Merge pull request #580 from Manasi2001/issue-579

8 Puzzle Problem using A* Algorithm

Author: smv1999

Searching Algorithms/8_Puzzle_Problem_using_A_star_Algorithm.py

@@ -0,0 +1,235 @@
+'''
+8 PUZZLE PROBLEM SOLVING USING A* ALGORITHM
+
+An instance of the n-puzzle game consists of a board holding n^{2}-1 
+distinct movable tiles, plus an empty space. The tiles are numbers from 
+the set 1,..,n^{2}-1. For any such board, the empty space may be legally 
+swapped with any tile horizontally or vertically adjacent to it. In this 
+assignment, the blank space is going to be represented with the number 0. 
+Given an initial state of the board, the combinatorial search problem is 
+to find a sequence of moves that transitions this state to the goal state; 
+that is, the configuration with all tiles arranged in ascending order 
+0,1,..,n^{2}-1.
+
+So, this is the goal state that we want to reach:
+[1, 2, 3]
+[8, 0, 4]
+[7, 6, 5] 
+
+The search space is the set of all possible states reachable from the 
+initial state. The blank space may be swapped with a component in one of 
+the four directions {‘Up’, ‘Down’, ‘Left’, ‘Right’}, one move at a time.
+
+A* algorithm has 3 parameters:
+g: the cost of moving from the initial cell to the current cell.
+h: also known as the heuristic value, it is the estimated cost of moving from 
+   the current cell to the final cell. The actual cost cannot be calculated until 
+   the final cell is reached. Hence, h is the estimated cost. We must make sure 
+   that there is never an over estimation of the cost.
+f: it is the sum of g and h. So, f = g + h
+We always go to the state that has minimum 'f' value.
+
+'''
+
+# importing the necessary libraries
+from time import time
+from queue import PriorityQueue
+
+# creating a class Puzzle
+class Puzzle:
+    # setting the goal state of 8-puzzle
+    goal_state=[1,2,3,8,0,4,7,6,5]
+    # setting up the members of a class
+    heuristic=None
+    evaluation_function=None
+    needs_hueristic=False
+    num_of_instances=0
+    
+    # constructor to initialize the class members
+    def __init__(self,state,parent,action,path_cost,needs_hueristic=False):
+        self.parent=parent
+        self.state=state
+        self.action=action
+        # calculating the path_cost as the sum of its parent cost and path_cost
+        if parent:
+            self.path_cost = path_cost + parent.path_cost
+        else:
+            self.path_cost = path_cost
+        if needs_hueristic:
+            self.needs_hueristic=True
+            self.generate_heuristic()
+            # calculating the expression as f = g + h
+            self.evaluation_function= path_cost + needs_hueristic
+        # incrementing the number of instance by 1
+        Puzzle.num_of_instances+=1
+    
+    # method used to display a state of 8-puzzle
+    def __str__(self):
+        return str(self.state[0:3])+'\n'+str(self.state[3:6])+'\n'+str(self.state[6:9])
+
+    # method used to generate a heuristic value
+    def generate_heuristic(self):
+        self.heuristic=0
+        for num in range(1,9):
+            # calculating the heuristic value as manhattan distance which is the absolute 
+            # difference between current state and goal state. 
+            # using index() method to get the index of num in state
+            distance= abs(self.state.index(num) - self.goal_state.index(num)) 
+            i=int(distance/3)
+            j=int(distance%3)
+            self.heuristic=self.heuristic+i+j
+
+    def goal_test(self):
+        # including a condition to compare the current state with the goal state
+        if self.state == self.goal_state:
+            return True
+        return False
+
+    @staticmethod
+    def find_legal_actions(i,j):
+        # find the legal actions as Up, Down, Left, Right based on each cell of state
+        legal_action = ['U', 'D', 'L', 'R']
+        if i == 0:  # up is disable
+            # if row is 0 in board then up is disable
+            legal_action.remove('U')
+        elif i == 2:  
+            legal_action.remove('D')
+        if j == 0:
+            legal_action.remove('L')
+        elif j == 2:
+            legal_action.remove('R')
+         # returnig legal_action
+        return legal_action
+
+    # method to generate the child of the current state of the board
+    def generate_child(self):
+        children=[]
+        x = self.state.index(0)
+        # generating the row (i) & col (j) position based on the current index of 0 on the board 
+        i = int(x/3)
+        j = int(x%3)
+        # calling the method to find the legal actions based on i and j values
+        legal_actions=self.find_legal_actions(i,j)
+
+        for action in legal_actions:
+            new_state = self.state.copy()
+            # if the legal action is UP
+            if action is 'U':
+                # swapping between current index of 0 with its up element on the board
+                new_state[x], new_state[x-3] = new_state[x-3], new_state[x]
+            elif action is 'D':
+                # swapping between current index of 0 with its down element on the board
+                new_state[x], new_state[x+3] = new_state[x+3], new_state[x]
+            elif action is 'L':
+                # swapping between the current index of 0 with its left element on the board
+                new_state[x], new_state[x-1] = new_state[x-1], new_state[x]
+            elif action is 'R':
+                # swapping between the current index of 0 with its right element on the board
+                new_state[x], new_state[x+1] = new_state[x+1], new_state[x]
+            # appending the new_state of Puzzle object with parent, action,path_cost is 1, its needs_hueristic flag
+            children.append(Puzzle(new_state, self, action, 1, self.needs_hueristic))
+        # returning the children
+        return children
+    
+    # method to find the solution
+    def find_solution(self):
+        solution = []
+        all_states = []
+        solution.append(self.action)
+        all_states.append(self)
+        path = self
+        while path.parent != None:
+            path = path.parent
+            solution.append(path.action)
+            all_states.append(path)
+        solution = solution[:-1]
+        solution.reverse
+
+        print('\nAll states from goal to initial: ')
+        for i in all_states:
+          print(i, '\n')
+        return solution
+    
+# method for A-star search
+# passing the initial_state as parameter to the breadth_first_search method
+def Astar_search(initial_state):
+    count=0
+    # creating an empty list of explored nodes
+    explored=[]
+    # creating a instance of Puzzle as initial_state, None, None, 0, True
+    start_node=Puzzle(initial_state, None, None, 0, True)
+    q = PriorityQueue()
+    # putting a tuple with start_node.evaluation_function, count, start_node into PriorityQueue
+    q.put((start_node.evaluation_function, count, start_node))
+
+    while not q.empty():
+        # getting the current node of a queue. Use the get() method of Queue
+        node=q.get()
+        # extracting the current node of a PriorityQueue based on the index of a tuple. 
+        # referring a tuple format put in PriorityQueue  
+        node=node[2]
+        # appending the state of node in the explored list as node.state
+        explored.append(node.state)
+        if node.goal_test():
+            return node.find_solution()
+        # calling the generate_child method to generate the child node of current node
+        children=node.generate_child()
+        for child in children:
+            if child.state not in explored:
+                count += 1
+                # putting a tuple with child.evaluation_function, count, child into PriorityQueue
+                q.put((child.evaluation_function, count, child))
+    return
+
+# starting executing the 8-puzzle with setting up the initial state
+# here we have considered 3 initial state intitalized using state variable
+state= [1, 3, 4,
+        8, 6, 2,
+        7, 0, 5]
+
+# initializing the num_of_instances to zero
+Puzzle.num_of_instances = 0
+# set t0 to current time
+t0 = time()
+astar = Astar_search(state)
+# getting the time t1 after executing the breadth_first_search method
+t1 = time() - t0
+print('A*:',astar)
+print('space:', Puzzle.num_of_instances)
+print('time:', t1)
+print()
+print('------------------------------------------')
+    
+'''
+Sample working:
+
+All states from goal to initial: 
+[1, 2, 3]
+[8, 0, 4]
+[7, 6, 5] 
+
+[1, 0, 3]
+[8, 2, 4]
+[7, 6, 5] 
+
+[1, 3, 0]
+[8, 2, 4]
+[7, 6, 5] 
+
+[1, 3, 4]
+[8, 2, 0]
+[7, 6, 5] 
+
+[1, 3, 4]
+[8, 0, 2]
+[7, 6, 5] 
+
+[1, 3, 4]
+[8, 6, 2]
+[7, 0, 5] 
+
+A*: ['D', 'L', 'U', 'R', 'U']
+space: 117
+time: 0.0029821395874023438
+
+'''