/**
 * Polynomials are algebraic expressions consisting of two or more algebraic terms.
 * Terms of a polynomial are:
 * 1. Coefficients e.g. 5, 4 in 5x^0, 4x^3 respectively
 * 2. Variables e.g. y in 3y^2
 * 3. Exponents e.g. 5 in y^5
 *
 * Class Polynomial constructs the polynomial using Array as an argument.
 * The members of array are coefficients and their indexes as exponents.
 */
class Polynomial {
  constructor (array) {
    this.coefficientArray = array // array of coefficients
    this.polynomial = '' // in terms of x e.g. (2x) + (1)
    this.construct()
  }

  /**
   * Function to construct the polynomial in terms of x using the coefficientArray
   */
  construct () {
    this.polynomial = this.coefficientArray.map((coefficient, exponent) => {
      if (coefficient === 0) {
        return '0'
      }
      if (exponent === 0) {
        return `(${coefficient})`
      } else if (exponent === 1) {
        return `(${coefficient}x)`
      } else {
        return `(${coefficient}x^${exponent})`
      }
    })
      .filter((x) => {
        if (x !== '0') {
          return x
        }
      })
      .reverse()
      .join(' + ')
  }

  /**
   * Function to display polynomial in terms of x
   * @returns {String} of polynomial representation in terms of x
   */
  display () {
    return this.polynomial
  }

  /**
   * Function to calculate the value of the polynomial by substituting variable x
   * @param {Number} value
   */
  evaluate (value) {
    return this.coefficientArray.reduce((result, coefficient, exponent) => {
      return result + coefficient * (Math.pow(value, exponent))
    }, 0)
  }
}

/**
 * Function to perform tests
 */
const tests = () => {
  const polynomialOne = new Polynomial([1, 2, 3, 4])
  console.log('Test 1: [1,2,3,4]')
  console.log('Display Polynomial ', polynomialOne.display())
  // (4x^3) + (3x^2) + (2x) + (1)
  console.log('Evaluate Polynomial value=2 ', polynomialOne.evaluate(2))
  // 49

  const polynomialTwo = new Polynomial([5, 0, 0, -4, 3])
  console.log('Test 2: [5,0,0,-4,3]')
  console.log('Display Polynomial ', polynomialTwo.display())
  // (3x^4) + (-4x^3) + (5)
  console.log('Evaluate Polynomial value=1 ', polynomialTwo.evaluate(1))
  // 4
}

tests()