Project Euler第2题代码结果异常求助：为何求和结果不符？

Let's break down why your original code gives an incorrect result, and why changing the condition accidentally gives the right answer (spoiler: it's a coincidence!).

First, Let's Walk Through Your Original Code #

Your code initializes a = b = 1, then builds a list i by appending a in each loop before updating a and b. Here's what happens step-by-step for the early terms:

• Start: a=1, b=1 → append 1 to i, then a=1, b=2
• Next loop: b=2 ≤ 4000000 → append 1 to i, then a=2, b=3
• Next loop: b=3 ≤4000000 → append 2 to i, then a=3, b=5
• ... and so on.

The critical problem comes at the end of the sequence:
When a=2178309 and b=3524578 (which is ≤4000000), your code appends 2178309 to i, then updates a=3524578 and b=5702887 (which is >4000000). The loop stops here, so the value 3524578 (a valid even Fibonacci number ≤4000000) never gets added to your list i.

That's why your original sum of even terms is 1089154—it's missing the largest even term 3524578. Adding that term gives the correct total: 1089154 + 3524578 = 4613732.

Why Changing the Condition Gave the Correct Answer (By Coincidence!) #

When you changed the filter to x % 2 (keep odd terms), you calculated the sum of all odd terms in your incomplete list i. Let's do the math:

• The sum of all Fibonacci terms ≤4000000 is 9227464 (this follows from the Fibonacci property: sum of first n terms = F(n+2)-1).
• The sum of your incomplete list i (all terms up to 2178309) is 5702886.
• Sum of odd terms in i = 5702886 - 1089154 = 4613732—which just happens to equal the sum of all even terms in the complete sequence. This is a coincidence, not a fix for your logic.

How to Fix Your Original Code #

To capture all valid Fibonacci terms ≤4000000, adjust your loop condition to check a instead of b, so you append each term before it's updated:

a = b = 1
i = []
while a <= 4000000:  # Check if current a is within the limit
    i.append(a)
    a, b = b, a + b
e = [x for x in i if not x % 2]
print(sum(e))

This will include 3524578 in your list i, and the sum will correctly output 4613732.

Alternatively, you can optimize the code to avoid building a list entirely (more efficient for large limits):

total = 0
a, b = 1, 2
while b <= 4000000:
    if b % 2 == 0:
        total += b
    a, b = b, a + b
print(total)

内容的提问来源于stack exchange，提问作者weakit