Approach金麟年会520

本文目录导读：

1. Solution Code
2. Explanation

To solve this problem, we need to write a Python function that calculates the factorial of a given positive integer ( n ). The factorial of a number ( n ) (denoted as ( n! )) is the product of all positive integers from 1 to ( n ). For example, the factorial of 5 (written as 5!) is 5 × 4 × 3 × 2 × 1, which equals 120. The approach to solve this problem involves using an iterative method to compute the factorial. This method is chosen for its efficiency and to avoid potential issues with recursion depth, especially for large values of ( n ). Here's the step-by-step approach:

1. Handle Edge Cases:

   • If ( n ) is 0, return 1 because ( 0! ) is defined as 1.
   • If ( n ) is negative, return 0 as factorials are not defined for negative numbers in this context.

2. Iterative Calculation:

   • Initialize a variable result to 1.
   • Loop from 2 to ( n ) (inclusive), multiplying result by each integer in this range.
   • This loop effectively computes the product of all integers from 1 to ( n ).

Solution Code

def factorial(n):
    if n < 0:
        return 0
    if n == 0:
        return 1
    result = 1
    for i in range(2, n + 1):
        result *= i
    return result

Explanation

• Edge Cases Handling: The function first checks if ( n ) is negative and returns 0, as factorials are not defined for negative numbers. If ( n ) is 0, it returns 1 immediately.
• Iterative Calculation: For positive ( n ), the function initializes result to 1. It then iterates from 2 to ( n ), multiplying result by each integer in this range. This efficiently computes the product of all integers from 1 to ( n ), giving the factorial of ( n ).

This approach ensures that we handle all valid inputs correctly and efficiently compute the factorial using an iterative method, which is both time and space efficient.