Fixing Heuristic h=2, 4 S h=6 A 3 В G h=0 h=5 h=1 D h=0 The heuristics values for the graph above are not correct. For which single state (S, A, B, C, D, or G) could you change the heuristics value to make everything admissible and consistent? What range of values are possible to make this correction (e.g., 10 <= S < 20)? State: Range: 5

Consider the following edge-weighted digraph with 8 vertices and 13 edges. V->W weight A->E 1 A->B B->C C->F 4 C->D D->G F->E 39 23 F->B 26 F->A 16 G->F G->C 40 34 H->D 95 H->G 17 Here is a graphical representation of the same edge-weighted digraph: (A) -3---->(B) -39-->(D) 16 95 (E)- -23- (F). 40 (G) (H) Suppose that you run the Bellman-Ford algorithm to compute the shortest paths from H to every other vertex. What is the distTo[] array immediately after the end of three passes of the algorithm (pass 1, 2, and 3)? Each pass consists of relaxing the 13 edges in the order given above. Here is the distTo[] array before the beginning of pass 1: v A B CDE F H. distTo(v] Answer Your answer should be a sequence of 8 integers, separated by whitespace,

Consider navigating the maze shown below. 3. 4. (z) 1. S 2. A 5. N L M G B F H 6. D 7. P 2 8. G 2 4 C E P 2 2 2 A S The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let S be the initial state and G be the goal state. List the first 8 vertices expanded by Uniform Cost Search (enter the single letter label of a node). B FL K 2 2 J 2 D H

Consider the following edge-weighted graph with 10 vertices and 17 edges. V-w weight A-B 8. F-A 6. G-B 15 B-F C-B D-C 16 C-G 12 C-H C-I D-I 17 D-E 11 I-E 13 J-E 10 G-F 9. H-G I-H 14 1 I-J Here is a graphical representation of the same edge-weighted graph: (A) -8- (C)------16----- (D)---- --11-----(E) 7|\ 13 10 (F) (G) Give the sequence of edges in the MST in the order that Prim's algorithm adds them to the MST, when starting Prim's algorithm from vertex H. To specify an edge, use its weight.

Consider the following descriptions for one sample of six zones: Z1 matches B or D; Z2 matches C, E, or F; Z3 matches A or F; Z4 matches B or D; Z5 matches C or F; and Z6 matches D. (a) (A-F). Draw the bipartite graph that models the zones (Z1-Z6) and the letters they match (b) district layout. Use Hall's theorem to determine if algorithm will be able to successfully create a

Consider the graph below: Provide the MST either as a drawn subgraph or the edges that comprise a valid MST. You may use either  algorithm but show your work/rationale . In other words, you cannot just provide the MST to receive credit .