Consider a constraint satisfaction problem where there are four variables A, B, C, and D with...

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Consider a constraint satisfaction problem where there are four variables A, B, C, and D with the following domains: A: 1, 2, 3, 4 B: 1, 2, 3, 4, 5 C: 1, 2, 3, 4, 5 D: 1, 2, 3, 4, 5 There are three constraints: A > B, B > C, C > D. (a) (8 pts) Show how backtracking can be use to solve this problem. To select variables, use the most constrained variable heuristic, breaking ties using the most constraining variable heuristic. If ties still exist, break them alphabetically. To select values, use the least constraining value heuristic. If ties still exist, break them numerically (e.g., 1 before 2). Indicate the first 30 branches visited in the search tree (or stop when the solution is reached). Write them in text form with each branch on one line. For example, suppose we had variables X, Y and Z with domains 0, 1, and constraints XY, Y=Z. The first three branches visited in the search tree should be written as: Y=0, X=0 failure Y=0, X=1, z=0 solution (b) (8 pts) Show how forward checking can be used to solve this problem. To select vari- ables, use the most constrained variable heuristic, breaking ties using the most con- straining variable heuristic. If ties still exist, break them alphabetically. To select values, use the least constraining value heuristic. Indicate the first 30 branches visited in the search tree (or stop when the solution is reached). (c) (2 pts) Apply constraint propagation to eliminate values from the initial domains of the variables. Show the resulting domain of each variable after constraint propagation is applied. Consider a constraint satisfaction problem where there are four variables A, B, C, and D with the following domains: A: 1, 2, 3, 4 B: 1, 2, 3, 4, 5 C: 1, 2, 3, 4, 5 D: 1, 2, 3, 4, 5 There are three constraints: A > B, B > C, C > D. (a) (8 pts) Show how backtracking can be use to solve this problem. To select variables, use the most constrained variable heuristic, breaking ties using the most constraining variable heuristic. If ties still exist, break them alphabetically. To select values, use the least constraining value heuristic. If ties still exist, break them numerically (e.g., 1 before 2). Indicate the first 30 branches visited in the search tree (or stop when the solution is reached). Write them in text form with each branch on one line. For example, suppose we had variables X, Y and Z with domains 0, 1, and constraints XY, Y=Z. The first three branches visited in the search tree should be written as: Y=0, X=0 failure Y=0, X=1, z=0 solution (b) (8 pts) Show how forward checking can be used to solve this problem. To select vari- ables, use the most constrained variable heuristic, breaking ties using the most con- straining variable heuristic. If ties still exist, break them alphabetically. To select values, use the least constraining value heuristic. Indicate the first 30 branches visited in the search tree (or stop when the solution is reached). (c) (2 pts) Apply constraint propagation to eliminate values from the initial domains of the variables. Show the resulting domain of each variable after constraint propagation is applied.