Integer To Roman Numeral

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Problem statement

Given an integer ‘N’, the task is to find its corresponding Roman numeral.

Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.

Symbol      Value
  I           1
  V           5
  X           10
  L           50
  C           100
  D           500
  M           1000

Example :

2 is written as II in the roman numeral, just two one’s added together. 
12 is written as XII, which is simply X(ten) + II(one+one). 
The number 27 is written as XXVII, which is XX + V + II.

Roman numerals are usually written largest to smallest from left to right. 
However, the numeral for four is not IIII. Instead, the number four is written as IV. Because the one is before the five we subtract it making four.
The same principle applies to the number nine, which is written as IX.

There are six instances where subtraction is used:

I can be placed before V (5) and X (10) to make 4 and 9.
X can be placed before L (50) and C (100) to make 40 and 90.
C can be placed before D (500) and M (1000) to make 400 and 900.
Detailed explanation ( Input/output format, Notes, Images )
Input Format : 
The first line of input contains an integer ‘T’ denoting the number of test cases.
Then the test cases follow.

The only line of each test case contains an integer ‘N’.
Output Format : 
For each test case, the only line of output prints the corresponding roman numeral for the given integer ‘N’.
Note: 
You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints: 
1 <= T <= 10^2
1 <= N <= 4*10^3 - 1

Time Limit : 1 sec
Sample Input 1 :
2
3
12
Sample Output 1 :
III
XII
Explanation For Sample Input 1 :
For the first test case, 3 is written as III in Roman numeral, just three one’s added together.

For the second test case, the number 12 can be represented as XII, which is simply X + II.
Sample Input 2 :
2
40
27
Sample Output 2 :
XL
XXVII
Explanation For Sample Input 2 :
For the first test case, 40 is written as XL in Roman numeral, which is L - X.

For the second test case, the number 27 can be represented as XXVII, which is simply X + X + V + II.
Hint

Convert the units, tens, hundreds, and thousands place of the given number separately.

Approaches (3)
Brute Force

The idea is to convert each digit present at units, tens, hundreds and thousands places of the given number into roman numerals separately. Also, the conversion of some digits are a little bit different from other digits because these digits follow subtractive notation, i.e. 4 can be represented as “IV”, 9 can be represented as “IX” and so on.

 

Here is the algorithm :

 

  1. Compare the given number with the base value in the order from largest to smallest.
  2. The base value which is just smaller or equal to the given number will be the initial base value.
  3. Divide the number by this base value and corresponding base symbol will be repeated number/base i.e. quotient number of times.
  4. Now, the remainder will be the number for next iterations.
  5. These steps will be repeated until the number becomes zero.

 

For example, the roman numeral for the number 1749 will be “MDCCXLIX”.

Explanation :

 

Step 1 :

  • Initially number = 1749
  • Since 1749 >= 1000; the largest base value will be 1000 initially.
  • Divide 1749/1000. Quotient = 1, Remainder = 749. The corresponding symbol M will be repeated once.

 

Step 2 :

  • Now, number = 749
  • 1000 > 749 >= 500; the largest base value will be 500.
  • Divide 749/500. Quotient = 1, Remainder = 249. The corresponding symbol D will be repeated once.

 

Step 3 :

  • Now, number = 249
  • 400 > 249 >= 100; the largest base value will be 100.
  • Divide 249/100. Quotient = 2, Remainder = 49. The corresponding symbol C will be repeated twice.

 

Step 4 :

  • Now, number = 49
  • 50 > 49 >= 40; the largest base value is 40.
  • Divide 49/40. Quotient = 1, Remainder = 9. The corresponding symbol XL will be repeated once.

 

Step 5 :

  • Now, number = 9
  • 10 > 9 >= 9; the largest base value is 9.
  • Divide 9/9. Quotient = 1, Remainder = 0. The corresponding symbol IX will be repeated once.

 

Step 6:

  • Finally, the number becomes 0, the algorithm stops here.
  • The output obtained “MDCCXLIX”.
Time Complexity

O(log(N)), where ‘N’ is the given number.

 

Since, we are looping through the given number ‘N’, having log(N) number of digits. Thus, the time complexity will be O(log(N)).

Space Complexity

O(1)

 

Since no extra memory is used except some variables, thus, the space complexity will be O(1).

Code Solution
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Integer To Roman Numeral
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