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on’t need it coded out.I need a loop invariant proof of it Similar to doing an induction proof with an equation.It is a proof of loop maintenance, initialization and termination.Common practice in discrete math

on’t need it coded out.I need a loop invariant proof of it Similar to doing an induction proof with an equation.It is a proof of loop maintenance, initialization and termination.Common practice in discrete math

Database System Concepts
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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I don’t need it coded out.I need a loop invariant proof of it Similar to doing an induction proof with an equation.It is a proof of loop maintenance, initialization and termination.Common practice in discrete math
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 v, 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 key[parentſu] > key[v] do 3. swap v and its parent Prove maintenance of Loop invariant 1. a Hint: think carefully about which nodes get a new parent! Also, use Loop invariant 2. b Prove termination: the resulting tree is indeed a min-heap.
Transcribed Image Text: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 v, 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 key[parentſu] > key[v] do 3. swap v and its parent Prove maintenance of Loop invariant 1. a Hint: think carefully about which nodes get a new parent! Also, use Loop invariant 2. b Prove termination: the resulting tree is indeed a min-heap.
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