roman_numeral_recursion.md

Instructions

1. Fork this gist, then "edit" the gist
2. Fill out the questions below
3. Click the "Add file" button and add your source code to the gist
4. Submit by the due time as instructed in Zoom

Do not publish your code on a public repl.it or repo or other public means.

Prompt

Write a recursive function that converts an integer into a string such that the number is represented in Roman Numerals in the most efficient way. eg, the number 4 could be written as 'IIII' but it's more efficient to use 'IV' since that's a shorter string Assume no number is greater than 4,000 Here are the Roman Numeral equivalents you'll need to know:

• M=1000
• CM=900
• D=500
• CD=400
• C=100
• XC=90
• L=50
• XL=40
• X=10
• IX=9
• V=5
• IV=4
• I=1

Rewrite the question in your own words:

What assumptions will you make about this problem if you cannot ask any more clarifying questions? What are your reasons for making those assumptions?

Write a function that takes in a integer and coverts it into roman numerals in the most effecient way.

What are your initial thoughts about this problem? (high level design, 2-3 sentences)

My initial thoughts on this problem is that I will need to store my numbers and their corresponding roman numerals in an array. I will then need to figure out the pattern for coverting the integer into a roman numeral string.

How would you identify the elements of this problem?

• Searching of Data
• Sorting of Data
• Pattern Recognition
• Build/Navigate a Grid
• Math
• Language API knowledge
• Optimization

Which data structure(s) do you think you'll use? What pros/cons do you see with that choice?

I will use arrays so that I can do my calculations with a forloop.

Write out a few lines of initial pseudocode: (mid-level design, this should be short, and not be real code!)

Store letters used in Roman numerals
Store corresponding numerical numbers in an array
Create a string builder
Check the number being input if it is less than or eqaul to the highest roman numeral
Add to the string builder
Reduce corresponding value from input number 
if input number is greater than highest roman then check with next highest roman numeral
repeat til inout number = 0
string builder will print roman numeral representation of our input 

What do you think the Big O complexity of your algorithm is? (time complexity and space complexity)

O(n)2, because we are working with two arrays and combining the information ti make 1.

JS Starter Code

function toRoman(num) {
  let values = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
  let romanLetters =["M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I"]
  let romanString = []
  for(i = 0; i < values.length; i++) {
    if (num => values[i]) {
      num -= values[i];
      
    }
  }
}

console.log(toRoman(128));  // should return "CXXVIII"
console.log(toRoman(2000)); // should return "MM"
console.log(toRoman(2017)); // should return "MMXVII"
console.log(toRoman(1999)); // should return "MCMXCIX"

Ruby Starter Code

def to_roman(num)
  # your code goes here
end

puts to_roman(128)   # should return "CXXVIII"
puts to_roman(2000)  # should return "MM"
puts to_roman(2017)  # should return "MMXVII"
puts to_roman(1999)  # should return "MCMXCIX"