Question

3. (8 points) Using the implementation of binary search tree operations we discussed in class, draw the trees that result from the following operations: (a) Inserting 142, 400, 205, 127, 100, 320, 160, 141, and 110 into an initially-empty tree (in that order). (b) Deleting 142 from the tree you drew for part (a). 4. (8 points) Draw the unique binary tree that has a preorder traversal of 4, 1, 6, 3, 7, 5, 9, 2, 8 and an inorder traversal of 6, 1, 7, 5, 3, 4, 9, 8, 2. Note that this will not necessarily be a binary search tree. 5. (a) (7 points) Consider the array of integers 5 2 3 6 14 Draw the sequence of swaps that result from sorting this array using insertion sort. (b) (9 points) The following array contains a min-heap (a heap where each node is smaller than its children): 10 38 18 175 53 142 249 i. Draw this heap in tree format. ii. Show the array after each swap in the process of sorting it into decreasing order using heapsort.

Answer 1

3) a) Inserting a) Insexling 142, 400,205, 127, 100, 320, 160, 141,6110 Binary search tree is a binary tree, where the left child contains only nodes with values less than or equal to the parent node, and where the right child only contains nodes with values greater than padent node. steps: Suto S (61) - 142 (52)-400 (3) – 205 Say_127 & - 100 I ) - 320 (59-160 h . no a los

& Deleting 142 from free drown for part can do if node to be deleted is leaf then simply remove from the tree 2) If node to be deleted has only one child then copy the child to the node and delete the child 3) of Node to be deleted has two childs then find in order predecessor of the no de (maximum value in left child of the node). ben & find inorder successor of of the morder successor to the inorder successor. the node. copy value node and delete (160) Here the inorder succenol is right child of the minimum value in node is "160"

Poecoder in order Traversal i traversal's 4, 1, 6, 3, 7, 5, 9, 2,8 6il 7,513, 4, 9, 8, 2 D from preorder sequence, left most elemen the root of tree. - so, 4 is sook of tree. - By searching & in inorder traversal. sequence, we can find out all ebements on left side of 4 are in left subtree and elements on right are in right subtree. 9,8,2 6, 1,75,3 which is left most 2) among 61107,513 , check in pop order travessal. So I' occurs first in peorder. so, next root 9, 8,2 7,513 process 3) until recuosively tree is continue formed

9,812 9,872 i) Among 9,812 , again find which one occurs first in preorder sequence. - Here a cours before 8 and 2. - so, doot will be 9. Then 812 are right childs of cal, since 8,2 are present right to 'a' in inorder travessal.

3), Gjesa lo la wey = 2 1.215, 13.461119 Ky= 213151610141 Kg =) 11 12 13 14 15 16 (9 doar unu SET 1 87 881 01 bhg 1271Es 8E-5) 01-05 @ @ § Sy 175 @

Heap sont 1) Build a min heap from input data 2) At this point, the smallest item is stored at the root of the heap. Replace it with the last item of the heap followed by reducing the size of heap byl [ 10. r 38 118 / 175 1 142 7749] = 7 201 59 | 142 | 10 | * * | 107 102. | 4 | 105 | 5 | 6 | 107

13s ( 142 (2487135153 (18/10 138 50 24 / 125 /142/18/10/ [1492 | 93 | 940 / 135 / at / 18 101 3 949 142 175 | 142 195 ) 4 153 | 38 | 18) 107 | 10 | 11 | 12 | 33 | 3s )a) 1/

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