Minimum Knight Steps on an Infinite Board

### Problem A knight starts at (0,0) on an infinite board. Each step changes the coordinates by (±2,±1) or (±1,±2). Return the minimum steps to (x,y). The target is guaranteed reachable. ```cpp class Solution { public: int minKnightMoves(int x, int y); }; ``` ### Examples **Example 1:** ```text Input: x = 1, y = 0 Output: 3 Explanation: One route is(0,0),(2,1),(0,2),(1,0). One move cannot reach the target, and two moves have even coordinate-sum parity, unlike the target. ``` **Example 2:** ```text Input: x = 0, y = 0 Output: 0 Explanation: The knight already occupies the target. ``` ### Constraints - Both target coordinates are integers in `[-300,300]`. - `0 <= abs(x)+abs(y) <= 300`. - The target is reachable on the infinite board. ### Contract considerations The board is infinite; the numeric bounds limit the target, not permissible intermediate cells. ```hint Read the boundary condition Must intermediate squares obey the target's numeric bounds, or only the knight's movement rules? ``` ### Boundary reminders The board is infinite; the numeric bounds limit the target, not permissible intermediate cells.