Knight's Tours of an 8 8 Chessboard
نویسنده
چکیده
We describe a computation that determined the number of knight's tours of a standard chessboard. We also verify Knuth's count of tours with a symmetry.
منابع مشابه
How good is the Warnsdorff's knight's tour heuristic?
Warnsdorff's rule for a knight's tour is a heuristic, i.e., it's a rule that does not produce the desired result all the time. It is a classic example of a greedy method in that it is based on a series of locally optimal choices. This note describes an analysis that determines how good the heuristic is on an 8 X 8 chessboard. The order of appearance in a permutation of the eight possible moves ...
متن کاملThe Theory of Zero-Suppressed BDDs and the Number of Knight's Tours
Zero{suppressed binary decision diagrams (ZBDDs) have been introduced by Minato ((14] { 17]) who presents applications for cube set representations, fault simulation , timing analysis and the n{queens{problem. Here the structural properties of ZBDDs are worked out and a generic synthesis algorithm is presented and analyzed. It is proved that ZBDDs can be at most by a factor n + 1 smaller or lar...
متن کاملAn Efficient Algorithm for the Knight's Tour Problem
A knight’s tour is a series of moves made by a knight visiting every square of an n x n chessboard exactly once. The knight’s tour problem is the problem of constructing such a tour, given n. A knight’s tour is called closed if the last square visited is also reachable from the first square by a knight’s move, and open otherwise. Define the knight’s graph for an n x n chessboard to be the graph...
متن کاملThe Theory of Zero - Suppressed
| Zero{suppressed binary decision diagrams (ZBDDs) have been introduced by Minato in 14]{{17]. Here the structural properties of ZBDDs are worked out and a generic synthesis algorithm is presented and analyzed. It is proved that ZBDDs can be at most by a factor n+1 smaller or larger than ordered BDDs (OBDDs) for the same function on n variables. Using ZBDDs the best known bounds on the number o...
متن کاملWhich Chessboards have a Closed Knight's Tour within the Cube?
A closed knight’s tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n × n boards that form the cube. The ot...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010