Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 5, Problem 13E
Explanation of Solution
Assertion
- Consider a MIN node whose children are terminal nodes.
- If MIN plays suboptimally, then the value of the node is greater than or equal to the value it would have if MIN played optimally...
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You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.
In a lecture the professor said that for every minimum spanning tree T of G there is an execution of the algorithm of Kruskal which delivers T as a result. ( Input is G).
The algorithm he was supposedly talking about is:
Kruskal()
Precondition. N = (G, cost) is a connected network with n = |V| node and m = |E| ≥ n − 1 edges.All edges of E are uncolored.
postcondition: All edges are colored. The green-colored edges together with V form one MST by N.
Grand Step 1: Sort the edges of E in increasing weight: e1 , e2, . . . , em
Grand step 2: For t = 0.1, . . . , m − 1 execute: Apply Kruskal's coloring rule to the et+1 edge
i dont really understand this statement or how it is done. can someone explain me what he meant?
a)
Why can Dijkstra's algorithm not work properly on graphs with negative
weighted edges? Explain with example.
Implement the greedy approach for coin change algorithm and show your step by
step approach to give change of 139 in coin change with {1, 3, 5, 25, 45, 60} unit
values.
c)
Write the procedure for calculating GCD and LCM of the following numbers.
Also write the answers at last.
2, 4, 5, 20
Chapter 5 Solutions
Artificial Intelligence: A Modern Approach
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