Merge pull request #1501 from Pranav016/rat-in-maze

Added RatInMaze.py

Python/README.md

@@ -68,6 +68,7 @@
 - [Hamiltonian Cycle](backtracking/Hamiltonian_Cycle.py)
 - [Sudoku Solver](backtracking/sudokuSolver.py)
 - [Subset Sum](backtracking/Subset_Sum.py)
+- [Rat-In-Maze problem](backracking/RatInMaze.py)
 
 
 ## Dynamic Programming

Python/backtracking/RatInMaze.py

@@ -0,0 +1,100 @@
+'''
+Problem statement- given a maze of 1s with obstacles (represented by 0).
+We have to print all the possible paths to the end.
+Logical intuition- We have to explore all the possible paths hence our mouse
+will move in all four directions untill it reaches the end
+'''
+
+
+def printPathHelper(i, j, maze, n, solution):
+    '''
+    Summary Line:
+    This funcion helps us to print the path followed by the rat in the maze.
+    It puts 1s at places that the mouse can go and 0s
+    at places where the mouse doesn't go.
+
+    Args:
+    i- current position on the maze horizontally
+    j- current position on the maze vertically
+    maze- The 2D matrix that was inputted through which the Rat has to pass
+    n- side of the 2D matrix
+    solution- solution matrix to be returned
+    '''
+    if i == n-1 and j == n-1:
+        print()
+        solution[i][j] = 1
+        for i in range(n):
+            for j in range(n):
+                print(solution[i][j], end=" ")
+            print()
+        solution[i][j] = 0
+        return
+    if i < 0 or j < 0 or i >= n or j >= n or\
+            maze[i][j] == 0 or solution[i][j] == 1:
+        return
+    solution[i][j] = 1
+    printPathHelper(i+1, j, maze, n, solution)
+    printPathHelper(i, j+1, maze, n, solution)
+    printPathHelper(i-1, j, maze, n, solution)
+    printPathHelper(i, j-1, maze, n, solution)
+    solution[i][j] = 0
+    return
+
+
+def printPath(maze):
+    '''
+    Summary Line:
+    This function helps us to take form a solution matrix and calls
+    another method printPathHelper() on the solution matrix
+    to print all possible paths for the mouse.
+
+    Args:
+    maze- The 2D matrix that was inputted through which the Rat has to pass
+    '''
+    n = len(maze)
+    solution = [[0 for j in range(n)]for i in range(n)]
+    printPathHelper(0, 0, maze, n, solution)
+
+if __name__ == '__main__':
+    n = int(input())
+    maze = []
+    for j in range(n):
+        arr = [int(i) for i in input().split()]
+        maze.append(arr)
+        j += 1
+    printPath(maze)
+
+'''
+Sample input-
+4
+1 1 1 1
+1 1 0 1
+1 0 1 1
+1 1 1 1
+
+Illustration for the maze-
+(Obstacles at positions where there is 0 in the input matrix)
+                0       1       2       3
+            +-------+-------+-------+-------+
+            |       |       |       |       |
+        0   |       |       |       |       |
+            |       |       |       |       |
+            +---------------+-------+-------+
+            |       |       |       |       |
+        1   |       |       |   x   |       |
+            |       |       |       |       |
+            +-------+-------+-------+-------+
+            |       |       |       |       |
+        2   |       |   x   |       |       |
+            |       |       |       |       |
+            +-------+-------+-------+-------+
+            |       |       |       |       |
+        3   |       |       |       |       |
+            |       |       |       |       |
+            +-------+-------+-------+-------+
+
+Sample Output-
+All possible paths will be printed
+
+Time complexity- O(2^(n^2))
+'''