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Peter Kim Frank
Peter Kim Frank

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Project Euler #6 - Sum Square Difference

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.

Latest comments (31)

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jacklangcreator profile image
Sagnik Ray

public class ProjectEuler{
static int n = 100;
public static void main(String []args){
System.out.println(differencehelper());

}
static int sumsquare(int n){
int sum = 0 ;
sum = (n*(n+1)(2*n+1))/6;
return sum;
}
static int squaresum(int n){
int sum = 0;
sum = (n
(n+1))/2;
return (sum *sum);
}
static int differencehelper(){
return squaresum(n) - sumsquare(n);
}



}

Easy Java Solution using Gauss' Formula Hope you liked it ;)

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crownedprinz profile image
Ademola John • 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;
}
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rahyhub profile image
rahy-hub

my code with C++

/*Sum square difference

Problem 6
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.*/

include

using namespace std;
int square_sum(int s);

int main()
{
int limit=100 ,sum=0 ,sumQ=0;
for(int i=1;i<=limit;i++)
{
sumQ=sumQ+(i*i);
sum =sum+i;
}

cout<<"the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum is \n ";
cout<< square_sum(sum)-sumQ ;  // without function : cout<<sum*sum-sumQ
return 0;

}

int square_sum(int s)
{
return s*s;
}
Output >> 25164150

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nurchikgit profile image
nurchikgit

not bad)))

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seyedmahmoudbayazid profile image
Mahmoud Bayazid

new_list = []

for i in range (1,101):
new_list.append(i*2)
a = sum(new_list)
b = sum(range(1,101))
*2
print(b-a)

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seyedmahmoudbayazid profile image
Mahmoud Bayazid • Edited

new_list = []

for i in range (1,101):
new_list.append(i^2)
a = sum(new_list)
b = sum(range(1,101))^2
print(b-a)

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hishamkhr profile image
hishamkhr

hi
i try this:
sum of numbers= n(n+1)/2
then i get the square.
after that i found an equation about sum of squares:
(2*n^3 +3*n^2+n )/6
but i didn't get right result !!!!
so where i lost the control ?
thanks

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olivierpicault profile image
Olivier Picault

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.

:)

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brightone profile image
Oleksii Filonenko

Elixir:

(1..100 |> Enum.map(&:math.pow(&1, 2)) |> Enum.sum()) -
  (1..100 |> Enum.sum() |> :math.pow(2))
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comaldave profile image
David Skinner

Go Gopher

goplay.space/#rQ0XekiCknZ

// func SumSquareDifference receives the max range
// and returns the difference of the sumSquare and the squareSum.
func SumSquareDifference(x int) int {
    sum := 0
    sumSquare := 0

    for i := 1; i <= x; i++ {
        sum += i
        sumSquare += i * i
    }

    squareSum := sum * sum

    return squareSum - sumSquare
}

You can see the complete program on the playground link.

  • I have included a block that confirms that my function provides the expected response.
  • I then start a timer so I can print the elapsed time to run the function.
  • After printing the results, I include a comment defining the Output, If the output changes it will generate an error on my computer.
  • The language is Go but it is more a C++ style, I am not the best Go programmer.
  • Code needs to be readable, compilers can do the optimization.
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fossilizeddev profile image
Carlos E. Barboza • Edited

Swift:

func sumSquareDifference(range: Int) -> Int {
    var sumOfSquares = 0
    var squareOfSum = 0
    for number in 1..<range+1 { //Is there a better way? Other than range+1?
        sumOfSquares += (number*number)
        squareOfSum += number
    }
    squareOfSum = squareOfSum*squareOfSum
    return (squareOfSum - sumOfSquares)
}

print(sumSquareDifference(range:100))
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flrnd profile image
Florian Rand • Edited

Some fun!

// with for loop
func sumSqDiffLoop(n int) int {
    var sOsq int
    var sOts int
    for i := 1; i <= 100; i++ {
        sOsq += i * i
        sOts += i
    }
    return (sOts * sOts) - sOsq
}
// no loop - thanks to @lmbarr for his solution
func sumSqDiffNoLoop(n int) int {
    return (((n * n) * ((n + 1) * (n + 1))) / 4) - (n * (n + 1) * (2*n + 1) / 6)
}

// Let's make some benchmarks!

import "testing"

func BenchmarkSumSquareDiff(b *testing.B) {
    benchs := []struct {
        name string
        fun  func(int) int
    }{
        {"Sum Square Diff Loop", sumSqDiffLoop},
        {"Sum Square Diff no Loop", sumSqDiffNoLoop},
    }
        // Let's test it with 1000 instead of 100 :D
    input := 1000

    for _, bench := range benchs {
        b.Run(bench.name, func(b *testing.B) {
            for i := 0; i < b.N; i++ {
                bench.fun(input)
            }
        })
    }
}

Benchmark result:

❯ go test -bench=.

goos: linux
goarch: amd64
/Sum_Square_Diff_Loop-4             20000000          62.7 ns/op
/Sum_Square_Diff_no_Loop-4          500000000         3.58 ns/op
PASS
ok      _/h/f/s/g/src/project-euler/06  3.474s
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hanachin profile image
Seiei Miyagi

Ruby 2.7

p (1..100).then { @1.sum ** 2 - @1.sum { @1 ** 2 } }
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badrecordlength profile image
Henry 👨‍💻

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
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lmbarr profile image
Luis Miguel • 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

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maxart2501 profile image
Massimo Artizzu

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.

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natonathan profile image
Nathan Tamez

Definitely highlights the need for maths in software development.

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badrecordlength profile image
Henry 👨‍💻

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

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lmbarr profile image
Luis Miguel

thanks, I'm going to check it.

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kip13 profile image
kip • 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
}