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Heap Data structure primarily focuses on representing priority queue.<\/p>\n
Min – Heap<\/strong> follows the property of a complete binary tree in which the value of the internal node is smaller than or equal to the value of the children of that node. Min heap is represented as an array. Below points shows indexes of other nodes for the ith node, i.e. Arr[i]:<\/p>\n<\/p>\n For Example 1:<\/em><\/strong> Using the above rules of array representation we can represent a heap in the array:<\/p>\n For node with value 2, its index value is 1 have left child is at (21) + 1 = 3 i.e. node with value 3 and right child is at (2<\/em>1) + 2 = 4 i.e. node with value 7. And we can see here that, both the children are bigger than their parent node.<\/p>\n For Example 2:<\/em><\/strong> Using the above rules of array representation we can represent a heap in the array:<\/p>\n For node with value 4, its index value is 2 have left child is at (22) + 1 = 5 i.e. node with value 16 and right child is at (2<\/em>2) + 2 = 6 i.e. node with value 18. And we can see here that, both the children are bigger than their parent node. Also its parent node will be at (2-1)\/2 = 0 i.e. node with value 2.<\/p>\n getMinimum():<\/strong> This function will return the root element of the max heap. O(1) will be its time complexity.<\/p>\n extractMinimum():<\/strong> This function will remove the minimum element from the Minheap. To maintain the heap property i.e. (calling heapify function) after removing the root, this function is having 0(Log n) time complexity.<\/p>\n insertNode():<\/strong> For inserting the new key, 0(Log n) time is required. Using this function, we will add a new key at the end of the binary tree. If the new key is greater than its parent, then we have to fix the heap property which is violated here.<\/p>\n Note:<\/em><\/strong> We have to do indexing to simplify the below implementation.<\/p>\n
\nIn 0 – based indexing, the node stored at k index in the array will have its left child held at index 2k + 1 and its right child at index 2k + 2.<\/p>\n![\"\"](\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655961742286-Image-01%20%281%29.png\")
<\/p>\nRepresentation of Min Heap:<\/h3>\n
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<\/p>\nOperations on Min Heap:<\/h3>\n
Code Implementation<\/h4>\n\t\t\t\t\t\t