Consider the 8-puzzle problem. Trace out the A* algorithm given the initial and goal states below. You are supposed to show the generated search tree until the search generates the goal state. For each state show the value of the evaluation function f(n) = g(n) + h(n). Recall that g(n) gives the path cost from the initial state to node n. Moreover, for this problem the step cost is 1 for any action (moving the empty tile). As a heuristic let h(n) be the number of misplaced tiles. Hence f(initial-state) = 0 + 3 = 3. The # symbol denotes the empty tile. Initial State Goal State 1 2 3 1 2 3 # 4 6 4 5 6 7 5 8 7 8 #

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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.