python学习 2数学公式

• 递归

def fact(n):
	if n <= 1:
		return 1
	else:
	  return n * fact(n - 1)

• 斐波那契数列: 第0项是0，第1项是1,从第2项开始，每一项都等于前两项之和

def fib(n):
  i = 2
  arr = [0, 1]
  while n > 2:
    arr.append(arr[i - 1] + arr[i - 2])
    n -= 1
    i += 1
  return arr

//
MemoTable = {}

def MemoizedFib(n):
    if n <= 2:
        return 1

    if n in MemoTable:
        return MemoTable[n]

    MemoTable[n] = MemoizedFib(n-1) + MemoizedFib(n-2)
    return MemoTable[n]

• 利用牛顿迭代法求平方根

def sqrt(x):
    def average(a, b):
        return (a + b) / 2.0

    def is_good_enough(guess):
        return (abs((guess * guess) - x) < 0.001)

    def improve(guess):
        return average(guess, x / guess)

    def sqrt_iter(guess):
        if is_good_enough(guess):
            return guess
        else:
            return sqrt_iter(improve(guess))

    return sqrt_iter(1.0)

• 求最大公约等数

def gcd(x, y):
    result = x
    if y != 0:
        result = gcd(y, x % y)
    return result

• 汉诺塔

def TowerOfHanoi(n, a, b, tmp):
    if n == 1:
        b.append(a.pop())
    else:
        TowerOfHanoi(n-1, a, tmp, b)
        b.append(a.pop())
        TowerOfHanoi(n-1, tmp, b, a)

stack1 = [4,3,2,1]
stack2 = []
stack3 = []

TowerOfHanoi(len(stack1), stack1, stack3, stack2)

• list map

def map(func, lst):
  if lst == []:
    return []
  else:
    return [func(lst[0])] + map(func, lst[1:])

def halveElements(lst):
    return map(lambda x: x / 2.0, lst)

input = [2, 4, 6, 8, 10]
output = halveElements(input)

• 求平方和

def summation(low, high, f, next):
    s = 0
    x = low
    while x <= high:
        s = s + f(x)
        x = next(x)
    return s

def sumsquares(low, high):
    return summation(low, high, lambda x: x**2, lambda x: x+1)