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, keyſparentfu]] < key[u). Loop invariant 2 if u has a parent, then for each child c of v, key[parent{v]] < 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[u) +k 2. while v is not the root and keyſparentſu]] > key[u] do 3. swap v and its parent a Prove maintenance of Loop invariant 1. Hint think carefully about which nodes get a new parent! Also, use Loop invariant 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, keyſparentfu]] < key[u). Loop invariant 2 if u has a parent, then for each child c of v, key[parent{v]] < 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[u) +k 2. while v is not the root and keyſparentſu]] > key[u] do 3. swap v and its parent a Prove maintenance of Loop invariant 1. Hint think carefully about which nodes get a new parent! Also, use Loop invariant 2.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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