Converteix el munt de mins a màxim
Tenint en compte una representació de matriu de Min HEAP, convertiu -la en un munt màxim.
Exemples:
Entrada: arr [] = {3 5 9 6 8 20 10 12 18 9}
3
/
5 9
//
6 8 20 10 10
/ /
12 18 9Sortida: arr [] = {20 18 10 12 9 9 3 5 6 8}
20
/
18 10
//
12 9 3 3
/ /
5 6 8Entrada: arr [] = {3 4 8 11 13}
Sortida: arr [] = {13 11 8 4 3}
La idea és simplement crear un munt màxim sense tenir cura de l’entrada. Comenceu des del node intern més baix i més dret de Min-Heap i heu de fer servir tots els nodes interns de la manera inferior a dalt per construir el munt màxim.
Seguiu els passos donats per resoldre el problema:
- Truqueu a la funció Heapify des del node intern dret de min-heap
- Agafeu tots els nodes interns de la manera de baix a dalt de crear un munt màxim
- Imprimeix el max-hap
Algoritme: Aquí hi ha un Algoritme per convertir un munt min en un munt màxim :
- Comenceu a l’últim node no de la fulla del munt (és a dir, el progenitor de l’últim node de fulla). Per a un munt binari, aquest node es troba al sòl de l'índex ((n - 1)/2) on n és el nombre de nodes del munt.
- Per a cada node sense fulles, realitzeu un "Heapify" Funcionament per arreglar la propietat. En un munt mínim, aquesta operació consisteix en comprovar si el valor del node és superior al dels seus fills i, si és així, canvia el node amb el menor dels seus fills. En un munt màxim, l’operació consisteix en comprovar si el valor del node és inferior al dels seus fills i, si és així, canviar el node amb el més gran dels seus fills.
- Repetiu el pas 2 per a cadascun dels nodes que no siguin de la fulla que funcionin fins al munt. Quan arribeu a l’arrel del munt, tot el munt hauria de ser un munt màxim.
A continuació es mostra la implementació de l’enfocament anterior:
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 ?>
Producció
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
Complexitat del temps: O (n) Per obtenir més informació, consulteu: Complexitat de temps de construir un munt
Espai auxiliar: O (n)
