Python 字典 setdefault() 方法用作递归 function 的返回值

Question

Say you want to get the nth Fibonacci Number. Then, one possibility is to use the recursive function

def Fib(n, d):
    """Assumes n is an int >= 0, d dictionary
    Returns nth Fibonacci number"""
    if n in d:
        return d[n]
    else:
        d[n] = Fib(n-1, d) + Fib(n-2, d)
        return d[n]

This works quite well. I tried to shorten this to

 def Fib(n, d):
        return d.setdefault(n, Fib(n-1, d) + Fib(n-2, d))

But when I can call it with

d={0:1, 1:1}
print(f(2, d))

, or even with f(1,d), it goes into infinite loop, and restarts the kernel. In fact, any function of this form, say

def f(n, d):
    return d.setdefault(n, f(n-1,d))

has the same problem. When I tried to debug this, I saw that n keeps decreasing pass the value 1. I guess I don't understand the implementation of this method. I presumed that the setdefault method first checks whether the key is in the dictionary and returns the value, and if not, then assigns the default value to the key and returns the default value. What am I missing here?(I am using Python 3.9.1 with Spyder 4.2.0)

Answer 1

You still need a base case otherwise there's nothing to stop it from calculating, fib(-1) , fib(-2) , fib(-99) , ...

def fib(n, d):
  return n if n < 2 else d.setdefault(n, fib(n-1, d) + fib(n-2, d))

print(fib(10, {0:0, 1:1}))

55

The problem you are experiencing with setdefault is that python is an applicative order language. That means a functions arguments are evaluated before a the function is called. In the case of setdefault , we will evaluate fib(n-1,d) + fib(n-2,d) before we attempt to lookup n in d .

A better interface might be dict.setdefault(key, lambda: somevalue) where the lambda is executed only if the default needs to be set. We could write this as lazydefault below -

def lazydefault(d, key, lazyvalue):
  if key not in d:
    d[key] = lazyvalue()
  return d[key]

def fib(n, d):
  return lazydefault(d, n, lambda: fib(n-1, d) + fib(n-2, d))

print(fib(10, {0:0, 1:1}))

55