Draw the binary tree for which the traversal sequences are given as follows:
(i) Pre order: ABDEFCGHIJK
In order: BEDFACIHKJG
(ii) Post order: IJHDKECLMGFBA
In order: I HJDCKEAFLGMB
(i) Given: Preorder: `A B D E F C G H I J K` Inorder: `B E D F A C I H K J G` To reconstruct the binary tree: Step 1: In preorder, the first element is the root → `A` Find `A` in inorder → Left subtree = `B E D F`, Right subtree = `C I H K J G` Step 2: Left subtree (inorder = `B E D F`) From preorder, next root = `B`, but `B` is first in inorder → must be leaf. Next in preorder: `D` → its inorder: `E D F`, root = `D`, left = `E`, right = `F` So Left Subtree: ``` B \ D / \ E F ``` Step 3: Right subtree (inorder = `C I H K J G`) Next root in preorder = `C`, find ___ ___ ____ _______ ________ ___.
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What is Splay tree? Explain the Zig zag and Zag zig rotations in Splay tree with the help of a suitable example.
What is a heap tree? Create a max heap tree for the following list of items inserted in the order. Also, explain the heap sort with the help of thus created heap tree. 10, 20, 5, 25, 30, 18, 3, 70, 55, 45, 12, 24
Draw the binary tree for which the traversal sequences are given as follows:
(i) Pre order: ABDEFCGHIJK
In order: BEDFACIHKJG
(ii) Post order: IJHDKECLMGFBA
In order: I HJDCKEAFLGMB
Apply Prim's Algorithm to find the minimum spanning tree for the following graph.
Apply Insertion and Selection sorting algorithms to sort the following list of items. So, all Intermediate steps. Also, analyze their best, worst and average case time complexity.
12, 5, 2, 15, 25, 30, 45, 8, 17, 50, 3, 7
Define a B-tree and its properties. Create a B-tree of order-5, if the data items are inserted into an empty B-tree in the following sequence:
12, 5, 15, 20, 60, 45, 35, 40, 25, 8, 7, 55, 50, 66, 65, 80 Further, delete the items 5, 12, 8, and 20 from the B-tree.
Write a program in 'C' to create a doubly linked list to store integer values and perform the following operations on it:
(i) Insert a new node at the beginning, in the middle or at the end of the linked list.
(ii) Delete a node from the linked list
(iii) Sort and display data of the doubly linked list in ascending order.
(iv) Count the number of items stored in a single linked list
Calculate the sum of all even integer numbers, stored in the doubly linked list.
Write a program in 'C' to implement a binary search tree (BST). Traverse and display the binary search tree in the Inorder, Preorder and Post order form.