# 7.11. The Knight’s Tour Problem¶

Another classic problem that we can use to illustrate a second common
graph algorithm is called the knight’s tour. The knight’s
tour puzzle is played on a chess board with a single chess piece, the
knight. The object of the puzzle is to find a sequence of moves that
allow the knight to visit every square on the board exactly once. One
such sequence is called a *tour*. The knight’s tour puzzle has
fascinated chess players, mathematicians, and now, computer scientists,
for over a thousand years. The upper bound on the number of possible legal tours
for an \(8 \times 8\) chessboard is known to be
\(1.305 \times 10^{35}\); however, there are even more possible
dead ends. Clearly this is a problem that requires some real brains,
some real computing power, or both.

Although researchers have studied many different algorithms to solve the knight’s tour problem, a graph search is one of the easiest to understand and program. Once again we will solve the problem using two main steps:

Represent the legal moves of a knight on a chessboard as a graph.

Use a graph algorithm to find a path of length \(rows \times columns - 1\) where every vertex on the graph is visited exactly once.