python基础练习

• 兔子问题
  内容：1个兔子，1个月后变3个，n月有几个
  公式 3^(n-i)

def rabbit_sum(m):
    sum = 0
    for i in range(1, m+1):
         sum += 3**(m-i)
    return sum

• 青蛙上台阶
  内容：当n = 1， 只有1中跳法；当n = 2时，有两种跳法；当n = 3 时，有3种跳法；当n = 4时，有5种跳法；当n = 5时，有8种跳法

def frog(n):
     if n == 1:
          return 1
     elif n == 2:
           return 2
     else:
           return frog(n-2) + frog(n-1)

回溯算法：

cout = 0
def dfs(cout, target):
      global cout
      if target <= 2:
           cout += target
            return
       dfs(cout, target-1)
       dfs(cout, target-2)

dfs(cout, 4)

• 三门问题
  内容：概率问题，三个门后有一个有car，你指定开一个门，主持人会吧一个有goat的门打开，求你要不要换开剩下的门

from random import choice
def switch():
     doors = ['car', 'goat', 'goat']
     choose = choice(doors)
     doors.remove(choose)
     doors.remove('goat')
     if doors == ['car']:
         return 'win'
     else:
          return 'failed'

def stay():
     doors = ['car', 'goat', 'goat']
     choose = choice(doors)
     if choose == 'car':
          return 'win'
     else:
          retuen 'failed'

if __name__ == "__main__"：
     total = 1000
     switch_sum, stay_num, win_switch, win_stay = 0, 0, 0, 0
     for i in range(total):
          choose = choice([1, 2])
          #1 switch
          if choose == 1:
               switch_num += 1
               if switch() == 'win':
                   win_switch += 1
          else:
               stay_num += 1
               if stay() == 'win':
                   win_stay += 1
      print float(stay_win)/stay_num, float(win_switch)/switch_num