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(Solved): The following sequence of integers will be inserted into a binary tree structure in the following or ...



The following sequence of integers will be inserted into a binary tree structure in the following order: 59, 45, 23, 91, 23, 17, 8.

Use the sequence Binary Search Tree (and BST property) and Max- heap (and Max-Heap property) to demonstrate the sequence Heapsort.


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To demonstrate the Heapsort operation using a BST, we can first insert the sequence of integers into a BST in the order given: 59, 45, 23, 91, 23, 17, 8. The resulting BST would look like this:




The given diagram represents a binary tree with 7 nodes. The tree is not a binary search tree since it violates the BST property. For example, the left subtree of the root node (59) contains a node with value 23, which is less than the value of the parent node. However, there is another node with value 23 in the right subtree of the root node, which is greater than the value of the parent node. This violates the BST property, which states that all nodes in the left subtree should have values less than the parent node, and all nodes in the right subtree should have values greater than the parent node.
The tree also does not satisfy the max-heap property since it violates the property that all parent nodes should have a value greater than or equal to their child nodes. For example, the parent node with value 45 has a left child with value 23, which is greater than the parent node, violating the max-heap property.


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