Merge pull request #159 from abhisheks008/patch-4

Rat in a Maze using Backtracking Algorithms

Author: prathimacode-hub

Backtracking/Rat in a Maze/Images/rat1.PNG

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+# RAT IN A MAZE Problem using Backtracking algorithm
+# Problem Statement : The aim of this problem is to find out
+#                     the matrix through which the rat can reach
+#                     it's destination by the shortest path
+#                     travelling through the given maze as a matrix
+#                     using 1 and 0, where 1 means open path and 0 means
+#                     blocked path.
+
+# Author : Abhishek Sharma, 2021
+
+# -----------------------------------------------------------------
+
+# Solution for the above problem statement using Python 3 language.
+# Algorithm used : Backtracking
+
+# -----------------------------------------------------------------
+
+
+# Initializing the constant N value (Here it is 4)
+N = 4
+ 
+# A utility function to print solution matrix sol
+def printSolution( sol ):
+     
+    for i in sol:
+        for j in i:
+            print(str(j) + " ", end ="")
+        print("")
+
+        
+# A utility function to check if x, y is valid
+# index for N * N Maze
+def isSafe( maze, x, y ):
+     
+    if x >= 0 and x < N and y >= 0 and y < N and maze[x][y] == 1:
+        return True
+     
+    return False
+ 
+    
+# This function solves the Maze problem using Backtracking.
+# It mainly uses solveMazeUtil() to solve the problem. It
+# returns false if no path is possible, otherwise return
+# true and prints the path in the form of 1s. Please note
+# that there may be more than one solutions, this function
+# prints one of the feasable solutions.
+
+# To check whether there is proper solution or not
+def solveMaze( maze ):
+     
+    # Creating a 4 * 4 2-D list
+    sol = [ [ 0 for j in range(4) ] for i in range(4) ]
+     
+    if solveMazeUtil(maze, 0, 0, sol) == False:
+        print("Solution doesn't exist");
+        return False
+     
+    printSolution(sol)
+    return True
+     
+    
+    
+# A recursive utility function to solve Maze problem
+def solveMazeUtil(maze, x, y, sol):
+     
+    # if (x, y is goal) return True
+    if x == N - 1 and y == N - 1:
+        sol[x][y] = 1
+        return True
+         
+    # Check if maze[x][y] is valid
+    if isSafe(maze, x, y) == True:
+        
+        # mark x, y as part of solution path
+        sol[x][y] = 1
+         
+        # Move forward in x direction
+        if solveMazeUtil(maze, x + 1, y, sol) == True:
+            return True
+             
+        # If moving in x direction doesn't give solution
+        # then Move down in y direction
+        if solveMazeUtil(maze, x, y + 1, sol) == True:
+            return True
+         
+        # If none of the above movements work then
+        # BACKTRACK: unmark x, y as part of solution path
+        sol[x][y] = 0
+        return False
+ 
+
+
+# Driver program to test above function
+if __name__ == "__main__":
+    # Initialising the maze
+    maze = [ [1, 0, 0, 0],
+             [1, 1, 0, 1],
+             [0, 1, 0, 0],
+             [1, 1, 1, 1] ]
+    print ("- RAT IN A MAZE Problem using Backtracking Algorithms -")
+    print ("-------------------------------------------------------")
+    print ()
+    print ("The path or maze given to the rat :")
+    printSolution (maze)
+    print ()
+    print ("The path recognised by the algorithm :")
+    solveMaze(maze)
+    
+# -----------------------------------------------------------------    
+# Input given :
+# The path of maze given to the rat :
+# 1 0 0 0 
+# 1 1 0 1 
+# 0 1 0 0 
+# 1 1 1 1 
+
+# -----------------------------------------------------------------
+
+# Output :
+
+# The path recognised by the algorithm :
+# 1 0 0 0 
+# 1 1 0 0 
+# 0 1 0 0 
+# 0 1 1 1 
+
+# -----------------------------------------------------------------
+
+# Abhishek Sharma, 2021 @abhisheks008