# Max Heap in Python

A Max-Heap is a complete binary tree in which the value in each internal node is greater than or equal to the values in the children of that node. Mapping the elements of a heap into an array is trivial: if a node is stored a index k, then its left child is stored at index 2k + 1 and its right child at index 2k + 2.

Examples of Max Heap :

## How is Max Heap represented?

A max Heap is a Complete Binary Tree. A max heap is typically represented as an array. The root element will be at Arr[0]. Below table shows indexes of other nodes for the ith node, i.e., Arr[i]:

• Arr[(i-1)/2] Returns the parent node.
• Arr[(2*i)+1] Returns the left child node.
• Arr[(2*i)+2] Returns the right child node.

## Operations on Max Heap:

1. getMax(): It returns the root element of Max Heap. Time Complexity of this operation is O(1).
2. extractMax(): Removes the maximum element from MaxHeap. Time Complexity of this Operation is O(log n) as this operation needs to maintain the heap property (by calling heapify()) after removing the root.
3. insert(): Inserting a new key takes O(log n) time. We add a new key at the end of the tree. If the new key is smaller than its parent, then we don&#x2019t need to do anything. Otherwise, we need to traverse up to fix the violated heap property.

Note: In the below implementation, we do indexing from index 1 to simplify the implementation.

## Python

 `# Python3 implementation of Max Heap``import` `sys` `class` `MaxHeap:` `    ``def` `__init__(``self``, maxsize):``        ` `        ``self``.maxsize ``=` `maxsize``        ``self``.size ``=` `0``        ``self``.Heap ``=` `[``0``] ``*` `(``self``.maxsize ``+` `1``)``        ``self``.Heap[``0``] ``=` `sys.maxsize``        ``self``.FRONT ``=` `1` `    ``# Function to return the position of``    ``# parent for the node currently``    ``# at pos``    ``def` `parent(``self``, pos):``        ` `        ``return` `pos ``/``/` `2` `    ``# Function to return the position of``    ``# the left child for the node currently``    ``# at pos``    ``def` `leftChild(``self``, pos):``        ` `        ``return` `2` `*` `pos` `    ``# Function to return the position of``    ``# the right child for the node currently``    ``# at pos``    ``def` `rightChild(``self``, pos):``        ` `        ``return` `(``2` `*` `pos) ``+` `1` `    ``# Function that returns true if the passed``    ``# node is a leaf node``    ``def` `isLeaf(``self``, pos):``        ` `        ``if` `pos >``=` `(``self``.size``/``/``2``) ``and` `pos <``=` `self``.size:``            ``return` `True``        ``return` `False` `    ``# Function to swap two nodes of the heap``    ``def` `swap(``self``, fpos, spos):``        ` `        ``self``.Heap[fpos], ``self``.Heap[spos] ``=` `(``self``.Heap[spos], ``                                            ``self``.Heap[fpos])` `    ``# Function to heapify the node at pos``    ``def` `maxHeapify(``self``, pos):` `        ``# If the node is a non-leaf node and smaller``        ``# than any of its child``        ``if` `not` `self``.isLeaf(pos):``            ``if` `(``self``.Heap[pos] < ``self``.Heap[``self``.leftChild(pos)] ``or``                ``self``.Heap[pos] < ``self``.Heap[``self``.rightChild(pos)]):` `                ``# Swap with the left child and heapify``                ``# the left child``                ``if` `(``self``.Heap[``self``.leftChild(pos)] > ``                    ``self``.Heap[``self``.rightChild(pos)]):``                    ``self``.swap(pos, ``self``.leftChild(pos))``                    ``self``.maxHeapify(``self``.leftChild(pos))` `                ``# Swap with the right child and heapify``                ``# the right child``                ``else``:``                    ``self``.swap(pos, ``self``.rightChild(pos))``                    ``self``.maxHeapify(``self``.rightChild(pos))` `    ``# Function to insert a node into the heap``    ``def` `insert(``self``, element):``        ` `        ``if` `self``.size >``=` `self``.maxsize:``            ``return``        ``self``.size ``+``=` `1``        ``self``.Heap[``self``.size] ``=` `element` `        ``current ``=` `self``.size` `        ``while` `(``self``.Heap[current] > ``               ``self``.Heap[``self``.parent(current)]):``            ``self``.swap(current, ``self``.parent(current))``            ``current ``=` `self``.parent(current)` `    ``# Function to print the contents of the heap``    ``def` `Print``(``self``):``        ` `        ``for` `i ``in` `range``(``1``, (``self``.size ``/``/` `2``) ``+` `1``):``            ``print``(``"PARENT : "` `+` `str``(``self``.Heap[i]) ``+``                  ``"LEFT CHILD : "` `+` `str``(``self``.Heap[``2` `*` `i]) ``+``                  ``"RIGHT CHILD : "` `+` `str``(``self``.Heap[``2` `*` `i ``+` `1``]))` `    ``# Function to remove and return the maximum``    ``# element from the heap``    ``def` `extractMax(``self``):` `        ``popped ``=` `self``.Heap[``self``.FRONT]``        ``self``.Heap[``self``.FRONT] ``=` `self``.Heap[``self``.size]``        ``self``.size ``-``=` `1``        ``self``.maxHeapify(``self``.FRONT)``        ` `        ``return` `popped` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``print``(``'The maxHeap is '``)``    ` `    ``maxHeap ``=` `MaxHeap(``15``)``    ``maxHeap.insert(``5``)``    ``maxHeap.insert(``3``)``    ``maxHeap.insert(``17``)``    ``maxHeap.insert(``10``)``    ``maxHeap.insert(``84``)``    ``maxHeap.insert(``19``)``    ``maxHeap.insert(``6``)``    ``maxHeap.insert(``22``)``    ``maxHeap.insert(``9``)` `    ``maxHeap.``Print``()``    ` `    ``print``(``"The Max val is "` `+` `str``(maxHeap.extractMax()))`

Output
```The maxHeap is
PARENT : 84LEFT CHILD : 22RIGHT CHILD : 19
PARENT : 22LEFT CHILD : 17RIGHT CHILD : 10
PARENT : 19LEFT CHILD : 5RIGHT CHILD : 6
PARENT : 17LEFT CHILD : 3RIGHT CHILD : 9
The Max val is 84

```

## Using Library functions:

We use heapq class to implement Heap in Python. By default Min Heap is implemented by this class. But we multiply each value by -1 so that we can use it as MaxHeap.

## Python3

 `# Python3 program to demonstrate working of heapq` `from` `heapq ``import` `heappop, heappush, heapify` `# Creating empty heap``heap ``=` `[]``heapify(heap)` `# Adding items to the heap using heappush``# function by multiplying them with -1``heappush(heap, ``-``1` `*` `10``)``heappush(heap, ``-``1` `*` `30``)``heappush(heap, ``-``1` `*` `20``)``heappush(heap, ``-``1` `*` `400``)` `# printing the value of maximum element``print``(``"Head value of heap : "` `+` `str``(``-``1` `*` `heap[``0``]))` `# printing the elements of the heap``print``(``"The heap elements : "``)``for` `i ``in` `heap:``    ``print``((``-``1``*``i), end``=``" "``)``print``(``"\n"``)` `element ``=` `heappop(heap)` `# printing the elements of the heap``print``(``"The heap elements : "``)``for` `i ``in` `heap:``    ``print``(``-``1` `*` `i, end ``=` `' '``)`

Output
```Head value of heap : 400
The heap elements :
400 30 20 10

The heap elements :
30 10 20

```

## Using Library functions with dunder method for Numbers, Strings, Tuples, Objects etc

We use heapq class to implement Heaps in Python. By default Min Heap is implemented by this class.

To implement MaxHeap not limiting to only numbers but any type of object(String, Tuple, Object etc) we should

1. Create a Wrapper class for the item in the list.
2. Override the __lt__ dunder method to give inverse result.

Following is the implementation of the method mentioned here.

## Python3

 `"""``Python3 program to implement MaxHeap Operation``with built-in module heapq``for String, Numbers, Objects``"""``from` `functools ``import` `total_ordering``import` `heapq` `# why total_ordering: https://www.geeksforgeeks.org/python-functools-total_ordering/`  `@total_ordering``class` `Wrapper:``    ``def` `__init__(``self``, val):``        ``self``.val ``=` `val` `    ``def` `__lt__(``self``, other):``        ``return` `self``.val > other.val` `    ``def` `__eq__(``self``, other):``        ``return` `self``.val ``=``=` `other.val`  `# Working on existing list of int``heap ``=` `[``10``, ``20``, ``400``, ``30``]``wrapper_heap ``=` `list``(``map``(``lambda` `item: Wrapper(item), heap))` `heapq.heapify(wrapper_heap)``max_item ``=` `heapq.heappop(wrapper_heap)` `# This will give the max value``print``(f``"Top of numbers are: {max_item.val}"``)` `# Working on existing list of str``heap ``=` `[``"this"``, ``"code"``, ``"is"``, ``"wonderful"``]``wrapper_heap ``=` `list``(``map``(``lambda` `item: Wrapper(item), heap))``heapq.heapify(wrapper_heap)` `print``(``"The string heap elements in order: "``)``while` `wrapper_heap:``    ``top_item ``=` `heapq.heappop(wrapper_heap)``    ``print``(top_item.val, end``=``" "``)` `# This code is contributed by Supratim Samantray (super_sam)`

Output
```Top of numbers are: 400
The string heap elements in order:
wonderful this is code

```

## Using internal functions used in the heapq library

This is by far the most simple and convenient way to apply max heap in python.

DISCLAIMER – In Python, there’s no strict concept of private identifiers like in C++ or Java. Python trusts developers and allows access to so-called “private” identifiers. However, since these identifiers are intended for internal use within the module, they are not officially part of the public API and may change or be removed in the future.

Following is the implementation.

## Python3

 `from` `heapq ``import` `_heapify_max, _heappop_max, _siftdown_max` `# Implementing heappush for max_heap``# Time Complexity = Î˜(1 + logn) ``def` `heappush_max(max_heap, item): ``    ``max_heap.append(item)``    ``_siftdown_max(max_heap, ``0``, ``len``(max_heap)``-``1``)` `def` `max_heap(arr):``    ``copy ``=` `arr.copy() ``# Just maintaining a copy for later use``    ` `    ``# Time Complexity = Î˜(n); n = no of elements in array``    ``_heapify_max(arr) ``# Converts array to max_heap ``    ` `    ``# Time Complexity = Î˜(logk); k = no of elements in heap``    ``while` `len``(arr) !``=` `0``: ``# popping items from max_heap``        ``print``(_heappop_max(arr)) ``# ... unless its empty``        ` `    ``arr ``=` `copy ``# since len(arr) = 0``    ``max_heap ``=` `[]``    ``# Time Complexity = Î˜(nlogk) - since inserting item one by one ``    ``for` `item ``in` `arr:``        ``heappush_max(max_heap, item)``    ``print``(``"Max Heap is Ready!"``)``    ``# Time Complexity = Î˜(logk); k = no of elements in heap``    ``while` `len``(max_heap) !``=` `0``: ``# popping items from max_heap``        ``print``(_heappop_max(max_heap)) ``# ... unless its empty``    `  `arr ``=` `[``6``,``8``,``9``,``2``,``1``,``5``]``max_heap(arr)``# This code is contributed by Swagato Chakraborty (swagatochakraborty123)`

Output

`986521Max Heap is Ready!986521`

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