骑士的最少移动次数
Minimum Knight Moves
题目详情
问题：骑士的最少移动次数
考察：广度优先搜索
来源：DSA Prep / Citadel
链接：https://leetcode.com/problems/minimum-knight-moves
英文原题
Problem: Minimum Knight Moves
Patterns: Breadth-First Search
Recency: 2yr
Link: https://leetcode.com/problems/minimum-knight-moves
Source: https://www.dsaprep.dev/blog/citadel-coding-interview-questions/
解析
思路：棋盘关于坐标轴和对角线对称，可把目标转到第一象限。用 BFS 从 (0,0) 搜索，限制到目标附近的合理边界；也可用数学递推处理大坐标。
复杂度：BFS 状态数与目标距离平方相关；常见约束下可接受，空间同状态数。
英文解析
Approach: Use symmetry to move the target into the first quadrant, then run BFS from `(0,0)` with a bounded search region slightly beyond the target. Each BFS layer is one knight move, so the first visit to the target is optimal.
Complexity: Time and space are proportional to the number of visited board states.