巧用Hint

一般计算fibonacci的方法：

def fibonacci (n):
    if n == 0 or n == 1:
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)

这样的 call graph for fibonacci with n=4:

当计算 fibonacci(30)的时候还可以，当计算 fibonacci(50)的时候就很慢了。

好的方法是：用dict记录下来之前计算过的值。

A previously computed value that is stored for later use is called a hint.

好的方法是：

previous = {0:1, 1:1}
def fibonacci(n):if previous.has_key(n):return previous[n]else:newValue = fibonacci(n-1) + fibonacci(n-2)previous[n] = newValuereturn newValue

这样就很快了。

 

类似的计算阶乘：

previous = {1:1,2:2}
def n(i):if previous.has_key(i):return previous[i]else:newValue = i*n(i-1)previous[i] = newValuereturn previous[i]

---How to Think Like a Computer Scientist（Learning with Python）