[Solved] Consider the array representation of a binary min-heap conta (2024)

FAQs

What is a binary min-heap representation? ›

A Min Heap Binary Tree is a Binary Tree where the root node has the minimum key in the tree. The above definition holds true for all sub-trees in the tree. This is called the Min Heap property. Almost every node other than the last two layers must have two children.

Answer: Explanation: A tree is min heap when data at every node in the tree is smaller than or equal to it's children' s data. So, only 8 10 12 25 14 17 generates required tree.

Therefore, after the deletion of 11 from the given min-heap, the array representation will become 5, 8, 14, 17, 20.

We compare each root node with its descendants. If each root node is greater than its children nodes, then the tree is a max-heap, and the given array represents a max-heap.

Array Representation :

The binary tree can be represented using an array of size 2n+1 if the depth of the binary tree is n. If the parent element is at the index p, Then the left child will be stored in the index ( 2 p ) + 1 (2p)+1 (2p)+1, and the right child will be stored in the index ( 2 p ) + 2 (2p)+2 (2p)+2.

The correct option is C [26, 15, 17, 14, 11, 9, 13] For max heap we will compare parent node (i) with its left-child (2×i) and right child (2×i+1); In first option node (2) < node (5) which is violating the max-heap property.

An array's type is written as type[] , where type is the data type of the contained elements; the brackets are special symbols indicating that this variable holds an array. The size of the array is not part of its type (which is why the brackets are empty).

Why is array-based representation preferred for a binary heap? ›

As mentioned above, a heap is a complete binary tree, which leads to the idea of storing it using an array. By utilizing array-based representation, we can reduce memory costs while tree navigation remains quite simple. As for the heapsort algorithm, array-based implementation is kind of native.

The binary heap is a binary tree (a tree in which each node has at most two children) which satisfies the following additional properties: The binary tree is complete, i.e. every level except the bottom-most level is completely filled and nodes of the bottom-most level are positioned as left as possible.

Answer: The array representation of the max heap after deleting the value of 19 would be: 46, 45, 41, 31, 23, 18, 17.

If the array is sorted in ascending order, then yes. However, you can still have a min heap with the same elements that isn't completely sorted as long as each node is greater than its parent.

A min heap is a binary tree where every node has a value less than or equal to its children. In JavaScript, you can implement a min heap using an array, where the first element represents the root node, and the children of a node at index i are located at indices 2i+1 and 2i+2.

Binary Representation of a number and Binomial Heaps

A Binomial Heap with n nodes has the number of Binomial Trees equal to the number of set bits in the binary representation of n. For example, let n be 13, there are 3 set bits in the binary representation of n (00001101), hence 3 Binomial Trees.

A binomial heap is implemented as a set of binomial trees that satisfy the binomial heap properties: Each binomial tree in a heap obeys the minimum-heap property: the key of a node is greater than or equal to the key of its parent. There can be at most one binomial tree for each order, including zero order.

The INT_MAX would be 01111111111111111111111111111111 and INT_MIN would be 10000000000000000000000000000000.