DEV Community

Project Euler #1 - Multiples of 3 and 5

Peter Kim Frank on June 11, 2018

I thought it would be fun to create a thread where the community could solve a problem from Project Euler. This is Problem #1: If we list all th...
Collapse
 
maxart2501 profile image
Massimo Artizzu • Edited

I'll take a mathematical approach.

The sum of the first n positive integers is n*(n + 1)/2. Multiply by k, and you get the sum of the first n multiples of k.

There are 333 multiples of 3 below 1000, and 199 multiples of 5, so we get 166833 and 99500, respectively. But we can't just sum them, as we'd count the multiples of 15 twice (15 is their least common multiple), so we have to subtract those once (total: 33165).

Result: 233168

In general, let's use JavaScript for example:

const limit = 1000;
const m = 3, n = 5;

const mulM = Math.floor((limit - 1) / m);
const mulN = Math.floor((limit - 1) / n);

const lcm = leastCommonMultiple(m, n);
const mulLcm = Math.floor((limit - 1) / lcm);

const result = m * mulM * (mulM + 1) / 2
  + n * mulN * (mulN + 1) / 2
  - lcm * mulLcm * (mulLcm + 1) / 2;
Enter fullscreen mode Exit fullscreen mode

There, no iterations, pure math 👍 And blazing fast

Using JavaScript's new support of BigInt, it's immediate even with huge numbers like 123456789012345678901234567890: it's 3556368375755728575115582031196717989244271707186887161545.

Collapse
 
nestedsoftware profile image
Nested Software

This is very clever and very nice!

Collapse
 
tttaaannnggg profile image
mari tang

yesss the Gaussian sum is such a good tool!

Collapse
 
pbouillon profile image
Pierre Bouillon

I did this in LOLCODE (first program that I'm writing with it, probably not the best implementation)

HAI 1.2
    CAN HAS STDIO?
    I HAS A GOAL ITZ 1000
    I HAS A TOTAL ITZ 0

    I HAS A VAR ITZ 0
    IM IN YR LOOP UPPIN YR VAR TIL BOTH SAEM VAR AN GOAL
        BOTH SAEM 0 AN MOD OF VAR AN 3
        O RLY?
            YA RLY
                TOTAL R SUM OF TOTAL AN VAR
            NO WAI
                BOTH SAEM 0 AN MOD OF VAR AN 5
                    O RLY?
                        YA RLY
                            TOTAL R SUM OF TOTAL AN VAR
                        OIC
        OIC 
    IM OUTTA YR LOOP

    VISIBLE TOTAL

KTHXBYE
Collapse
 
philnash profile image
Phil Nash

👏👏👏👏👏

Collapse
 
pbouillon profile image
Pierre Bouillon

You can try it here

Collapse
 
dance2die profile image
Sung M. Kim

Answer in C# using LINQ.

Enumerable
    .Range(1, 1000)
    .Where(i => i % 3 == 0 || i % 5 == 0)
    .Sum();

Explanation

  1. Enumerable.Range generates a number between 1 & 1000
  2. Where filters records that matches a condition (It's like filter in JS)
  3. Sum is a convenience method for summing up a sequence (instead of doing Aggregate((acc, n) => acc + n)), which is equivalent to reduce in JS)

Source & Tests on Github.

Collapse
 
thejoezack profile image
Joe Zack

short AND legible!

Collapse
 
dance2die profile image
Sung M. Kim

Thanks Joe :)

Collapse
 
philnash profile image
Phil Nash • Edited

Ruby

(1...1000).select { |n| n % 3 == 0 || n % 5 == 0 }.sum
# => 233168

JavaScript

It's a shame getting a range and a sum isn't quite as easy in JS.

Array.from(Array(1000).keys())
  .filter(n => n % 3 === 0 || n % 5 === 0)
  .reduce((acc, n) => acc + n);
// => 233168
Collapse
 
ndc profile image
NC • Edited

Or generate the range with the es6 spread operator:

[...Array(1000).keys()]
    .filter(n => n % 3 === 0 || n % 5 === 0)
    .reduce((acc, n) => acc + n)

There's also a nasty (but shorter) eval hack to use in place of reduce. You can use .join(+) to convert the array into a string containing each number joined by the '+' sign, then evaluate that string as if it's a JavaScript expression to get the sum:

eval([...Array(1000).keys()].filter(n => n % 3 === 0 || n % 5 === 0).join('+'))

It's a bad practice to use eval, of course, but useful for JS code golf.

Or with lodash:

_(_.range(1, 1000)).filter(n => n % 3 === 0 || n % 5 === 0).sum()
Collapse
 
matheus profile image
Matheus Calegaro • Edited

Here it is ¯\_(ツ)_/¯
I'm looking forward for feedbacks

let sum = 0,                                        
    i = 0

  for (i = 0; i < 1000; i++) {
    if (i % 3 === 0 || i % 5 === 0) sum += i
  }

console.log('The sum is %d', sum)
Collapse
 
gmartigny profile image
Guillaume Martigny

Smallest nitpicking ever: declare i inside the for loop.

for (let i = 0; i < 1000; i++)

It will prevent it from leaking outside the loop.

Collapse
 
jacobmgevans profile image
Jacob Evans

I wouldn't even call that nitpicking, that is solid best practice advice to avoid memory leaks.

Collapse
 
r0f1 profile image
Florian Rohrer

Python

print(sum(i for i in range(1001) if i % 3 == 0 or i % 5 == 0))
Collapse
 
r0f1 profile image
Florian Rohrer

For fun: A shorter solution.

sum({*range(3, 1000, 3)} | {*range(5, 1000, 5)})
Collapse
 
aswathm78 profile image
Aswath KNM

Great solution. Since I lost touch of python it was a little difficult. Now I understand.

Collapse
 
aspittel profile image
Ali Spittel
def sum_natural_numbers_below_n(n):
    # O(N) complexity
    mult_3 = range(3, n, 3)
    mult_5 = range(5, n, 5)
    all_multiples = set(mult_3 + mult_5)
    return sum(all_multiples)

print(sum_natural_numbers_below_n(1000))
Collapse
 
hanachin profile image
Seiei Miyagi

Ruby✨💎✨

require "set"

multiples_of_3 = Enumerator.new {|y| x = 0; y << x while x += 3 }
multiples_of_5 = Enumerator.new {|y| x = 0; y << x while x += 5 }

puts [multiples_of_3, multiples_of_5].each_with_object(Set.new) { |e, s|
  s.merge(e.take_while(&1000.method(:>)))
}.sum
Collapse
 
alainvanhout profile image
Alain Van Hout

In Java

    final int sum = IntStream.range(0, 1000)
            .filter(x -> x % 3 == 0 || x % 5 == 0)
            .sum();
    System.out.println(sum);
Collapse
 
blackbird profile image
Omkar Ajnadkar • Edited

Python

sum = 0
for i in range(0,1000):
    if i % 3 == 0 or i % 5 == 0:
        sum = sum + i
print(sum)

or Python One-Liner

print(sum(i for i in range(1000) if i % 3 == 0 or i % 5 == 0))
Collapse
 
gabriela profile image
Gabi • Edited

Hi, I am adding my first thought on this in Java.

private int sum(int inputValue) {
int sum = 0;
for (int i = 1; i < inputValue; i++) {
if (i % 5 == 0 || i % 3 == 0) {
sum += i;
}
}
return sum;
}

Collapse
 
nektro profile image
Meghan (she/her) • Edited
new Uint16Array(1000)
.map((v,i) => i)
.filter((v) => v % 3 == 0 || v % 5 === 0)
.reduce((ac,cv) => ac + cv)

// 233168
Collapse
 
ronaldoperes profile image
Ronaldo Peres

Hi,
I am trying to solve this one, and already solved.

I am going to ask, what is the sum of all the multiples of 3 or 5 below 100000??

I am trying to do this but is giving me a timeout, when using loops.

Collapse
 
srleyva profile image
Stephen Leyva (He/Him)

Python implementation that runs in Θ(1) time

def solve(n):
    three = 3 * sum_all(math.floor(n/3))
    fives = 5 * sum_all(math.floor(n/5))
    sames = 15 * sum_all(math.floor(n/15))
    return three + fives - sames


def sum_all(n):
    return n*(n+1)/2

Collapse
 
_bigblind profile image
Frederik 👨‍💻➡️🌐 Creemers
result = sum(x for x in range(1001) if x % 3 == 0 or x % 5 == 0)
Collapse
 
derfugu profile image
Daniel Bruynooghe • Edited

q){sum x where 0=min x mod/:(3,5)}til 1000
k) {+/ &: 0=min x {x-y*x div y}/:(3,5)}(!)1000

or mix and match without lambdas is even shorter and more obfuscated
q)sum (&:) 0=min ((!)1000) mod/: (3,5)

Collapse
 
rahyhub profile image
rahy-hub • Edited

/*Multiples of 3 and 5

Problem 1
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000. */

include

using namespace std;

int main()
{
int sum=0;
for(int i=1;i<1000;i++)
{
if(i%3==0 ||i%5==0)
{cout<<i<<" ";
sum+=i;}

}
cout<<"\n\n"<<"the sum of all the multiples of 3 or 5 below 1000 = "<<sum<<"\n";

return 0;
}

C++ >> Output >> 233168

Collapse
 
likelocusts profile image
LikeLocusts

Scala:

def sumOfMultiples(max: Int): Int = {
    if (max <= 0) 0
    else if (max % 3 == 0 || max % 5 == 0) max + sumOfMultiples(max - 1)
    else sumOfMultiples(max - 1)
  }  
Collapse
 
bigzude profile image
Big-Zude

function multiple(){
var a=Math.trunc(999/3)
var b=Math.trunc(999/5)
var c=Math.trunc(999/15)

var multi3=((3*a)(a+1))/2
var multi5=((5*b)
(b+1))/2
var multi15=((15*c)*(c+1))/2

var sum=(multi3+multi5)-multi15
return sum
}
console.log(multiple())

Collapse
 
mraza007 profile image
Muhammad

I did that a while ago in C++

Collapse
 
jvarness profile image
Jake Varness
Collapse
 
rrampage profile image
Raunak Ramakrishnan

Here's one in Haskell using list comprehension:

sum [x | x <- [1..999], x `mod` 3 == 0 || x `mod` 5 == 0]
Collapse
 
sawankrr profile image
sawankrr

Java

 Long sum = LongStream.range(1, 100)
                    .filter(i -> i % 3 == 0 || i % 5 == 0)
                    .sum();
    System.out.println(sum);
Collapse
 
erhankilic profile image
Erhan Kılıç

I started to solve problems but, well, you know little time so I couldn't continue :) I created a repository at github.

github.com/erhankilic/project-eule...

Collapse
 
sait profile image
Sai gowtham • Edited
let sum=0;
let start=999;

 while(start){
    if(start % 3 === 0 || start % 5===0){
       sum +=start;
    }  
   start--;  
 }

console.log(sum);
Collapse
 
derfugu profile image
Daniel Bruynooghe • Edited

q)sum (&) 0=min mod/:[; 3 5](!)1000

Collapse
 
derfugu profile image
Daniel Bruynooghe • Edited

k) +/&0=min{x-y*x div y}/:[;3 5](!)1000

For a change my k solution is more wordy because the mod function is rather long. Said that, the q above has k in it as well. In pure q it would read

q)sum where 0=min mod/:[;3 5]til 1000

terse and somewhat obfuscated, though the main elements are recognizable, i.e. create the list up to 1000, compute the remainders when dividing by 3 and by 5 and sum across all where either remainder is 0.

Collapse
 
jurituuti profile image
JuriTuuti

Julia:
sum([n for n=1:999 if n%5==0 || n%3==0])