Integer To Roman InterviewBit Solution
Problem: Integer To Roman
Problem Description:
Given an integer A, convert it to a roman numeral, and return a string corresponding to its roman numeral version.
Input Format
The only argument given is integer A. Output Format
Return a string denoting roman numeral version of A. Constraints
1 <= A <= 3999 For Example
Input 1:
A = 5
Output 1:
"V"
Input 2:
A = 14
Output 2:
"XIV"Solution Approach:
The approach to this problem is quite straightforward, you just need to understand how Roman Numeral Systems is assigned to a number.
Time Complexity:
When you will see the solution you will realize that, in the first while loop, we keep decreasing the number by 1000 until it becomes less than 1000.
Once it is less than 1000, then the number of operations is more or less the same for any input, so we can consider the time complexity for the rest of the while loops as constant.
Now the problem comes with the first while loop, so the number of times it runs depends on input number N, for example:
For N < 1000, No. of operation = 0
For N < 2000, No. of operation = 1
For N < 3000, No. of operation = 2So time complexity would be O(N/1000), so it should be O(N) for very large N.
Keeping the subtractive cases like IV and IX in the mapping table is what finally made the logic click for me—it turns Roman numerals into the same kind of fixed-denomination problem you see in currency conversion, like at https://onlinecasinospaysafecard.com. The O(N/1000) analysis also makes sense, though in practice the bound is tiny since A is capped at 3999. I’d probably still use an array of pairs to avoid the repeated while loops.