# 1197. Minimum Knight Moves
In an infinite chess board with coordinates from -infinity to +infinity, you have a knight at square [0, 0].
A knight has 8 possible moves it can make, as illustrated below. Each move is two squares in a cardinal direction, then one square in an orthogonal direction.
Return the minimum number of steps needed to move the knight to the square [x, y]. It is guaranteed the answer exists.
Example 1:
Input: x = 2, y = 1
Output: 1
Explanation: [0, 0] → [2, 1]
Example 2:
Input: x = 5, y = 5
Output: 4
Explanation: [0, 0] → [2, 1] → [4, 2] → [3, 4] → [5, 5]
Constraints:
|x| + |y| <= 300
# Solution
Approach 1: BFS.
# Code (Python)
Approach 1:
def minKnightMoves(self, x: int, y: int) -> int:
# BFS -- optimized by pruning coordinates in the wrong directions
if x == 0 and y == 0:
return 0
queue = deque([(0, 0, 0)])
added = set([(0, 0)])
while queue:
position = queue.popleft()
for delta in [(1, 2), (2, 1), (2, -1), (1, -2), (-1, 2), (-2, 1), (-2, -1), (-1, -2)]:
new_x, new_y = position[0] + delta[0], position[1] + delta[1]
if new_x == x and new_y == y:
return position[2] + 1
if (new_x, new_y) in added:
continue
added.add((new_x, new_y))
if new_x * x < 0 or new_y * y < 0:
# about the right direction
continue
queue.append((new_x, new_y, position[2] + 1))
return -1
# Code (C++)
Approach 1:
Approach 2: