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UnrelatedString's solution

to Difference Of Squares in the Clojure Track

Published at Feb 06 2019 · 0 comments
Instructions
Test suite
Solution

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.

Source

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.

difference_of_squares_test.clj

(ns difference-of-squares-test
  (:require [clojure.test :refer [deftest is]]
            [difference-of-squares :as dos]))

(deftest square-of-sum-to-5
  (is (= 225 (dos/square-of-sum 5))))

(deftest sum-of-squares-to-5
  (is (= 55 (dos/sum-of-squares 5))))

(deftest difference-of-squares-to-5
  (is (= 170 (dos/difference 5))))

(deftest square-of-sum-to-10
  (is (= 3025 (dos/square-of-sum 10))))

(deftest sum-of-squares-to-10
  (is (= 385 (dos/sum-of-squares 10))))

(deftest difference-of-squares-to-10
  (is (= 2640 (dos/difference 10))))

(deftest square-of-sum-to-100
  (is (= 25502500 (dos/square-of-sum 100))))

(deftest sum-of-squares-to-100
  (is (= 338350 (dos/sum-of-squares 100))))

(deftest difference-of-squares-to-100
  (is (= 25164150 (dos/difference 100))))

src/difference_of_squares.clj

(ns difference-of-squares)

(defn sum-of-squares [n]
    (->> n
        (inc)
        (range)
        (transduce
            (map #(* % %))
            +)))

(defn square-of-sum [n]
    (as-> n x
        (inc x)
        (range x)
        (reduce + x)
        (* x x)))

(defn difference [n]
    (-
        (square-of-sum n)
        (sum-of-squares n)))

src/difference_of_squares_math.clj

(ns difference-of-squares)

(defn sum-of-squares [n]
    (/
        (*
            n
            (inc n)
            (inc (* 2 n)))
        6))

(defn square-of-sum [n]
    (/
        (*
            n
            n
            (inc n)
            (inc n))
        4))

(defn difference [n]
    (-
        (square-of-sum n)
        (sum-of-squares n)))

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