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📜  将最小堆转换为最大堆

📅  最后修改于: 2021-10-28 02:13:10             🧑  作者: Mango

给定最小堆的数组表示，在 O(n) 时间内将其转换为最大堆。
例子 ： 

Input: arr[] = [3 5 9 6 8 20 10 12 18 9]
         3
      /     \
     5       9
   /   \    /  \
  6     8  20   10
 /  \   /
12   18 9 


Output: arr[] = [20 18 10 12 9 9 3 5 6 8] OR 
       [any Max Heap formed from input elements]

         20
       /    \
     18      10
   /    \    /  \
  12     9  9    3
 /  \   /
5    6 8

乍一看，这个问题可能看起来很复杂。但我们的最终目标是只构建最大堆。这个想法很简单——我们只是简单地构建 Max Heap，而不关心输入。我们从min Heap的最底层和最右边的内部模式开始，以自下而上的方式堆化所有内部模式来构建Max堆。
下面是它的实现

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 mode and heapify all internal
    // modes 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 program to test above functions
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);
 
    convertMaxHeap(arr, n);
 
    printf("\nMax 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 mode and heapify all internal
        // modes 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 program
    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);
  
        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 mode and heapify all
    # internal modes 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)
 
    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 mode and
        // heapify all internal modes
        // 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 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);
 
        convertMaxHeap(arr, n);
 
        Console.Write("\nMax Heap array : ");
        printArray(arr, n);
    }
}
 
// This code is contributed by nitin mittal.

PHP
 $arr[$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, $n)
{
    // Start from bottommost and rightmost
    // internal mode and heapify all internal
    // modes in bottom up way
    for ($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("\nMax Heap array : ");
    printArray($arr, $n);
 
 
// This code is contributed by mits
?>

Javascript

输出 ： 

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

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