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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Students have asked these similar questions
The book demonstrated that a poisoned reverse will prevent the count-to-infinity problem caused when there is a loop involving three directly connected nodes. However, other loops are possible. Will the poisoned reverse solve the general case count-to-infinity problem encountered by Bellman-Ford?
-Yes, the poisoned reverse will prevent a node from offering a path that includes preceding nodes in the loop.
-It will not, preceeding nodes may still be used in the computation of the distance vector offered by a given node.
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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- If n points are connected to fom a closed polygon as shown below, the area of the polygon can be compuled as n-2 Area = (%)E (*»1 + x ) (y»1 - y ) =0 Notice that although the ilustrated polygon has only 6 distinct comers, n for his polygon is 7 because the algorithmexpects that the last point (x.ya) will be repeat of the initial point, (Ko.yo). Define a structure for a point. Each point contains x coordinate and y coordinate. The represe ntation of a Polygon must be an array of structures in your program. Write a C program that takes the number of actual points (n-1) from the user. After that, user enters x and y coordinates of each point. (The last point will be repeat of the initial point). Writo a compute Are a function which returns the area of the Polygon. Print he area of the Polygon in main. Display the area with wo digts after the decimal point. Note: The absolute value can be computed with fabs function. Example: double x.50: fabs(x) is 5.0 double x 0.0: fabs(x) is 0.0 double…arrow_forwardPython implementation of algorithm has three nested f or loops and the adjacency matrix T passed to this procedure simply multiplies this matrix with itselfusing logical operators. A test is carried to check whether all elements ofT is 1 which means graph G is connected, otherwise G is not connected as returned to the caller along with the connectivity matrix.arrow_forwardRaj Shaker is learning Combinatorics in his college. He finds it very interesting to calculate number of ways of going to point (c, d) from point (a, b) in co-ordinate plane. We can take horizontal and vertical steps only and cannot visit at a point twice. In a step, you can move one unit only. We have to reach to the point (c, d) from the point (a, b) using abs(a-c) + abs(b-d) steps only. Raj Shaker has two sets of points. Set A contains points having X co- ordinate 0 and Y co-ordinates varying from 1 to N (both inclusive). Set B contains points having X co-ordinate K and Y co-ordinates varying from 1 to N (both inclusive). Both sets contain N number of integral points. He wants to calculate the sum of number of ways to going to each point of set B from each point of set A. Note: Answer the question using python language only. Input 1 45 Output 236arrow_forward
- If n1, n, ., nk is a sequence of nodes in the tree such that n; is the parent of n41 for 1arrow_forwardComputer Networks The book demonstrated that a poisoned reverse will prevent the count-to-infinity problem caused when there is a loop involving three directly connected nodes. However, other loops are possible. Will the poisoned reverse solve the general case count-to-infinity problem encountered by Bellman-Ford? Yes, the poisoned reverse will prevent a node from offering a path that includes preceding nodes in the loop. It will not, preceding nodes may still be used in the computation of the distance vector offered by a given node.arrow_forwardYou are given a graph G = (V, E) with positive edge weights, and a minimum spanning tree T = (V, E') with respect to these weights; you may assume G and T are given as adjacency lists. Now suppose the weight of a particular edge e in E is modified from w(e) to a new value w̃(e). You wish to quickly update the minimum spanning tree T to reflect this change, without recomputing the entire tree from scratch. There are four cases. In each case give a linear-time algorithm for updating the tree. Note, you are given the tree T and the edge e = (y, z) whose weight is changed; you are told its old weight w(e) and its new weight w~(e) (which you type in latex by widetilde{w}(e) surrounded by double dollar signs). In each case specify if the tree might change. And if it might change then give an algorithm to find the weight of the possibly new MST (just return the weight or the MST, whatever's easier). You can use the algorithms DFS, Explore, BFS, Dijkstra's, SCC, Topological Sort as…arrow_forwardAlgorithm to Element as Product of Strong GeneratorsInput : a group G acting on f~ = { 1,2 ..... n };an element g of G;a base and strong generating set for G;Schreier vectors v (i), 1 < i < k, for the stabiliser chain;Output : a symbolic product, word, expressing g in terms of the strong generators;arrow_forwardYou have to show (no explanations necessary) how the following reductions work. Please remember that ifwe are looking at a reduction from A to B, the A instance might be a YES instance or might be a NO instance.(a) In class we saw the reduction from the Hamiltonian cycle problem to the 0-1 TSP problem. Show what will bethe TSP instance (by showing the graph G′and the number K′) if we start with the Hamiltonian cycle instanceG in Fig HW4Q2a.(b) In class we studied the reduction from CLIQUE to I.S. Show what will be the I.S. instance (by showing the graphG′and the number K′) if we start with the CLIQUE instance with K = 3 and the graph in Fig HW4Q2b.(c) In class we studied the reduction from SAT to CLIQUE. Show what will be the CLIQUE instance (by showingthe graph G and the number K) if we start with the following SAT instance: (complement is shown with the −sign, so −x stands for the complement of x.(x ∨(−w) ∨(−z)) ∧((−x) ∨w ∨(z)) ∧((−x) ∨(−w))arrow_forwardThe algorithm to perform the task is Algorithm 4.Algorithm 4 : Element as Product of Strong GeneratorsInput : a group G acting on f~ = { 1,2 ..... n };an element g of G;a base and strong generating set for G;Schreier vectors v (i), 1 < i < k, for the stabiliser chain;Output : a symbolic product, word, expressing g in terms of the strong generators;arrow_forward2. Let (Finite_DFA) = {w, Mx is a DFA and L(Mx) is finite}. Show that (Finite_DFA) is decidable.arrow_forwardGiven a DAG and two vertices v and w, find the lowest commonancestor (LCA) of v and w. The LCA of v and w is an ancestor of v and w that has nodescendants that are also ancestors of v and w. Computing the LCA is useful in multipleinheritance in programming languages, analysis of genealogical data (find degree ofinbreeding in a pedigree graph), and other applications. Hint : Define the height of avertex v in a DAG to be the length of the longest path from a root to v. Among verticesthat are ancestors of both v and w, the one with the greatest height is an LCA of v and w.arrow_forwardLet G = (V, E) be a connected, undirected graph, and let s be a fixed vertex in G. Let TB be the spanning tree of G found by a bread first search starting from s, and similarly TD the spanning tree found by depth first search, also starting at s. (As in problem 1, these trees are just sets of edges; the order in which they were traversed by the respective algorithms is irrelevant.) Using facts, prove that TB = TD if and only if TB = TD = E, i.e., G is itself a tree.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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