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Write an algorithm that, for a given tree T, calculates the maximum sum achievable across all sets S (where no two elements have a parent/child relationship). You only need to return the maximal sum and not a set of nodes that achieves it (for simplicity). What is the runtime and space complexity of the algorithm? Hint: For any given node n, come up with a recursive solution MAX-SUM(n, include) which calculates the maximum possible sum over a non parent/child subset S over a tree rooted at node n. The parameter 'include' determines if node n should be included in a set S or not (this impacts which of the descendants of n can be used). Note that the maximum sum for the entire tree is given by MAX-SUM(T.root, true) + MAX-SUM(T.root, false). Then, use dynamic programming techniques to avoid solving the same call to MAX-SUM more than once. Memoization can be done by adding two new fields to each node (n.maxSumNodelncluded and n.maxSumNodeExcluded).

Write an algorithm that, for a given tree T, calculates the maximum sum achievable across all sets S (where no two elements have a parent/child relationship). You only need to return the maximal sum and not a set of nodes that achieves it (for simplicity). What is the runtime and space complexity of the algorithm? Hint: For any given node n, come up with a recursive solution MAX-SUM(n, include) which calculates the maximum possible sum over a non parent/child subset S over a tree rooted at node n. The parameter 'include' determines if node n should be included in a set S or not (this impacts which of the descendants of n can be used). Note that the maximum sum for the entire tree is given by MAX-SUM(T.root, true) + MAX-SUM(T.root, false). Then, use dynamic programming techniques to avoid solving the same call to MAX-SUM more than once. Memoization can be done by adding two new fields to each node (n.maxSumNodelncluded and n.maxSumNodeExcluded).

Computer Networking: A Top-Down Approach (7th Edition)
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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(S 10 3 Max Sum= 10 + 6 + 8 = 24 S Max Sum= 2 + 3 + 5 = 10 Write an algorithm that, for a given tree T, calculates the maximum sum achievable across all sets S (where no two elements have a parent/child relationship). You only need to return the maximal sum and not a set of nodes that achieves it (for simplicity). What is the runtime and space complexity of the algorithm? Hint: For any given node n, come up with a recursive solution MAX-SUM(n, include) which calculates the maximum possible sum over a non parent/child subset S over a tree rooted at node n. The parameter 'include' determines if node n should be included in a set S or not (this impacts which of the descendants of n can be used). Note that the maximum sum for the entire tree is given by MAX-SUM(T.root, true) + MAX-SUM(T.root, false). Then, use dynamic programming techniques to avoid solving the same call to MAX-SUM more than once. Memoization can be done by adding two new fields to each node (n.maxSumNodelncluded and n.maxSumNodeExcluded).
Transcribed Image Text:(S 10 3 Max Sum= 10 + 6 + 8 = 24 S Max Sum= 2 + 3 + 5 = 10 Write an algorithm that, for a given tree T, calculates the maximum sum achievable across all sets S (where no two elements have a parent/child relationship). You only need to return the maximal sum and not a set of nodes that achieves it (for simplicity). What is the runtime and space complexity of the algorithm? Hint: For any given node n, come up with a recursive solution MAX-SUM(n, include) which calculates the maximum possible sum over a non parent/child subset S over a tree rooted at node n. The parameter 'include' determines if node n should be included in a set S or not (this impacts which of the descendants of n can be used). Note that the maximum sum for the entire tree is given by MAX-SUM(T.root, true) + MAX-SUM(T.root, false). Then, use dynamic programming techniques to avoid solving the same call to MAX-SUM more than once. Memoization can be done by adding two new fields to each node (n.maxSumNodelncluded and n.maxSumNodeExcluded).
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