python实现：无刻度的一大一小水罐取水问题

问题描述：You have two jugs: a A-gallon jug and a B-gallon jug ( A > B ). Neither of the jugs have markings on them. There is a pump that can be used to fill the jugs with water. How can you get exactly C gallons of water in the A-gallon jug? Suppose the B <= C <= A and they are integer.
算法实现：

def jar(large_size, small_size, want, jar_large=0, jar_small=0, round=1):
    """
    large_size: 大罐的容积
    small_size: 小罐的容积
    want: 希望最终取到的水的体积
    jar_large: 此时大罐中的水的体积
    jar_small: 此时小罐中的水的体积
    round: 进行了多少轮取水
    """
    print('round:%s' % round)
    # 若大罐尺寸和小罐头线性相关，
    # 除非want和他们俩也线性相关，
    # 否则不可能完成
    if large_size % small_size == 0 and \
       large % want != 0 and \
       small_size != 1:
        return False
    # 如果want是小罐容量的倍数，
    # 且小于大罐容量，则进行want/small_size次就可以完成
    if want % 3 == 0 and want < large_size:
        return want, 0
    # 基本情况（base case）
    if jar_large == want:
        return jar_large, jar_small
    elif jar_small == want:
        jar_large = jar_small
        jar_small = 0
        return jar_large, jar_small
    # 正常递归程序（normal process）
    # 如果大罐为空，将大罐灌满
    elif jar_large == 0:
        jar_display(large_size, jar_small)
        return jar(large_size, small_size, want,
                   large_size, jar_small, round+1)
    # 如果大罐中的水大于小罐的最大容量
    # 用大罐将小罐灌满，然后将小罐倒空
    elif jar_large > small_size:
        jar_display(jar_large-small_size+jar_small, 0)
        return jar(large_size, small_size, want,
                   jar_large-small_size+jar_small, 0, round+1)
    # 否则，大罐中的水少于小罐容量，
    # 将大罐中的水倒入小罐
    else:
        jar_display(0, jar_large)
        return jar(large_size, small_size, want,
                   0, jar_large, round+1)

def jar_display(jar_large, jar_small):
    print('------------------')
    print('large:%s\nsmall:%s' % (jar_large, jar_small))
    print('------------------')

程序测试代码：

def main():
    large_size = 10
    small_size = 3
    for i in range(1, large_size+1):
        jarLarge, jarSmall = jar(large_size, small_size, i)
        print('finished:\nlarge:%s\nsmall:%s' % (jarLarge, jarSmall))

main()