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 is 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. Below table shows indexes of other nodes for the ith node, i.e.,
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:
- getMax(): It returns the root element of Max Heap. Time Complexity of this operation is O(1).
- 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 root.
- insert(): Inserting a new key takes O(Log n) time. We add a new key at the end of the tree. If new key is smaller than its parent, then we don’t need to do anything. Otherwise, we need to traverse up to fix the violated heap property.
Note : In below implementation, we do indexing from index 1 to simplify the implementation.
The maxHeap is PARENT : 84 LEFT CHILD : 22 RIGHT CHILD : 19 PARENT : 22 LEFT CHILD : 17 RIGHT CHILD : 10 PARENT : 19 LEFT CHILD : 5 RIGHT CHILD : 6 PARENT : 17 LEFT CHILD : 3 RIGHT CHILD : 9 The Max val is 84
Using Library functions :
We use heapq class to implement Heaps 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.
Head value of heap : 400 The heap elements : 400 30 20 10 The heap elements : 30 10 20
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