Consider the following directed search graph where S is the starting node and G1 and G2 are goal nodes, costs are on edges, heuristic values on nodes. I. G2 B With A* o Gl reached first o G2 reached first o Incomplete None of the answers
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- Given N cities represented as vertices V₁, V2, 9 un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge ei, connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to vn (the destination). Assume that all edges have different values, and e₁, has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.Vertex S denotes the start state and vertices G1 and G2 denote the two goal states. Directed edges are labelled with the actual costs of traversing the edge. What path from S to a goal would be found by Breadth-First Search (BFS)? If all else is equal, consider states in alphabetic order.Consider the following graph. If we run breadth first search on this graph starting at any vertex, which one of the following is a possible order for visiting the nodes? NQMPOR QMNPOR MNOPQR QMNPRO Assume the following adjacency list for a graph. After you draw the graph, what is the path to reach D from A. Vertex Edges A --------> B, C B --------> C C --------> B, E D --------> B E --------> B, D Both (B) and (C) A->B->C->E->D A->B->C->D A->C->E->D
- Vertex S denotes the start state and vertices G1 and G2 denote the two goal states. Directed edges are labelled with the actual costs of traversing the edge. What path from S to a goal would be found by Iterative deepening Depth-First Search? If all else is equal, consider states in alphabetic order. options are : a. S, A, B, C, D, E, F, G1 b. S, A, B, C, E, F, D, G1 c. S, A, B, C, E, F, G1 d. S, A, B, C, G1 e. S, A, C, G1 f. S, A, E, G1 g. S, B, A, C, E, G1 h. S, B, F, D, G2 i. S, C, B, F, A, D, E, G1 j. S, C, G1Vertex S denotes the start state and vertices G1 and G2 denote the two goal states. Directed edges are labelled with the actual costs of traversing the edge. In what order would Best-First Search retrieve the states from the frontier when starting the search in S? If all else is equal, consider states in alphabetic order. options are : a. S, A, B, C, D, E, F, G1 b. S, A, B, C, E, F, D, G1 c. S, A, B, C, E, F, G1 d. S, A, B, C, G1 e. S, A, C, G1 f. S, A, E, G1 g. S, B, A, C, E, G1 h. S, B, F, D, G2 i. S, C, B, F, A, D, E, G1 j. S, C, G1Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge ei,j connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to UN (the destination). Assume that all edges have different values, and e₁,N has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
- Algebraic Preis’ AlgorithmAlgorithm due to Preis provides a different way to solve the maximal weightedmatching problem in a weighted graph. The algorithm consists of the followingsteps.1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e}show two ways of implementing this algorithm in PythonAlgebraic Preis’ AlgorithmAlgorithm due to Preis provides a different way to solve the maximal weightedmatching problem in a weighted graph. The algorithm consists of the followingsteps.1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e} show two ways of implementing this algorithm in Pythonconsider the following graph.if there is over a decision between multiple neighbor nodes in the breadth first search(BFS) alhorithm.assume we always choose the letter closest to the beginning of the alphabet first.write an algorithm for BFS traversal of a graph and shsow that in what order will the nodes be visited using BFS when traversing is starting from "D"?
- consider the following graph.if there is over a decision between multiple neighbor nodes in the breadth first search(BFS) alhorithm.assume we always choose the letter closest to the beginning of the alphabet first.write an algorithm for BFS traversal of a graph and shsow that in what order will the nodes be visited using BFS when traversing is starting from "D"? answer should only in algorithm justConsider the following edge-weighted undirected graph: 4 A В 13 4 D E F 3 In the algorithms below, assume that any ties when choosing vertices are resolved by taking the first in alphabetical order. Any ties between edges are resolved in favor of the edge with the smallest vertex or (if both have that vertex), to the second-smallest vertex (so (А, E)<(В, D) and (A, C)<(A, E).) a. If we run Dijkstra's algorithm on the graph starting at node A, which edges are in the resulting tree? Mark all that apply. iO (A, B) (A, D) ii U (В, С) iv O (B, E) v O (C, E) ii vi O (C, F) (D, G) (Е, F) ix O (F, G) vii viii b. If we run Prim's algorithm on this graph starting at node A, what are the edges in the resulting minimal spanning tree? Mark all that apply. iO (A, B) ii D (A, D) ii U (В, С) iv U (В, Е) v O (C, E) vi O (C, F) vii U (D, G) viii O (E, F) ix O (F, G) c. If we run Kruskal's algorithm on the graph, then just before we add edge (C, F) to the resulting tree, what are the subsets of 2 or more…2. The greedy algorithm for the vertex cover problem picks a highest degree vertex v, includes v in the cover, deletes all edges incident to v, and repeats until there are no edges left. Show that this algorithm is not a c-approximation algorithm for any c. Hint: consider a bipartite graph G = (A, B, E) with |A| = n and B ULBi, where |B;| = [n/i]. Vertices in B; have degree i, and the neigh- borhoods of different vertices are disjoint.