Question

(a) (8 points) Given a set S of records with keys {17, 12, 7,5,6,8, 13, 1, 21, 10, 15, 19}, construct a min pairing heap for S by inserting the elements in S, in the given order, into an initially empty heap.

Answer 1

(a):

(b):

// Mention in comments if any mistakes or errors are found. Thank you.

Answer 2

(a):

@ Insert S={17, 12, 7,5, 6, 8, 13, 1, 21, 10, 15, 17) I into min heap. Tot Min Heap property: The value at a node must be 1 smaller than a child mede values. If Min heap property is violated, then we need to Convert into minheap by swapping values. o Insert 17 @ Insert 12 Minheap property is violated at 17, so swap 17,12 Insert: 7 Minheap property is violated at 12, So swap 12,7

- Insert 5 Min hear property is violated at 17, 5 Again nunheap property is nolated at 37, So swap 7.5. 5 Insert 6 Min hap property is violated at t @ @ so swap 76.

© Insert: 8 Min heap property is volated at 12, so op 12,8 Insert 13 Min heap property is e satisfied at every node. ② Insert : 1 Min heap property is violated at 17, so swap 17, 1.

at 6 Again min heap property is viol ty is violated so swap 6, 1. at 5, Again minheap property is violated so swap 5,1 (13) @ Insert 21 og er nur Min heap property is satisfied at all

10 Insert: 10 Min heap property is satisfied at all nodes. 1 Insert: 15 Minheap property is satisfied at all nodes. @ Insert: 19 Minheap property is satished at all nodes . | මම

tinal required munheap is: 01-

(b):

@ Algorithm to delete Min(); posting at the ① Swap 1st & last model & remove last node check for minheap property from root, it violated then swap values till tree satisfies man heap property. O → Swap Ist & last nedes: 19 . remove last node :

② Check for min heap property rows of writing Min heap property, is violated at node 19, so swap 19,5. Min heap property violated at 19. So swap 19,6

at 19, so Mon heap property is violated Swap 19,17 tinal resultant minheap :

// Mention in comments if any mistakes or errors are found. Thank you.