Added (Open) Knight Tour Algorithm (#2132)

* Added (Open) Knight Tour Algorithm

* Implemented Suggestions

backtracking/knight_tour.py

@@ -0,0 +1,98 @@
+# Knight Tour Intro: https://www.youtube.com/watch?v=ab_dY3dZFHM
+
+from typing import List, Tuple
+
+
+def get_valid_pos(position: Tuple[int], n: int) -> List[Tuple[int]]:
+    '''
+    Find all the valid positions a knight can move to from the current position.
+
+    >>> get_valid_pos((1, 3), 4)
+    [(2, 1), (0, 1), (3, 2)]
+    '''
+
+    y, x = position
+    positions = [
+        (y + 1, x + 2),
+        (y - 1, x + 2),
+        (y + 1, x - 2),
+        (y - 1, x - 2),
+        (y + 2, x + 1),
+        (y + 2, x - 1),
+        (y - 2, x + 1),
+        (y - 2, x - 1)
+    ]
+    permissible_positions = []
+
+    for position in positions:
+        y_test, x_test = position
+        if 0 <= y_test < n and 0 <= x_test < n:
+            permissible_positions.append(position)
+
+    return permissible_positions
+
+
+def is_complete(board: List[List[int]]) -> bool:
+    '''
+    Check if the board (matrix) has been completely filled with non-zero values.
+
+    >>> is_complete([[1]])
+    True
+
+    >>> is_complete([[1, 2], [3, 0]])
+    False
+    '''
+
+    return not any(elem == 0 for row in board for elem in row)
+
+
+def open_knight_tour_helper(board: List[List[int]], pos: Tuple[int], curr: int) -> bool:
+    '''
+    Helper function to solve knight tour problem.
+    '''
+
+    if is_complete(board):
+        return True
+
+    for position in get_valid_pos(pos, len(board)):
+        y, x = position
+
+        if board[y][x] == 0:
+            board[y][x] = curr + 1
+            if open_knight_tour_helper(board, position, curr + 1):
+                return True
+            board[y][x] = 0
+
+    return False
+
+
+def open_knight_tour(n: int) -> List[List[int]]:
+    '''
+    Find the solution for the knight tour problem for a board of size n. Raises
+    ValueError if the tour cannot be performed for the given size.
+
+    >>> open_knight_tour(1)
+    [[1]]
+
+    >>> open_knight_tour(2)
+    Traceback (most recent call last):
+    ...
+    ValueError: Open Kight Tour cannot be performed on a board of size 2
+    '''
+
+    board = [[0 for i in range(n)] for j in range(n)]
+
+    for i in range(n):
+        for j in range(n):
+            board[i][j] = 1
+            if open_knight_tour_helper(board, (i, j), 1):
+                return board
+            board[i][j] = 0
+
+    raise ValueError(f"Open Kight Tour cannot be performed on a board of size {n}")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()