# Convert Min Heap to Max Heap

Given an array representation of min Heap, convert it to max Heap.

Examples:

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}

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

Input: arr[] = {3, 4, 8, 11, 13}
Output:  arr[] = {13, 11, 8, 4, 3}

Approach: To solve the problem follow the below idea:

The idea is, simply build Max Heap without caring about the input. Start from the bottom-most and rightmost internal node of Min-Heap and heapify all internal nodes in the bottom-up way to build the Max heap.

Follow the given steps to solve the problem:

• Call the Heapify function from the rightmost internal node of Min-Heap
• Heapify all internal nodes in the bottom-up way to build max heap
• Print the Max-Heap

Algorithm: Here’s an algorithm for converting a min heap to a max heap:

1. Start at the last non-leaf node of the heap (i.e., the parent of the last leaf node). For a binary heap, this node is located at the index floor((n – 1)/2), where n is the number of nodes in the heap.
2. For each non-leaf node, perform a “heapify” operation to fix the heap property. In a min heap, this operation involves checking whether the value of the node is greater than that of its children, and if so, swapping the node with the smaller of its children. In a max heap, the operation involves checking whether the value of the node is less than that of its children, and if so, swapping the node with the larger of its children.
3. Repeat step 2 for each of the non-leaf nodes, working your way up the heap. When you reach the root of the heap, the entire heap should now be a max heap.

Below is the implementation of the above approach:

## 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``(``"\nMax Heap array : "``);` `    ``printArray(arr, N);`   `    ``return` `0;` `}`

## 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``(``"\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 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.`

## 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 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``(``"\nMax Heap array : "``);` `    ``printArray(``\$arr``, ``\$n``);`     `// This code is contributed by mits` `?>`

## Javascript

 ``

Output

```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 ```

Time Complexity: O(N), for details, please refer: Time Complexity of building a heap
Auxiliary Space: O(N)

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