Question

我写了一个简单的猜谜游戏和猜测它的方法......

    from gasp import *

    number = random_between(1, 1000)
    guesses = 0

    while True:
        guess = input("Guess the number between 1 and 1000: ")
        guesses += 1
        if guess > number:
            print "Too high!"
        elif guess < number:
            print "Too low!"
        else:
            print "\n\nCongratulations, you got it in %d guesses!\n\n" % guesses
            break

现在根据问题，如果使用正确的策略，最大猜测数应该等于11.我使用二进制搜索来获得正确的数字，但是猜测的数量绝不会超过10.检查我做了以下操作，它产生了一个非终止循环。

    from gasp import *


    guesses = 0
    big = 1000
    small = 1
    while guesses != 11
        number = random_between(1, 1000)
        while True:
            guess = (big + small) / 2
            guesses += 1
            if guess > number:
                print "Too high!"
                big = guess
            elif guess < number:
                print "Too low!"
                small = guess
            else:
                print "\n\nCongratulations, you got it in %d guesses!\n\n" % guesses
                break

所以谁是对的，我犯了一些错误或所需的猜测次数不能超过10次，问题是错误的。

Answer 1

>>> from math import log, ceil
>>> ceil(log(1000, 2))
10.0

Answer 2

让我们看看：

A number between 1 and  1 requires 1 guess
A number between 1 and  3 requires 2 guesses at most
A number between 1 and  7 requires 3 guesses at most
A number between 1 and 15 requires 4 guesses at most
A number between 1 and 31 requires 5 guesses at most
...

换句话说，n猜测足以覆盖从1到(2**n)-1的范围。

对于n=10，此范围是1到1023。自1023 >= 1000以来，您对十个猜测的结论是正确的。

也就是说，您用来验证此结论的代码是错误的，因为每当您转到下一个数字时，它都无法重新初始化big和small以及guesses。此外，您可以只测试1到1000之间的每个数字，而不是随机生成数字，并使用具有有限运行时间的确定性算法。

执行二进制搜索以猜测随机数，但猜测的数量不匹配

2 个答案: