Peter Kim Frank

Posted on May 30, 2019

Project Euler #6 - Sum Square Difference

#projecteuler #challenge

Continuing the wonderful community solutions to Project Euler.

This is Problem 6, sum square difference.

The sum of the squares of the first ten natural numbers is,

1² + 2² + ... + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Top comments (31)

Luis Miguel • May 30 '19 • Edited

no loops!

python3

def sum_square_difference(n):
return (((n**2) * (n + 1)**2) / 4) - (n * (n + 1) * (2*n + 1) / 6)

print(sum_square_difference(100))

I dont know why when I tried to upload images they dont appear

Massimo Artizzu • May 30 '19

Aw yeah 👌

If some are wondering, that comes from well-known formulas for the sum of the first n integers and n squares. There's a generalization, too, but also a pretty common formula for the first n cubes.

A solid mathematical approach can really simplify programming challenges. It almost feels like cheating.

Nathan Tamez • May 30 '19

Definitely highlights the need for maths in software development.

Henry 👨‍💻 • May 30 '19

Woah, alright, you win 😲.
Also, there's a guide here to embed code and images in markdown (what dev.to uses).

Luis Miguel • May 30 '19

thanks, I'm going to check it.

Ali Spittel • May 30 '19 • Edited

Python!

def sum_square_difference(n):
    numbers = range(1, n+1)
    sum_squares = sum(i**2 for i in numbers)
    square_sum = sum(numbers)**2
    return square_sum - sum_squares

print(sum_square_difference(100))

Florian Rand • May 30 '19

I surrender!

Dídac • May 30 '19 • Edited

Ruby:

def sum_square_difference(n)
  numbers = (1..n)
  square_of_sum = numbers.sum ** 2
  sum_of_square = numbers.map { |n| n ** 2 }.sum
  square_of_sum - sum_of_square
end

puts sum_square_difference(10)

Nans Dumortier • May 30 '19

Ruby is so elegant 😍

Nans Dumortier • May 30 '19

Javascript !

const sumSquareDifference = (n) => {
  const numbers = [...Array(n + 1).keys()];
  const sumOfSquares = numbers.reduce((accumulator, number) => accumulator + (number ** 2));
  const squareOfSum = numbers.reduce((accumulator, number) => accumulator + number) ** 2;
  return squareOfSum - sumOfSquares;
}
console.log(sumSquareDifference(10));

Nathan Tamez • May 30 '19

Yours is good. But I have a feeling it uses more then one for/for each loop. May explain why it is a bit slower then mine. Not sure.

Nans Dumortier • May 30 '19

Yeah, also the fact that I'm iterating 2 times the same array !

Nathan Tamez • May 30 '19 • Edited

Here is my nodejs solution

function sumSquareDifference(min, max) {
    let sumOfSquares = 0;
    let squareOfSums = 0;
    for (i = min; i < max + 1; i++) {
        sumOfSquares += i ** 2;
        squareOfSums += i;
    }

    return (squareOfSums ** 2) - sumOfSquares;
}
const startTime = Date.now();
console.log(`The difference between the sum of the squares of the first one
 hundred natural numbers and the square of the sum,
is ${sumSquareDifference(1, 100)}`);
console.log(`Time Taken: ${Math.round(Date.now() - startTime)}ms`);

output

The difference between the sum of the squares of the first one hundred natural numbers and the square of the sum,is 25164150
Time Taken: 2ms

Nans Dumortier • May 30 '19 • Edited

Yours performs faster than the one I submitted, and still looks nice, well done !

EDIT: some of the lets could be replaced with const though 🙈

Nathan Tamez • May 30 '19

true

Olivier Picault • May 30 '19

From ProjectEuler:

Please do not deprive others of going through the same process by publishing your solution outside of Project Euler; for example, on other websites, forums, blogs, or any public repositories (e.g. GitHub), et cetera. Members found to be spoiling problems will have their accounts locked.

Jay • May 30 '19

Rust Solution: Playground

fn main() {
    println!("{}", get_difference(100));
}

fn get_difference(end: usize) -> u32 {
    ((1..=end).sum::<usize>().pow(2) - (1..=end).map(|n| n.pow(2)).sum::<usize>()) as u32
}

Henry 👨‍💻 • May 30 '19

My take on this problem in python:

def challenge():
    sumOfSquares = 0
    squareOfSums = 0
    difference = 0
    for i in range(101):
        sumOfSquares += i ** 2
        squareOfSums += i
    squareOfSums = squareOfSums ** 2
    difference =  squareOfSums - sumOfSquares
    print("The difference between the sum of squares and the square of sums up to 100 is {}".format(difference))

Output:

The difference between the sum of squares and the square of sums up to 100 is 25164150

Ademola John • May 18 '20 • Edited

Here is my Javascript Solution


function sumSquareDifference(n) {
  // Good luck!
  let a = 0,b=0,c=0;
  for(let i = 1;i<=n;i++){
    a+= (Math.pow(i,2));
    b+=i
  }
c=Math.pow(b,2)-a

console.log(a);
console.log(b);
  return c;
}

kip • May 30 '19 • Edited

Rust

fn get_sum_square_difference(end: usize) -> usize {
    let mut sum: usize = 0;
    let square_sum = (1..=end).fold(0usize, |fin, num| { sum += num; fin + num.pow(2) });

    sum.pow(2) - square_sum
}

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Project Euler #6 - Sum Square Difference

Top comments (31)

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