Konvertuoti min Heap į „Max Heap“
Atsižvelgiant į masyvą „Min Heap“ vaizdas, konvertuokite jį į „Max Heap“.
Pavyzdžiai:
Įvestis: arr [] = {3 5 9 6 8 20 10 12 18 9}
3
/
5 9
//
6 8 20 10
/ / /
12 18 9Išvestis: arr [] = {20 18 10 12 9 9 3 5 6 8}
20
/
18 10
//
12 9 3
/ / /
5 6 8Įvestis: arr [] = {3 4 8 11 13}
Išvestis: arr [] = {13 11 8 4 3}
Idėja yra tiesiog pastatyti „Max Heap“ nesirūpindamas įvestimi. Pradėkite nuo žemiausio ir dešiniojo vidinio mazgo mazgo ir pakelkite visus vidinius mazgus iš apačios į viršų, kad pastatytumėte maksimalią krūvą.
Atlikite pateiktus veiksmus, kad išspręstumėte problemą:
- Paskambinkite į krūvos funkciją iš dešiniojo vidinio mazgo mazgo
- Kremkite visus vidinius mazgus iš apačios į viršų, kad sukurtumėte „Max Heap“
- Atspausdinkite maksimalų krūvą
Algoritmas: Štai Min krūvos konvertavimo į maksimalią krūvą algoritmas :
- Pradėkite nuo paskutinio krūvos ne lapų mazgo (t. Y. Paskutinio lapų mazgo tėvo). Dvejetainėje krūvoje šis mazgas yra rodyklės grindyse ((n - 1)/2), kur n yra mazgų skaičius krūvoje.
- Kiekvienam ne lapo mazgui atlikite a „Heapify“ operacija, kad būtų galima sutvarkyti krūvos nuosavybę. Min minoje ši operacija apima tikrinimą, ar mazgo vertė yra didesnė nei jo vaikų, ir jei taip keičiasi mazgą su mažesniais savo vaikais. Maksimalioje krūvoje operacija apima tikrinimą, ar mazgo vertė yra mažesnė nei jo vaikų, ir jei taip keičiasi mazgą su didesniais jo vaikais.
- Pakartokite 2 veiksmą kiekvienam iš lapo mazgų, veikiančių jūsų kelią į krūvą. Kai pasieksite krūvos šaknį, visa krūva dabar turėtų būti maksimali krūva.
Žemiau yra aukščiau pateikto požiūrio įgyvendinimas:
C++ // A C++ program to convert min Heap to max Heap #include using namespace std ; // to heapify a subtree with root at given index void MaxHeapify ( int arr [] int i int N ) { int l = 2 * i + 1 ; int r = 2 * i + 2 ; int largest = i ; if ( l < N && arr [ l ] > arr [ i ]) largest = l ; if ( r < N && arr [ r ] > arr [ largest ]) largest = r ; if ( largest != i ) { swap ( arr [ i ] arr [ largest ]); MaxHeapify ( arr largest N ); } } // This function basically builds max heap void convertMaxHeap ( int arr [] int N ) { // Start from bottommost and rightmost // internal node and heapify all internal // nodes in bottom up way for ( int i = ( N - 2 ) / 2 ; i >= 0 ; -- i ) MaxHeapify ( arr i N ); } // A utility function to print a given array // of given size void printArray ( int * arr int size ) { for ( int i = 0 ; i < size ; ++ i ) cout < < arr [ i ] < < ' ' ; } // Driver's code int main () { // array representing Min Heap int arr [] = { 3 5 9 6 8 20 10 12 18 9 }; int N = sizeof ( arr ) / sizeof ( arr [ 0 ]); printf ( 'Min Heap array : ' ); printArray ( arr N ); // Function call convertMaxHeap ( arr N ); printf ( ' n Max Heap array : ' ); printArray ( arr N ); return 0 ; }
C // C program to convert min Heap to max Heap #include void swap ( int * a int * b ) { int temp = * a ; * a = * b ; * b = temp ; } // to heapify a subtree with root at given index void MaxHeapify ( int arr [] int i int N ) { int l = 2 * i + 1 ; int r = 2 * i + 2 ; int largest = i ; if ( l < N && arr [ l ] > arr [ i ]) largest = l ; if ( r < N && arr [ r ] > arr [ largest ]) largest = r ; if ( largest != i ) { swap ( & arr [ i ] & arr [ largest ]); MaxHeapify ( arr largest N ); } } // This function basically builds max heap void convertMaxHeap ( int arr [] int N ) { // Start from bottommost and rightmost // internal node and heapify all internal // nodes in bottom up way for ( int i = ( N - 2 ) / 2 ; i >= 0 ; -- i ) MaxHeapify ( arr i N ); } // A utility function to print a given array // of given size void printArray ( int * arr int size ) { for ( int i = 0 ; i < size ; ++ i ) printf ( '%d ' arr [ i ]); } // Driver's code int main () { // array representing Min Heap int arr [] = { 3 5 9 6 8 20 10 12 18 9 }; int N = sizeof ( arr ) / sizeof ( arr [ 0 ]); printf ( 'Min Heap array : ' ); printArray ( arr N ); // Function call convertMaxHeap ( arr N ); printf ( ' n Max Heap array : ' ); printArray ( arr N ); return 0 ; }
Java // Java program to convert min Heap to max Heap class GFG { // To heapify a subtree with root at given index static void MaxHeapify ( int arr [] int i int N ) { int l = 2 * i + 1 ; int r = 2 * i + 2 ; int largest = i ; if ( l < N && arr [ l ] > arr [ i ] ) largest = l ; if ( r < N && arr [ r ] > arr [ largest ] ) largest = r ; if ( largest != i ) { // swap arr[i] and arr[largest] int temp = arr [ i ] ; arr [ i ] = arr [ largest ] ; arr [ largest ] = temp ; MaxHeapify ( arr largest N ); } } // This function basically builds max heap static void convertMaxHeap ( int arr [] int N ) { // Start from bottommost and rightmost // internal node and heapify all internal // nodes in bottom up way for ( int i = ( N - 2 ) / 2 ; i >= 0 ; -- i ) MaxHeapify ( arr i N ); } // A utility function to print a given array // of given size static void printArray ( int arr [] int size ) { for ( int i = 0 ; i < size ; ++ i ) System . out . print ( arr [ i ] + ' ' ); } // driver's code public static void main ( String [] args ) { // array representing Min Heap int arr [] = { 3 5 9 6 8 20 10 12 18 9 }; int N = arr . length ; System . out . print ( 'Min Heap array : ' ); printArray ( arr N ); // Function call convertMaxHeap ( arr N ); System . out . print ( 'nMax Heap array : ' ); printArray ( arr N ); } } // Contributed by Pramod Kumar
Python3 # A Python3 program to convert min Heap # to max Heap # to heapify a subtree with root # at given index def MaxHeapify ( arr i N ): l = 2 * i + 1 r = 2 * i + 2 largest = i if l < N and arr [ l ] > arr [ i ]: largest = l if r < N and arr [ r ] > arr [ largest ]: largest = r if largest != i : arr [ i ] arr [ largest ] = arr [ largest ] arr [ i ] MaxHeapify ( arr largest N ) # This function basically builds max heap def convertMaxHeap ( arr N ): # Start from bottommost and rightmost # internal node and heapify all # internal nodes in bottom up way for i in range ( int (( N - 2 ) / 2 ) - 1 - 1 ): MaxHeapify ( arr i N ) # A utility function to print a # given array of given size def printArray ( arr size ): for i in range ( size ): print ( arr [ i ] end = ' ' ) print () # Driver Code if __name__ == '__main__' : # array representing Min Heap arr = [ 3 5 9 6 8 20 10 12 18 9 ] N = len ( arr ) print ( 'Min Heap array : ' ) printArray ( arr N ) # Function call convertMaxHeap ( arr N ) print ( 'Max Heap array : ' ) printArray ( arr N ) # This code is contributed by PranchalK
C# // C# program to convert // min Heap to max Heap using System ; class GFG { // To heapify a subtree with // root at given index static void MaxHeapify ( int [] arr int i int n ) { int l = 2 * i + 1 ; int r = 2 * i + 2 ; int largest = i ; if ( l < n && arr [ l ] > arr [ i ]) largest = l ; if ( r < n && arr [ r ] > arr [ largest ]) largest = r ; if ( largest != i ) { // swap arr[i] and arr[largest] int temp = arr [ i ]; arr [ i ] = arr [ largest ]; arr [ largest ] = temp ; MaxHeapify ( arr largest n ); } } // This function basically // builds max heap static void convertMaxHeap ( int [] arr int n ) { // Start from bottommost and // rightmost internal node and // heapify all internal nodes // in bottom up way for ( int i = ( n - 2 ) / 2 ; i >= 0 ; -- i ) MaxHeapify ( arr i n ); } // A utility function to print // a given array of given size static void printArray ( int [] arr int size ) { for ( int i = 0 ; i < size ; ++ i ) Console . Write ( arr [ i ] + ' ' ); } // Driver's Code public static void Main () { // array representing Min Heap int [] arr = { 3 5 9 6 8 20 10 12 18 9 }; int n = arr . Length ; Console . Write ( 'Min Heap array : ' ); printArray ( arr n ); // Function call convertMaxHeap ( arr n ); Console . Write ( 'nMax Heap array : ' ); printArray ( arr n ); } } // This code is contributed by nitin mittal.
JavaScript < script > // javascript program to convert min Heap to max Heap // To heapify a subtree with root at given index function MaxHeapify ( arr i n ) { var l = 2 * i + 1 ; var r = 2 * i + 2 ; var largest = i ; if ( l < n && arr [ l ] > arr [ i ]) largest = l ; if ( r < n && arr [ r ] > arr [ largest ]) largest = r ; if ( largest != i ) { // swap arr[i] and arr[largest] var temp = arr [ i ]; arr [ i ] = arr [ largest ]; arr [ largest ] = temp ; MaxHeapify ( arr largest n ); } } // This function basically builds max heap function convertMaxHeap ( arr n ) { // Start from bottommost and rightmost // internal node and heapify all internal // nodes in bottom up way for ( i = ( n - 2 ) / 2 ; i >= 0 ; -- i ) MaxHeapify ( arr i n ); } // A utility function to print a given array // of given size function printArray ( arr size ) { for ( i = 0 ; i < size ; ++ i ) document . write ( arr [ i ] + ' ' ); } // driver program // array representing Min Heap var arr = [ 3 5 9 6 8 20 10 12 18 9 ]; var n = arr . length ; document . write ( 'Min Heap array : ' ); printArray ( arr n ); convertMaxHeap ( arr n ); document . write ( '
Max Heap array : ' ); printArray ( arr n ); // This code is contributed by 29AjayKumar < /script>
PHP // A PHP program to convert min Heap to max Heap // utility swap function function swap ( & $a & $b ) { $tmp = $a ; $a = $b ; $b = $tmp ; } // to heapify a subtree with root at given index function MaxHeapify ( & $arr $i $n ) { $l = 2 * $i + 1 ; $r = 2 * $i + 2 ; $largest = $i ; if ( $l < $n && $arr [ $l ] > $arr [ $i ]) $largest = $l ; if ( $r < $n && $arr [ $r ] > $arr [ $largest ]) $largest = $r ; if ( $largest != $i ) { swap ( $arr [ $i ] $arr [ $largest ]); MaxHeapify ( $arr $largest $n ); } } // This function basically builds max heap function convertMaxHeap ( & $arr $n ) { // Start from bottommost and rightmost // internal node and heapify all internal // nodes in bottom up way for ( $i = ( int )(( $n - 2 ) / 2 ); $i >= 0 ; -- $i ) MaxHeapify ( $arr $i $n ); } // A utility function to print a given array // of given size function printArray ( $arr $size ) { for ( $i = 0 ; $i < $size ; ++ $i ) print ( $arr [ $i ] . ' ' ); } // Driver code // array representing Min Heap $arr = array ( 3 5 9 6 8 20 10 12 18 9 ); $n = count ( $arr ); print ( 'Min Heap array : ' ); printArray ( $arr $n ); convertMaxHeap ( $arr $n ); print ( ' n Max Heap array : ' ); printArray ( $arr $n ); // This code is contributed by mits ?>
Išvestis
Min Heap array : 3 5 9 6 8 20 10 12 18 9 Max Heap array : 20 18 10 12 9 9 3 5 6 8
Laiko sudėtingumas: O (n) Norėdami gauti daugiau informacijos, skaitykite: Krūvos kūrimo laiko sudėtingumas
Pagalbinė erdvė: O (n)
