猜数字问题

前言

猜一个 1～31 的数字，若没猜中，电脑会说太大或太小，此时使用者可以继续猜。请问要猜中至少要几次。

这问题是二进位相当经典的问题。在这专案，将了解二分法，与二进位的概念。此外，也利用 Python 的 input 指令，来达成一个互动式程式。

研究與探索

1 猜骰子所踯出的点数

1.a 用 random 隨機產生數

使用 random 的 randomint 来模拟丢一颗骰子的情况。

In [1]:

import random 
ans = random.randint(1,6)
print(ans)

1

1.b 使用 input 來讓使用者輸入

让使用者输入一个数，再显示结果。

利用 input 取得使用者输入的数字

In [0]:

import random
ans = random.randint(1,6)
guess = input("Guess a number between 1 and 6: ")
print("Answer {}. Guesss: {}".format(ans,guess))

1.c 让使用者反覆猜测直到猜中才结束

使用 while 回圈让使用者反覆输入

但在比對答案時要記住將資料轉為 int

In [0]:

import random
ans = random.randint(1,6)
guess = int(input("Guess a number between 1 and 6: "))
while(guess != ans):
  guess = int(input("Wrong! Guess again! "))
print("Bingo!!! The Answer is {}.".format(ans))

1.d 显示猜测的次数。

请修改上述程式，增加计数器 guessTime 。让猜对时，显示次数。

In [0]:

import random
ans = random.randint(1,6)
guess = int(input("Guess a number between 1 and 6: "))
guessTime = 1
while(guess != ans):
  guess = int(input("Wrong! Guess again! "))
  guessTime += 1
print("Bingo!!! The Answer is {}. You used {} time(s).".format(ans,guessTime))

2 猜 1~31 内的数字，并显示太大或大小。

2.a 猜测后，判断太大或太小。

修正 1.d 猜骰子的程式，在 while 回圈内加入判断。数字范围先设定在 1~31

In [0]:

import random
ans = random.randint(1,31)
guess = int(input("Guess a number between 1 and 31: "))
guessTime = 1
while(guess != ans):
  if guess < ans:
    guess = int(input("Too Small! Guess again! "))
  else:
    guess = int(input("Too Large! Guess again! "))
  guessTime += 1
print("Bingo!!! The Answer is {}. You used {} time(s).".format(ans,guessTime))

2.b 猜测后，更新可能范围

修正 2.a 的程式。新增两个变数 lower, upper 来纪录最大最小范围。

当猜测后，更新可能值的范围。

In [0]:

import random
lower = 1
upper = 31
ans = random.randint(lower, upper)
guess = int(input("Guess a number between {} and {}: ".format(lower,upper)))
guessTime = 1
while(guess != ans):
  if guess < ans:
    lower = guess + 1
    guess = int(input("Too small! Guess a number between {} and {}: ".format(lower,upper)))
  else:
    upper = guess - 1
    guess = int(input("Too Large! Guess a number between {} and {}: ".format(lower,upper)))
  guessTime += 1
print("Bingo!!! The Answer is {}. You used {} time(s).".format(ans,guessTime))

2.c 错误输入的侦测

在上述程式，使用者若输入不在范围内的程式仍可执行。

请修正程式让程式提出紧告，只能显示在范围内的数。

In [0]:

import random
lower = 1
upper = 31
ans = int(random.randint(lower, upper))
guess = int(input("Guess a number between {} and {}: ".format(lower,upper)))
guessTime = 1
while(guess != ans):
  if  lower <= guess and  guess <= upper:
    if guess < ans:
      lower = guess + 1
      guess = int(input("Too small! Guess a number between {} and {}: ".format(lower,upper)))
    else:
      upper = guess - 1
      guess = int(input("Too Large! Guess a number between {} and {}: ".format(lower,upper)))
    guessTime += 1
  else:
    guess = int(input("Error! Guess a number between {} and {}: ".format(lower,upper)))b
print("Bingo!!! The Answer is {}. You used {} time(s).".format(ans,guessTime))

2.d 答案会动态调整

程式能动态给答案，让使用者用最多次输出

In [1]:

import random#設立一個random
lower = 1
upper = 31
guess = int(input("Guess a number : "))
guessTime = 1
while(lower != upper):
    if guess-lower < upper-guess:
      lower = guess+1
      guess = int(input("Too small! Guess a number between {} and {} : ".format(lower,upper)))
    else:
      upper = guess-1
      guess = int(input("Too Large! Guess a number between {} and {} : ".format(lower,upper)))
    guessTime += 1
print("Bingo!!! The Answer is {}. You used {} time(s).".format(ans,guessTime))

Guess a number : 

補充資料

In [0]: