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骑士周游问题

取一块国际象棋棋盘和一颗骑士棋子（马）。目标是找到一系列走法，使得骑士对棋
盘上的每一格刚好都只访问一次。这样的一个移动序列被称为“周游路径”

1.构建骑士周游图

from myGraph import Graph


def knightGraph(bdsize):
    g = Graph()
    for row in range(bdsize):
        for col in range(bdsize):
            nodeId = posToNodeId(row, col, bdsize)
            newPositions = genLegalMoves(row, col, bdsize)
            for i in newPositions:
                newid = posToNodeId(i[0], i[1], bdsize)
                g.addEdge(nodeId, newid)
    return g

def genLegalMoves(row, col, bdsize):
    newmoves = []
    moveOffsets = [(-1, -2), (-1, 2), (-2, -1), (-2, 1), (1, -2), (1, 2), (2, -1), (2, 1)]
    for i in moveOffsets:
        newrow = row + i[0]
        newcol = col + i[1]
        if legalCoord(newrow, bdsize) and legalCoord(newcol, bdsize):
            newmoves.append((newrow, newcol))
    return newmoves


def legalCoord(x, bdsize):
    if x >= 0 and x < bdsize:
        return True
    else:
        return False


def posToNodeId(row, col, bdsize):
    return row * bdsize + col

2.实现骑士周游

def knightTour(n, path, u, limit):
    u.setColor('Gray')
    path.append(u)
    done = False
    if n < limit:
        nbrList = list(orderByAvail(u))
        i = 0
        while i < len(nbrList) and not done:
            if nbrList[i].color == 'White':
                done = knightTour(n+1, path, nbrList[i], limit)
            i += 1
        if not done:
            path.pop()
            u.setColor('White')

    else:
        done = True
    return done

def orderByAvail(n):
    resList = []
    for v in n.getConnections():
        if v.getColor() == 'White':
            c = 0
            for w in v.getConnections():
                if w.getColor() == 'White':
                    c += 1
            resList.append((c, v))
    resList.sort(key=lambda x: x[0])
    return [y[1] for y in resList]


if __name__ == '__main__':
    g = knightGraph(8)
    path = []
    startVertex = g.getVertex(4)
    knightTour(0, path, startVertex, 63)
    for i in path:
        print(i.getId(), end=' ')

输出：

4 14 31 46 63 53 47 62 52 58 48 33 16 1 11 5 15 21 6 23 38 55 61 51 57 40 50 56 41 24 9 3 13 7 22 39 54 60 45 30 36 26 20 37 43 28 18 8 2 12 29 35 25 19 34 44 59 49 32 42 27 17 0 10