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to Rational Numbers in the JavaScript Track

Published at Jan 29 2021 · 0 comments
Instructions
Test suite
Solution

A rational number is defined as the quotient of two integers a and b, called the numerator and denominator, respectively, where b != 0.

The absolute value |r| of the rational number r = a/b is equal to |a|/|b|.

The sum of two rational numbers r₁ = a₁/b₁ and r₂ = a₂/b₂ is r₁ + r₂ = a₁/b₁ + a₂/b₂ = (a₁ * b₂ + a₂ * b₁) / (b₁ * b₂).

The difference of two rational numbers r₁ = a₁/b₁ and r₂ = a₂/b₂ is r₁ - r₂ = a₁/b₁ - a₂/b₂ = (a₁ * b₂ - a₂ * b₁) / (b₁ * b₂).

The product (multiplication) of two rational numbers r₁ = a₁/b₁ and r₂ = a₂/b₂ is r₁ * r₂ = (a₁ * a₂) / (b₁ * b₂).

Dividing a rational number r₁ = a₁/b₁ by another r₂ = a₂/b₂ is r₁ / r₂ = (a₁ * b₂) / (a₂ * b₁) if a₂ is not zero.

Exponentiation of a rational number r = a/b to a non-negative integer power n is r^n = (a^n)/(b^n).

Exponentiation of a rational number r = a/b to a negative integer power n is r^n = (b^m)/(a^m), where m = |n|.

Exponentiation of a rational number r = a/b to a real (floating-point) number x is the quotient (a^x)/(b^x), which is a real number.

Exponentiation of a real number x to a rational number r = a/b is x^(a/b) = root(x^a, b), where root(p, q) is the qth root of p.

Implement the following operations:

  • addition, subtraction, multiplication and division of two rational numbers,
  • absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.

Your implementation of rational numbers should always be reduced to lowest terms. For example, 4/4 should reduce to 1/1, 30/60 should reduce to 1/2, 12/8 should reduce to 3/2, etc. To reduce a rational number r = a/b, divide a and b by the greatest common divisor (gcd) of a and b. So, for example, gcd(12, 8) = 4, so r = 12/8 can be reduced to (12/4)/(8/4) = 3/2.

Assume that the programming language you are using does not have an implementation of rational numbers.

Setup

Go through the setup instructions for Javascript to install the necessary dependencies:

https://exercism.io/tracks/javascript/installation

Requirements

Please cd into exercise directory before running all below commands.

Install assignment dependencies:

$ npm install

Making the test suite pass

Execute the tests with:

$ npm test

In the test suites all tests but the first have been skipped.

Once you get a test passing, you can enable the next one by changing xtest to test.

Submitting Solutions

Once you have a solution ready, you can submit it using:

exercism submit rational-numbers.js

Submitting Incomplete Solutions

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

Exercise Source Credits

Wikipedia https://en.wikipedia.org/wiki/Rational_number

rational-numbers.spec.js

import { Rational } from './rational-numbers';

describe('Addition', () => {
  test('Add two positive rational numbers', () => {
    const expected = new Rational(7, 6);
    expect(new Rational(1, 2).add(new Rational(2, 3))).toEqual(expected);
  });

  xtest('Add a positive rational number and a negative rational number', () => {
    const expected = new Rational(-1, 6);
    expect(new Rational(1, 2).add(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Add two negative rational numbers', () => {
    const expected = new Rational(-7, 6);
    expect(new Rational(-1, 2).add(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Add a rational number to its additive inverse', () => {
    const expected = new Rational(0, 1);
    expect(new Rational(1, 2).add(new Rational(-1, 2))).toEqual(expected);
  });
});

describe('Subtraction', () => {
  xtest('Subtract two positive rational numbers', () => {
    const expected = new Rational(-1, 6);
    expect(new Rational(1, 2).sub(new Rational(2, 3))).toEqual(expected);
  });

  xtest('Subtract a positive rational number and a negative rational number', () => {
    const expected = new Rational(7, 6);
    expect(new Rational(1, 2).sub(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Subtract two negative rational numbers', () => {
    const expected = new Rational(1, 6);
    expect(new Rational(-1, 2).sub(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Subtract a rational number from itself', () => {
    const expected = new Rational(0, 1);
    expect(new Rational(1, 2).sub(new Rational(1, 2))).toEqual(expected);
  });
});

describe('Multiplication', () => {
  xtest('Multiply two positive rational numbers', () => {
    const expected = new Rational(1, 3);
    expect(new Rational(1, 2).mul(new Rational(2, 3))).toEqual(expected);
  });

  xtest('Multiply a negative rational number by a positive rational number', () => {
    const expected = new Rational(-1, 3);
    expect(new Rational(-1, 2).mul(new Rational(2, 3))).toEqual(expected);
  });

  xtest('Multiply two negative rational numbers', () => {
    const expected = new Rational(1, 3);
    expect(new Rational(-1, 2).mul(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Multiply a rational number by its reciprocal', () => {
    const expected = new Rational(1, 1);
    expect(new Rational(1, 2).mul(new Rational(2, 1))).toEqual(expected);
  });

  xtest('Multiply a rational number by 1', () => {
    const expected = new Rational(1, 2);
    expect(new Rational(1, 2).mul(new Rational(1, 1))).toEqual(expected);
  });

  xtest('Multiply a rational number by 0', () => {
    const expected = new Rational(0, 1);
    expect(new Rational(1, 2).mul(new Rational(0, 1))).toEqual(expected);
  });
});

describe('Division', () => {
  xtest('Divide two positive rational numbers', () => {
    const expected = new Rational(3, 4);
    expect(new Rational(1, 2).div(new Rational(2, 3))).toEqual(expected);
  });

  xtest('Divide a positive rational number by a negative rational number', () => {
    const expected = new Rational(-3, 4);
    expect(new Rational(1, 2).div(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Divide two negative rational numbers', () => {
    const expected = new Rational(3, 4);
    expect(new Rational(-1, 2).div(new Rational(-2, 3))).toEqual(expected);
  });

  xtest('Divide a rational number by 1', () => {
    const expected = new Rational(1, 2);
    expect(new Rational(1, 2).div(new Rational(1, 1))).toEqual(expected);
  });
});

describe('Absolute value', () => {
  xtest('Absolute value of a positive rational number', () => {
    const expected = new Rational(1, 2);
    expect(new Rational(1, 2).abs()).toEqual(expected);
  });

  xtest('Absolute value of a negative rational number', () => {
    const expected = new Rational(1, 2);
    expect(new Rational(-1, 2).abs()).toEqual(expected);
  });

  xtest('Absolute value of zero', () => {
    const expected = new Rational(0, 1);
    expect(new Rational(0, 1).abs()).toEqual(expected);
  });
});

describe('Exponentiation of a rational number', () => {
  xtest('Raise a positive rational number to a positive integer power', () => {
    const expected = new Rational(1, 8);
    expect(new Rational(1, 2).exprational(3)).toEqual(expected);
  });

  xtest('Raise a negative rational number to a positive integer power', () => {
    const expected = new Rational(-1, 8);
    expect(new Rational(-1, 2).exprational(3)).toEqual(expected);
  });

  xtest('Raise zero to an integer power', () => {
    const expected = new Rational(0, 1);
    expect(new Rational(0, 1).exprational(5)).toEqual(expected);
  });

  xtest('Raise one to an integer power', () => {
    const expected = new Rational(1, 1);
    expect(new Rational(1, 1).exprational(4)).toEqual(expected);
  });

  xtest('Raise a positive rational number to the power of zero', () => {
    const expected = new Rational(1, 1);
    expect(new Rational(1, 2).exprational(0)).toEqual(expected);
  });

  xtest('Raise a negative rational number to the power of zero', () => {
    const expected = new Rational(1, 1);
    expect(new Rational(-1, 2).exprational(0)).toEqual(expected);
  });
});

describe('Exponentiation of a real number to a rational number', () => {
  xtest('Raise a real number to a positive rational number', () => {
    const expected = 16.0;
    expect(new Rational(4, 3).expreal(8)).toEqual(expected);
  });

  xtest('Raise a real number to a negative rational number', () => {
    expect(new Rational(-1, 2).expreal(9)).toBeCloseTo(0.33, 2);
  });

  xtest('Raise a real number to a zero rational number', () => {
    const expected = 1.0;
    expect(new Rational(0, 1).expreal(2)).toEqual(expected);
  });
});

describe('Reduction to lowest terms', () => {
  xtest('Reduce a positive rational number to lowest terms', () => {
    const expected = new Rational(1, 2);
    expect(new Rational(2, 4).reduce()).toEqual(expected);
  });

  xtest('Reduce a negative rational number to lowest terms', () => {
    const expected = new Rational(-2, 3);
    expect(new Rational(-4, 6).reduce()).toEqual(expected);
  });

  xtest('Reduce a rational number with a negative denominator to lowest terms', () => {
    const expected = new Rational(-1, 3);
    expect(new Rational(3, -9).reduce()).toEqual(expected);
  });

  xtest('Reduce zero to lowest terms', () => {
    const expected = new Rational(0, 1);
    expect(new Rational(0, 6).reduce()).toEqual(expected);
  });

  xtest('Reduce an integer to lowest terms', () => {
    const expected = new Rational(-2, 1);
    expect(new Rational(-14, 7).reduce()).toEqual(expected);
  });

  xtest('Reduce one to lowest terms', () => {
    const expected = new Rational(1, 1);
    expect(new Rational(13, 13).reduce()).toEqual(expected);
  });
});
// calculate the Greatest Common Denominator (GCD) between 2 numbers
// recursive call has x = prior value of y and y is the remainder of x/y
// examples:
// 5,9 ==> 9,5 ==> 5,4 ==> 4,1 == 1,0 returns 1
// 3, 12 ==> 12,3 ==> 3,0 returns 3
// 9,9 ==> 9,0 returns 9
const calcGCD = (x, y) => {
  if (y === 0) return x;
  return calcGCD(y, x % y);
};

export class Rational {
  constructor(a, b) {
    this.a = a;
    this.b = b;
  }

  add({ a, b }) {
    const a1 = this.a * b + a * this.b;
    const b1 = a1 == 0 ? 1 : this.b * b;
    return new Rational(a1, b1).reduce();
  }

  sub({ a, b }) {
    const a1 = this.a * b - a * this.b;
    const b1 = a1 == 0 ? 1 : this.b * b;
    return new Rational(a1, b1).reduce();
  }

  mul({ a, b }) {
    return new Rational(this.a * a, this.b * b).reduce();
  }

  div({ a, b }) {
    return new Rational(this.a * b, this.b * a).reduce().switchSign();
  }

  abs() {
    return new Rational(Math.abs(this.a), Math.abs(this.b));
  }

  exprational(exponent) {
    return new Rational(this.a ** exponent, this.b ** exponent);
  }

  expreal(exponent) {
    return Math.round((exponent ** this.a) ** (1 / this.b) * 100) / 100;
  }

  reduce() {
    // x and y for gcd need to be in absolute value sequence low to high
    let absA = Math.abs(this.a);
    let absB = Math.abs(this.b);
    const x = absA <= absB ? absA : absB;
    const y = absA >= absB ? absA : absB;

    const gcd = calcGCD(x, y);

    this.a /= gcd;
    this.b /= gcd;
    this.switchSign();
    return this;
  }

  switchSign() {
    if (this.b < 0) {
      this.a *= -1;
      this.b *= -1;
    }
    return this;
  }
}

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