Consider the following graph and a heuristic function h. Please check if h is admissible * A 1 S h=4 h=1 h=2 1 2 В h=1 h=0 3.
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- A manufacturer of chemical goods is faced with the problem that certain goods cannot be stored at the same place due to the danger of unwanted reactions. What he seeks is a storage scheme such that goods that cannot be located at the same place are indeed separated. Provide a graph model to solve this problem. Do not write details of any algorithms. Simply describe your graph vertices, edges, and the classic graph theory problem that is useful for the design of the storage scheme here.*Data Structures and Algorithm(C Programming) Question: Answer the following questions about graphs. (a) What is the maximum number of edges that can exist in an undirected graph? Why? Explain. (b) What is a cycle in a directed graph? (c) Given a graph G(V, E), its inverse consists of a graph G′ where the edges of the original graph is inverted. That is, for all (u, v) ∈ G.E, ∃(v, u) ∈ G′ .E. Describe a nonempty directed graph G such that G = G′ . (d) Topological sorting in a directed graph is a linear ordering of its vertices. Does existence of a cycle in a graph violate a topological sorting? Why/why not? (e) Depth First Search can be used as a subroutine to solve other problems, topological sorting being an example of this. Explain the intuition behind using DSF in the calculation of topological sort. (Note: I'm not asking you about how DFS is used in topological sorting. Rather, I'm asking what is needed to topologically sort graphs and how DFS becomes useful to achieve…Write a boolean function, called universalSink, to determine weather a directed graph has a universal sink. A universal sink is a vertex which has no outgoing edges, and all other vertices have an incoming edge to the sink vertex. Hint: it has to be a C++ function just the function, not the program.
- True or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|. (b) If an A* heuristics is admissible then it satisfies the monotone restriction. (c) Best-first search guarantees optimality in its returned solution. (d) Least-cost-first search guarantees optimality in its returned solution. (e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.Suppose we want to use UCS and the A* algorithm on the graph below to find the shortest path from node S to node G. Each node is labeled by a capital letter and the value of a heuristic function. Each edge is labeled by the cost to traverse that edge. Perform A*, UCS, and BFS on this graph. Indicate the f, g, and h values of each node for the A*. e.g., S = 0 + 6 = 6 (i.e. S = g(S) + h(S) = f(S)). Additionally, show how the priority queue changes with time. Show the order in which the nodes are visited for BFS and UCS. Show the path found by the A*, UCS, and BFS algorithms on the graph above. Make this example inadmissible by changing the heuristic value at one of the nodes. What node do you choose and what heuristic value do you assign? What would be the A* algorithm solution then.Let G = (V, E) be an undirected graph. Design algorithms for the following and discuss the complexity of your algorithm (b) Determine whether it is possible to direct the edges of G s.t. for each u, indegree(u) ≥ 1. If it is possible, your algorithm should provide a way to do so.
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- Draw a graph with the following conditions: a. 11 nodes total b. Directed, Acyclic c. Would have 5 possible options on the first iteration of topological sortWrite a boolean function, called universalSink, to determine weather a directed graph has a universal sink. A universal sink is a vertex which has no outgoing edges, and all other vertices have an incoming edge to the sink vertex. Hint: it has to be a C++ functionPlease state if the next two statements about an undirected and connected graph P are true or false. Justify your answer. (a) The shortest path between two nodes is always part of some minimum spanning tree. (b)Prim’s algorithm will work properly if P has negative edge weights.