Plz solve this now in one hour and take a thumb up plz this is data Structure and algorithm subject plz solve this according to question i need a proof that they ask in question so don't take the answer from google and chegg etc plz solve according to your mind nd take a thumb up plz don't reject 2 Exercise 2Consider the pseudocode given for Decreasekey on a min-heap. The two loop invariants below together leadto proving that, after Decreasekey is performed, the tree satisfies the min-heap property again.Loop invariant 1: for all nodes u in H except v and its root, key[parent{u]] < key[u).Loop invariant 2 if u has a parent, then for each child c of U, key[parentſu]] < key[c).Decreasekey(H, v, k)Input a min-heap H containing node vOutput. a min-heap in which the key of node v has been set of k1. key[v) +k2. while v is not the root and keyſparentſu] > key[u] do3. swap v and its parentノーProve maintenance of Loop invariant 1.Hint think careruuy about which nodes get a new parent! Also, use Loop invariant 2.

Min Heap: Min Heap means the root node is always less than or equal to its child nodes Example:

Answered: Consider the pseudocode given for…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Plz solve this now in one hour and take a thumb up plz this is data Structure and algorithm subject plz solve this according to question i need a proof that they ask in question so don't take the answer from google and chegg etc plz solve according to your mind nd take a thumb up plz don't reject

2 Exercise 2
Consider the pseudocode given for Decreasekey on a min-heap. The two loop invariants below together lead
to proving that, after Decreasekey is performed, the tree satisfies the min-heap property again.
Loop invariant 1: for all nodes u in H except v and its root, key[parent{u]] < key[u).
Loop invariant 2 if u has a parent, then for each child c of U, key[parentſu]] < key[c).
Decreasekey(H, v, k)
Input a min-heap H containing node v
Output. a min-heap in which the key of node v has been set of k
1. key[v) +k
2. while v is not the root and keyſparentſu] > key[u] do
3. swap v and its parent
ノー
Prove maintenance of Loop invariant 1.
Hint think careruuy about which nodes get a new parent! Also, use Loop invariant 2.

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