Knights_Problem.py

from pythonds.graphs import Graph, Vertex

def genLegalMoves(x,y,bdSize):
    newMoves = []
    moveOffsets = [(-1,-2),(-1,2),(-2,-1),(-2,1),
                   ( 1,-2),( 1,2),( 2,-1),( 2,1)]
    for i in moveOffsets:
        newX = x + i[0]
        newY = y + i[1]
        if legalCoord(newX,bdSize) and legalCoord(newY,bdSize):
            newMoves.append((newX,newY))
    return newMoves

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


def knightGraph(bdSize):
    ktGraph = Graph()
    for row in range(bdSize):
       for col in range(bdSize):
           nodeId = posToNodeId(row,col,bdSize)
           newPositions = genLegalMoves(row,col,bdSize)
           for e in newPositions:
               nid = posToNodeId(e[0],e[1],bdSize)
               ktGraph.addEdge(nodeId,nid)
    return ktGraph

def posToNodeId(row, column, board_size):
    return (row * board_size) + column


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 = c + 1
            resList.append((c,v))
    resList.sort(key=lambda x: x[0])
    #resList.reverse()
    return [y[1] for y in resList]

def knightTour(n,path,u,limit):
        u.setColor('gray')
        path.append(u)
        if n < limit:
            nbrList = orderByAvail(u)
            i = 0
            done = False
            while i < len(nbrList) and not done:
                if nbrList[i].getColor() == 'white':
                    done = knightTour(n+1, path, nbrList[i], limit)
                i = i + 1
            if not done:  # prepare to backtrack
                path.pop()
                u.setColor('white')
        else:
            done = True
        return done


Board_Size=8
K=knightGraph(Board_Size)
pos=posToNodeId(0, 4, Board_Size) #Starting_Cell_X, Starting_Cell_Y
way=[]
knightTour(0, way, K.getVertex(pos), Board_Size**2-1)
for x in way:
    print(x.getId())