Add all_possible_paths_between_two_points_in_matrix_using_dfs.py

path_tracing/all_possible_paths_between_two_points_in_matrix_using_dfs.py

@@ -0,0 +1,99 @@
+"""
+This is an implementation for finding all possible paths of a
+non symmetrical matrix between given start and end points including
+consideration of obstacles using depth first search approach
+
+For doctests run following command:
+python3 -m doctest -v all_possible_paths_between_two_points_in_matrix_using_dfs.py
+
+For manual testing run:
+python3 all_possible_paths_between_two_points_in_matrix_using_dfs.py
+"""
+
+OBSTACLE_POS = -1
+VALID_POS = 1
+START_POS = "s"
+END_POS = "e"
+VISITED_POS = None
+
+
+def find_all_possible_paths(matrix: list, row: int, col: int) -> int:
+    """
+    Pure implementation of recursive depth first search algorithm to find out
+    all the possible paths of a given symmetrical/non-symmetrical matrix
+
+    :param matrix: symmetrical or non-symmetrical matrix which contains
+    start, end, valid and obstacle positions
+    :param row: currently traversing row index of the matrix in a given point of time
+    :param col: currently traversing column index of the matrix in a given point of time
+
+    Examples:
+    >>> find_all_possible_paths([['s', 1, 1], [1, -1, 1], [-1, 1, 'e']], 0, 0)
+    1
+    >>> find_all_possible_paths([[1, 'e', -1], [-1, 1, 1], [-1, 1, 's']], 2, 2)
+    2
+    >>> find_all_possible_paths([['s'], [1, 1], [1, 1, 1], [1, 1, 'e', 1]], 0, 0)
+    7
+    >>> find_all_possible_paths([[-1, 1], ['s', 1], [-1, -1], [-1, 'e']], 1, 0)
+    0
+    >>> find_all_possible_paths([[-1, 's'], [-1, -1, 1], [1, -1], ['e', 1, 1]], 0, 1)
+    0
+    """
+    if (
+        row < 0
+        or row >= len(matrix)
+        or col < 0
+        or col >= len(matrix[row])
+        or matrix[row][col] == OBSTACLE_POS
+        or matrix[row][col] == VISITED_POS
+    ):
+        return 0
+    if matrix[row][col] == END_POS:
+        return 1
+
+    visited = matrix[row][col]
+    matrix[row][col] = VISITED_POS
+
+    result = (
+        find_all_possible_paths(matrix, row + 1, col)
+        + find_all_possible_paths(matrix, row - 1, col)
+        + find_all_possible_paths(matrix, row, col + 1)
+        + find_all_possible_paths(matrix, row, col - 1)
+    )
+    matrix[row][col] = visited
+
+    return result
+
+
+def helper(matrix: list) -> int:
+    """
+    Examples:
+    >>> helper([['s', 1, 1], [1, -1, 1], [-1, 1, 'e']])
+    1
+    >>> helper([[1, 'e', -1], [-1, 1, 1], [-1, 1, 's']])
+    2
+    >>> helper([['s'], [1, 1], [1, 1, 1], [1, 1, 'e', 1]])
+    7
+    >>> helper([[-1, 1], ['s', 1], [-1, -1], [-1, 'e']])
+    0
+    >>> helper([[-1, 's'], [-1, -1, 1], [1, -1], ['e', 1, 1]])
+    0
+    """
+
+    for i in range(len(matrix)):
+        for j in range(len(matrix[i])):
+            if matrix[i][j] == START_POS:
+                return find_all_possible_paths(matrix, i, j)
+    return -1
+
+
+if __name__ == "__main__":
+    matrix = [
+        [START_POS, VALID_POS, VALID_POS],
+        [VALID_POS, VALID_POS, VALID_POS],
+        [END_POS, VALID_POS, VALID_POS],
+        [OBSTACLE_POS, OBSTACLE_POS, OBSTACLE_POS],
+    ]
+
+    shortest_path_distance = helper(matrix)
+    print(shortest_path_distance)