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atmantree's solution

to Difference Of Squares in the C++ Track

Published at Jul 20 2018 · 0 comments
Test suite


This exercise has changed since this solution was written.

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

The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)² = 55² = 3025.

The sum of the squares of the first ten natural numbers is 1² + 2² + ... + 10² = 385.

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

Getting Started

Make sure you have read the C++ page on exercism.io. This covers the basic information on setting up the development environment expected by the exercises.

Passing the Tests

Get the first test compiling, linking and passing by following the three rules of test-driven development. Create just enough structure by declaring namespaces, functions, classes, etc., to satisfy any compiler errors and get the test to fail. Then write just enough code to get the test to pass. Once you've done that, uncomment the next test by moving the following line past the next test.


This may result in compile errors as new constructs may be invoked that you haven't yet declared or defined. Again, fix the compile errors minimally to get a failing test, then change the code minimally to pass the test, refactor your implementation for readability and expressiveness and then go on to the next test.

Try to use standard C++11 facilities in preference to writing your own low-level algorithms or facilities by hand. CppReference is a wiki reference to the C++ language and standard library. If you are new to C++, but have programmed in C, beware of C traps and pitfalls.


Problem 6 at Project Euler http://projecteuler.net/problem=6

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.


#include "difference_of_squares.h"
#include <boost/test/unit_test.hpp>

    BOOST_REQUIRE_EQUAL(225, squares::square_of_sums(5));
    BOOST_REQUIRE_EQUAL(55, squares::sum_of_squares(5));
    BOOST_REQUIRE_EQUAL(170, squares::difference(5));

    BOOST_REQUIRE_EQUAL(3025, squares::square_of_sums(10));
    BOOST_REQUIRE_EQUAL(385, squares::sum_of_squares(10));
    BOOST_REQUIRE_EQUAL(2640, squares::difference(10));

    BOOST_REQUIRE_EQUAL(25502500, squares::square_of_sums(100));
    BOOST_REQUIRE_EQUAL(338350, squares::sum_of_squares(100));
    BOOST_REQUIRE_EQUAL(25164150, squares::difference(100));
#include "difference_of_squares.h"

#include <cmath>

int squares::square_of_sums(int num) {
    return std::pow((num*(num+1)/2), 2);

int squares::sum_of_squares(int num) {
    return num*(num+1)*(2*num+1)/6;

int squares::difference(int num) {
    return squares::square_of_sums(num) - squares::sum_of_squares(num);

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