Problem 1: Factorial (100pts)

Problem

Write a function that takes a non-negative integer \(n \ge 0\) and returns its factorial.

Factorial of \(n\) is defined as

\[n!=\prod_{i=1}^ni=1\times2\times3\times\cdots\times n.\]

编写一个函数，接受一个非负整数 \(n \ge 0\)，并返回它的阶乘。

\(n\) 的阶乘定义为：

\[n!=\prod_{i=1}^ni=1\times2\times3\times\cdots\times n.\]

def factorial(n):
    """Return the factorial of a non-negative integer n.

    >>> factorial(3)
    6
    >>> factorial(5)
    120
    """
    "*** YOUR CODE HERE ***"

Hints

Hint1: You may want to use a while loop to solve this problem. Be careful when to stop!

Hint2: What is the factorial of 0?

Hint3: Use return to return the result, don't print it. That's the correct way of defining a function.

• 你可能希望使用 while 循环来解决这个问题。注意何时停止循环！

• 0 的阶乘是多少？

• 使用 return 来返回结果，不要 print 它。这是定义函数的正确方式。

• while 循环可以解决这个问题，递归也可以。

Solutions

使用 while 循环：

def factorial(n):
    if n == 0:
        return 1

    result = 1
    current_number = 1

    while current_number <= n:
        result *= current_number
        current_number += 1

    return result

---

使用 for 循环：

def factorial(n):
    if n == 0:
        return 1
    else:
        result = 1
        for i in range(1, n + 1):
            result *= i
        return result

---

递归：

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n - 1)