Compute Minimum L-Moves on Infinite Grid
Problem Description
On an infinite 2D grid, a chess-like piece moves in L-shapes: from (x, y) it can go to (x±1, y±2) or (x±2, y±1).
Given integer target coordinates (tx, ty) with absolute values |tx|, |ty| ≤ 1e9, implement a function minLMoves(tx, ty) that returns the minimum number of moves needed to reach (tx, ty) starting from (0, 0).
Requirements
- Exploit symmetry to optimize your solution.
- Handle edge cases carefully.
- Explain your algorithm.
- Prove correctness intuitively.
- Analyze time and space complexity.
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Core dilemma
The central engineering conflict is finding the shortest path on an effectively infinite 2D grid with extremely large target coordinates (up to 1e9). This requires transforming a seemingly graph-search problem (BFS) into a mathematical or pattern-based solution, leveraging symmetry and number theory, rather than a direct state-space exploration.
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Compute Minimum L-Moves on Infinite Grid
Problem Description
On an infinite 2D grid, a chess-like piece moves in L-shapes: from (x, y) it can go to (x±1, y±2) or (x±2, y±1).
Given integer target coordinates (tx, ty) with absolute values |tx|, |ty| ≤ 1e9, implement a function minLMoves(tx, ty) that returns the minimum number of moves needed to reach (tx, ty) starting from (0, 0).
Requirements
- Exploit symmetry to optimize your solution.
- Handle edge cases carefully.
- Explain your algorithm.
- Prove correctness intuitively.
- Analyze time and space complexity.