# Project Euler Problem 1

*August 28, 2011 / Mad Coding, CPython, Project Euler, Python*

Found out about Project Euler from my friend Shu Wu’s tweet. I figured I’ll also use it to help me learn Python and have fun solving problems. One of the cool things is that they give you an image to show off your progress. At the time of writing, I’ve solved 10 problems so far.

The first problem is: Add all the natural numbers below one thousand that are multiples of 3 or 5.

Below is my initial naive solution which ran fast enough for the small (999) limit. However, there are more efficient solutions.

```
import time
target = 999
start = time.time()
sum = 0
for i in range(3, target + 1, 3):
if i % 5 != 0:
sum += i
for i in range(5, target + 1, 5):
sum += i
end = time.time()
print sum, "took:", end - start
```

Looking at my friend Shu’s solution on GitHub exposed me to two things:

- using set() to eliminate duplicates
- combining two lists, as returned by range(), together using + operator

Using the set class makes his solution slightly faster than mine. If I’m not mistaken, a quick browse through the CPython set class source code reveals that it uses a dictionary underneath, and the dictionary is implemented in C using hashtable. So by using set(), one could eliminate the more expensive % operations done in the loop.

The fastest method (by orders of magnitude) which is shown on the problem overview on Project Euler requires one to make further observations about the problem to spot patterns. Always a good thing to do before jumping into the naive approach.

My naive solution: 0.000167846679688 seconds

Same naive solution with % operation taken out: 0.000125169754028 seconds

Shu’s solution: 0.0001540184021 seconds

Project Euler Overview solution: 4.05311584473e-06 seconds