骑士巡游问题 python

# -*- coding: utf-8 -*-import numpy as npdef printP():    global n    global pieces    for i in range(n):        for j in range(n):            print "%d\t"%pieces[i][j],        print ""def init():    '''    初始化棋盘    '''    global n    global pieces    global point #用于记录剩余的点    pieces = [([0]*100)for j in range(100)]    pieces = np.array(pieces)        point = []    for i in range(n):        for j in range(n):            point.append((i,j))def checkXY(x,y):    '''    检查点（x,y）是否在棋盘上    '''    global n    if x>=0 and x<n and y>=0 and y<n:        return True    return False        def out1(x,y):    '''    找出所有方向（包括已经被走过的点）    '''    global n    global pieces    global direction    outLine1 = []    for i in range(8):        x1 = x+direction[i][0]        y1 = y+direction[i][1]        if checkXY(x1,y1):            outLine1.append((x1,y1))    return outLine1def out(x,y):    '''    找出所有可能走的路径    '''    outLine1 = out1(x,y)    outLine = []    for item in outLine1:        if pieces[item[0]][item[1]]==0:            outLine.append(item)    return outLinedef check1():    '''    剪枝1： 判断初始点各个方向上的点是否已经全走过    '''    global point    global direction    global x0    global y0        for i in range(8):        x1 = x0+direction[i][0]        y1 = y0+direction[i][1]        if checkXY(x1,y1):            if (x1,y1) in point:                return True    return Falsedef check2(x,y):    '''    判断剩余点中是否存在孤立点    '''    global point        for p in point:        if p[0]==x and p[1]==y:            continue        if len(out(p[0],p[1]))<1:            return True    return True            def play(x,y,k):    global n    global x0,y0    global succ    global point        pieces[x][y] = k        point.remove((x,y))    if k==n*n:#找到一条巡游路径        if (x0,y0) in out1(x,y):#判断能否回到初始点            succ = True        return       k += 1    outLine = out(x,y)    l = len(outLine)    if l == 0:#该点没有出路回溯        return    else:        outDic=dict()        for item in outLine:            outDic[item] = len(out(item[0],item[1]))        #按出路从小到达排序        outDic = sorted(outDic.iteritems(),key=lambda d:d[1], reverse = False)                for item in outDic:            if check1()==False:                continue            if check2(x,y)==False:                continue            play(item[0][0],item[0][1],k)            if succ:#如果已经找到则跳出循环                break            pieces[item[0][0],item[0][1]]=0#还原步骤，继续搜索            point.append((item[0][0],item[0][1]))        return#搜索不到则回溯if __name__=="__main__":    pieces = []#记录巡游顺序    point = []#记录剩余的点    direction = [(2,1),(2,-1),(-2,1),(-2,-1),(1,2),(1,-2),(-1,2),(-1,-2)]#八个方向    succ = False        n = 8 #棋盘维n*n维        #起始点    x0 = 1    y0 = 1        '''    #控制台输入    while checkXY(x0,y0)==False:        print "左上角坐标为（0,0）"        n = int(raw_input("n:").strip())        x0 = int(raw_input("x0:").strip())        y0 = int(raw_input("y0:").strip())    '''    print "n:",n    print "起始点:(%d,%d)\n"%(x0,y0)    init()#初始化    play(x0,y0,1)#开始巡游        if succ:        print "找到一条巡游路径"        printP()    else:        print "不存在巡游路径"