Lab 4: 15 Puzzle with A* Grade: 30 pts Solve a given 4x4 sliding puzzle (Goal: _123456789ABCDEF) by using A* Searching algorithm. LastName_FirstInitial_U1_L4.py Step 1: Modify your 8-puzzle methods to work for 15-puzzle. Step 2: Complete inversion_count function. Decide if the slide puzzle is solvable or not by counting inversions. If N(height) is odd like 8 puzzle, then puzzle instance is solvable if : number of inversions is even in the input state. If N is even like 15 puzzle, puzzle instance is solvable if : the blank is on an even row counting from the bottom (second-last, fourth-last, etc.) and number of inversions is even. the blank is on an odd row counting from the bottom (last, third-last, fifth-last, etc.) and number of inversions is odd. Step 3: Research possible heuristic functions you can use for this lab and define one or more heuristic function(s). You may use multiple heuristic depends on situations. • • • • • Number of mis-placed tiles Manhattan distance Linear conflict Gaschnig’s … def dist_heuristic(start, goal, size): Step 4: Complete A* algorithm by implementing: def swap(node, i, j): def generate_children(node, size=4): def display_path(path_list, size=4): def a_star(start, goal, heuristic=dist_heuristic, size = 4): frontier = HeapPriorityQueue() # Hint: check ‘path’(closed set) before add a new node to frontier Sample outputs: Case 1: Type initial State: 152349678_ABCDEF 1523 1523 1_23 _123 4967 4_67 4567 4567 8_AB 89AB 89AB 89AB CDEF CDEF CDEF CDEF The shortest path length is : 4 Duration: 0.0 Case 2: Type initial State: 2_63514B897ACDEF 2_63 _263 5263 5263 5263 514B 514B _14B 1_4B 14_B 897A 897A 897A 897A 897A CDEF CDEF CDEF CDEF CDEF 5263 147B 89_A CDEF …… …… …… …… _123 4567 89AB CDEF 8943 C2_6 A71F DB5E …… …… …… …… _123 4567 89AB CDEF The shortest path length is : 16 Duration: 0.005014657974243164 Case 3: Type initial state: 8936C_24A71FDB5E 8936 8936 8936 893_ 89_3 C_24 C2_4 C24_ C246 C246 A71F A71F A71F A71F A71F DB5E DB5E DB5E DB5E DB5E The shortest path length is : 37 Duration: 0.27825474739074707 Case 4: Type initial state: 8293AC4671FEDB5_ …… The shortest path length is : 39 Duration: 0.7709157466888428
