hw9-fig - CS 325 Due Fri 3 Dec Homework#9 The Knights Tour...

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CS 325 Due: Fri 3 Dec Homework #9 The Knight’s Tour Problem A knight is a chesspiece which can legally move from a square ( i, j ) on a chessboard (where i is the row index, and j is the column index) to any of the eight squares ( i - 1 , j - 2) , ( i - 1 , j + 2) , ( i + 1 , j - 2) , ( i + 1 , j + 2) , ( i - 2 , j - 1) , ( i - 2 , j + 1) , ( i + 2 , j - 1) , ( i + 2 , j + 1), as long as they are on the chessboard. You are interested in finding knight’s tours of various n × m gameboards. A knight’s tour is a sequence of squares from the gameboard so that each square appears exactly once in the sequence, and each square is a legal knight’s move from its previous square. A tour is closed if there is a legal knight’s move from the last square of the sequence back to the first square. Otherwise, the tour is open. You will study a heuristic for this problem. A heuristic (without backtracking) will usually find a tour, but may occasionally fail to find a tour. Given a partial tour, you will try to lengthen the tour by adding the next possible square with lowest degree. A square is possible if it is not already in the partial
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