A knight at position (r, c) can move in an L-shaped pattern to any of eight positions: moving over one row and up/down two columns to positions (r± 1, c±2), or moving two rows over and one column up/down to positions (r ±2, c ± 1). A rook at position (r, c) can move in a straight line either horizontally or vertically, moving any integral number x of squares. The rook ends up in positions (r±x, c) for a vertical move, or (r, c + x) for a horizontal move. Figure 5.13 A chess board, and the legal moves for a knight (left) or rook (right).
A knight at position (r, c) can move in an L-shaped pattern to any of eight positions: moving over one row and up/down two columns to positions (r± 1, c±2), or moving two rows over and one column up/down to positions (r ±2, c ± 1). A rook at position (r, c) can move in a straight line either horizontally or vertically, moving any integral number x of squares. The rook ends up in positions (r±x, c) for a vertical move, or (r, c + x) for a horizontal move. Figure 5.13 A chess board, and the legal moves for a knight (left) or rook (right).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
In chess, a walk for a particular piece is a sequence of legal moves for that piece, starting from a square of your choice, that visits every square of the board. A tour is a walk that visits every square only once. (See Figure 5.13.)
5.13 Prove by induction that there exists a knight’s walk of an n-by-n chessboard for any n ≥ 4. (It turns out that knight’s tours exist for all even n ≥ 6, but you don’t need to prove this fact.)
Transcribed Image Text:A knight at position (r, c) can move in an L-shaped pattern to any of eight
positions: moving over one row and up/down two columns to positions
(r± 1, c±2), or moving two rows over and one column up/down to
positions (r ±2, c ± 1).
A rook at position (r, c) can move in a straight line either horizontally or
vertically, moving any integral number x of squares. The rook ends up in
positions (r±x, c) for a vertical move, or (r, c + x) for a horizontal move.
Figure 5.13 A chess board, and the legal moves for a knight (left) or rook (right).
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