TOTAL_NUMBER_OF_UNIQUE_ENGLISH_LOST_MY_NAME_BOOKS

TOTAL_NUMBER_OF_UNIQUE_ENGLISH_LOST_MY_NAME_BOOKS.js

/* eslint semi: [2, "never"] */

var STORY_COUNT = 45 // [34, 48, 48, 31, 45, 36, 43, 38, 40, 34]
var HELPERS = range(0, 3)
var LENGTHS = range(3, 12)
var ALPHABET = 26 // Needs per country
var HELPER_COUNT = 3
var DIVERSITY = 6 // OR: [6, 6, 2, 2, 2, 2, 2, 2, 2, 2]

function range(start, end) {
  var arr = []
  while (start <= end) {
    arr.push(start++)
  }
  return arr
}

function sum(arr) {
  return arr.reduce(function (x, y) {
    return x + y
  })
}

function product(arr) {
  return arr.reduce(function (x, y) {
    return x * y
  })
}

function factorial(n) {
  var result = n

  if (n < 1) {
    return 1
  }
  while (--n) {
    result = n * result
  }
  return result
}

function C(sets) {
  var c = Math.round(factorial(sum(sets)) / product(sets.map(factorial)))
  console.log('C(' + sets.join(', ') + ')', c)
  return c
}

function P(elements, sample) {
  var p = Math.round(factorial(elements) / factorial(elements - sample))
  console.log('P(' + elements + ', ' + sample + ')', p)
  return p
}

function totalNumberOfUniqueBooks(options) {
  return options.diversity * sum(options.bookLengths.map(function (s) {
    return sum(options.helperLengths.map(function (h) {
      return (
        P(options.totalStories, s - h)
        * P(options.totalHelpers, h)
        * Math.pow(options.alphabet, h)
        * C([s - h, h])
      )
    }))
  }))
}

function defaultOptions(options) {
  options = options || {}
  options.totalHelpers = options.totalHelpers || 0
  options.totalStories = options.totalStories || 1
  options.diversity = options.diversity || 1
  options.helperLengths = options.helperLengths || range(0, options.totalHelpers)
  options.bookLengths = options.bookLengths || range(options.totalStories, options.totalStories)
  options.alphabet = options.alphabet || options.totalStories
  return options
}

function assert(expected, options, msg) {
  console.log()
  console.log('========' + (msg || '') + '========')
  options = defaultOptions(options)
  console.log(options)
  var actual = totalNumberOfUniqueBooks(options)
  console.log()
  console.log(actual, actual == expected ? '==' : '!=', expected)
  if (actual != expected) {
    throw "Fail"
  }
}

assert(1)
assert(2, {
  bookLengths: [2],
  totalStories: 2
})
assert(2, {
  totalHelpers: [1],
  helperLengths: [1],
  alphabet: 2
})

assert(4, {
  totalStories: 2,
  bookLengths: range(1, 2)
})

assert(100, {
  totalStories: 10,
  bookLengths: range(1, 2)
})

assert(200, {
  totalStories: 10,
  bookLengths: [2],
  helperLengths: [1],
  totalHelpers: 1,
  alphabet: 10,
})

assert(290, {
  totalStories: 10,
  bookLengths: [2],
  helperLengths: [0, 1],
  totalHelpers: 1,
  alphabet: 10,
})

assert(400, {
  totalStories: 10,
  bookLengths: [2],
  helperLengths: [1],
  totalHelpers: 2,
  alphabet: 10,
})

assert(490, {
  totalStories: 10,
  bookLengths: [2],
  helperLengths: [0, 1],
  totalHelpers: 2,
  alphabet: 10,
})

assert(1, {
  totalHelpers: 3,
  totalStories: 45,
  diversity: 6,
  bookLengths: range(3, 12),
  helperLengths: range(0, 3),
  alphabet: 26
})