V2EX chessboard distance

Chessboard Distance

释义 Definition

chessboard distance(棋盘距离):在方格网/棋盘上两点之间的一种距离度量,通常指切比雪夫距离(Chebyshev distance),即在横纵坐标差中取最大值:
\[ d=\max(|\Delta x|,|\Delta y|) \]
它也常被理解为国际象棋中“王(king)”从一格走到另一格所需的最少步数(因为王可以横、竖、斜走)。

发音 Pronunciation (IPA)

/tesbrd dstns/

词源 Etymology

“chessboard”来自“chess(国际象棋)+ board(棋盘)”,表示方格棋盘;“distance”表示距离。该短语用于描述像棋盘格点那样的离散平面上的距离概念,因其与棋子(尤其是“王”)的走法直观对应而得名。在数学与计算机科学中,它通常与“Chebyshev distance(切比雪夫距离)”同义使用。

例句 Examples

The chessboard distance between (2, 3) and (5, 7) is 4.
点 (2, 3) 和 (5, 7) 的棋盘距离是 4。

We used chessboard distance to estimate how many king moves it would take to reach the target square on the grid.
我们用棋盘距离来估计在网格上到达目标格子需要走多少步“王”的步数。

相关词 Related Words

文学与著名作品 Notable Works

  • Introduction to Algorithms(Cormen, Leiserson, Rivest, Stein):在算法与几何/网格问题语境中常讨论不同距离度量(包括与切比雪夫距离相关的“棋盘距离”概念)。
  • Artificial Intelligence: A Modern Approach(Russell & Norvig):在搜索、路径规划与启发式函数(heuristics)的背景下会涉及网格上的距离度量(常与“王步数/切比雪夫距离”类比)。
  • Pattern Recognition and Machine Learning(Christopher M. Bishop):在距离度量与特征空间的讨论中会提到多种“距离/范数”,其中包含与切比雪夫距离同一思想体系的内容。
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