 0
Piezīme: Šķiet, ka iepriekšminētajiem Python un JS kodiem ir nepieciešama papildu vieta. Pastāstiet mums komentāros par savām domām un jebkādām alternatīvām ieviešanām.
[Paredzamā pieeja — 2] — O(n Log n) laiks un O(1) telpa
Vēl viena efektīva pieeja problēmas risināšanai O(1) palīgtelpā ir ar Izmantojot negatīvo reizināšanu .
Iesaistītās darbības ir šādas:
- Reiziniet visus elementus pāra indeksā ar -1.
- Kārtojiet visu masīvu. Tādā veidā mēs varam iegūt visus pat novietotos indeksus sākumā, jo tie tagad ir negatīvi skaitļi.
- Tagad atgrieziet šo elementu zīmi.
- Pēc tam apgrieziet masīva pirmo pusi, kurā ir pāra numurs, lai padarītu to augošā secībā.
- Un pēc tam apgrieziet pārējo masīva pusi, lai nepāra skaitļus izveidotu dilstošā secībā.
Piezīme: Šī metode ir piemērojama tikai tad, ja visi masīva elementi nav negatīvi.
Iepriekš minētās pieejas ilustratīvs piemērs:
Ļaujiet dotajam masīvam: arr[] = {0 1 2 3 4 5 6 7}
Masīvs pēc reizināšanas ar -1 līdz pat novietotiem elementiem: arr[] = {01-23-45-67}
Masīvs pēc šķirošanas: arr[] = {-6 -4 -2 0 1 3 5 7}
Masīvs pēc negatīvo vērtību atgriešanas: arr[] = {6 4 2 0 1 3 5 7}
Pēc masīva pirmās puses apvēršanas: arr[] = 0 2 4 6 1 3 5 7}
Pēc masīva otrās puses maiņas: arr[] = 0 2 4 6 7 5 3 1}
Tālāk ir norādīts iepriekš minētās pieejas kods:
C++ #include using namespace std ; void bitonicGenerator ( vector < int >& arr ) { // Making all even placed index // element negative for ( int i = 0 ; i < arr . size (); i ++ ) { if ( i % 2 == 0 ) arr [ i ] = -1 * arr [ i ]; } // Sorting the whole array sort ( arr . begin () arr . end ()); // Finding the middle value of // the array int mid = ( arr . size () - 1 ) / 2 ; // Reverting the changed sign for ( int i = 0 ; i <= mid ; i ++ ) { arr [ i ] = -1 * arr [ i ]; } // Reverse first half of array reverse ( arr . begin () arr . begin () + mid + 1 ); // Reverse second half of array reverse ( arr . begin () + mid + 1 arr . end ()); } // Driver Program int main () { vector < int > arr = { 1 5 8 9 6 7 3 4 2 0 }; bitonicGenerator ( arr ); for ( int i = 0 ; i < arr . size (); i ++ ) cout < < arr [ i ] < < ' ' ; return 0 ; }
Java import java.util.Arrays ; import java.util.List ; public class BitonicGenerator { public static void bitonicGenerator ( List < Integer > arr ) { // Making all even placed index // element negative for ( int i = 0 ; i < arr . size (); i ++ ) { if ( i % 2 == 0 ) arr . set ( i - 1 * arr . get ( i )); } // Sorting the whole array Collections . sort ( arr ); // Finding the middle value of // the array int mid = ( arr . size () - 1 ) / 2 ; // Reverting the changed sign for ( int i = 0 ; i <= mid ; i ++ ) { arr . set ( i - 1 * arr . get ( i )); } // Reverse first half of array Collections . reverse ( arr . subList ( 0 mid + 1 )); // Reverse second half of array Collections . reverse ( arr . subList ( mid + 1 arr . size ())); } // Driver Program public static void main ( String [] args ) { List < Integer > arr = Arrays . asList ( 1 5 8 9 6 7 3 4 2 0 ); bitonicGenerator ( arr ); for ( int i : arr ) System . out . print ( i + ' ' ); } }
Python def bitonic_generator ( arr ): # Making all even placed index # element negative for i in range ( len ( arr )): if i % 2 == 0 : arr [ i ] = - 1 * arr [ i ] # Sorting the whole array arr . sort () # Finding the middle value of # the array mid = ( len ( arr ) - 1 ) // 2 # Reverting the changed sign for i in range ( mid + 1 ): arr [ i ] = - 1 * arr [ i ] # Reverse first half of array arr [: mid + 1 ] = reversed ( arr [: mid + 1 ]) # Reverse second half of array arr [ mid + 1 :] = reversed ( arr [ mid + 1 :]) # Driver Program arr = [ 1 5 8 9 6 7 3 4 2 0 ] bitonic_generator ( arr ) print ( ' ' . join ( map ( str arr )))
C# using System ; using System.Collections.Generic ; using System.Linq ; class BitonicGenerator { public static void BitonicGeneratorMethod ( List < int > arr ) { // Making all even placed index // element negative for ( int i = 0 ; i < arr . Count ; i ++ ) { if ( i % 2 == 0 ) arr [ i ] = - 1 * arr [ i ]; } // Sorting the whole array arr . Sort (); // Finding the middle value of // the array int mid = ( arr . Count - 1 ) / 2 ; // Reverting the changed sign for ( int i = 0 ; i <= mid ; i ++ ) { arr [ i ] = - 1 * arr [ i ]; } // Reverse first half of array arr . Take ( mid + 1 ). Reverse (). ToList (). CopyTo ( arr ); // Reverse second half of array arr . Skip ( mid + 1 ). Reverse (). ToList (). CopyTo ( arr mid + 1 ); } // Driver Program public static void Main () { List < int > arr = new List < int > { 1 5 8 9 6 7 3 4 2 0 }; BitonicGeneratorMethod ( arr ); Console . WriteLine ( string . Join ( ' ' arr )); } }
JavaScript function bitonicGenerator ( arr ) { // Making all even placed index // element negative for ( let i = 0 ; i < arr . length ; i ++ ) { if ( i % 2 === 0 ) arr [ i ] = - 1 * arr [ i ]; } // Sorting the whole array arr . sort (( a b ) => a - b ); // Finding the middle value of // the array const mid = Math . floor (( arr . length - 1 ) / 2 ); // Reverting the changed sign for ( let i = 0 ; i <= mid ; i ++ ) { arr [ i ] = - 1 * arr [ i ]; } // Reverse first half of array arr . slice ( 0 mid + 1 ). reverse (). forEach (( val index ) => arr [ index ] = val ); // Reverse second half of array arr . slice ( mid + 1 ). reverse (). forEach (( val index ) => arr [ mid + 1 + index ] = val ); } // Driver Program let arr = [ 1 5 8 9 6 7 3 4 2 0 ]; bitonicGenerator ( arr ); console . log ( arr . join ( ' ' ));
Izvade
1 2 3 6 8 9 7 5 4 0
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