Convert between Roman numerals and integers (both ways)

• Integer to Roman: go through a table of the 13 values (1000, 900, 500, 400, …, 1) from largest to smallest, and take each value as many times as it fits.
• Roman to integer: a symbol is subtracted when a larger symbol follows it.

Integer → Roman (greedy). With the table 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, repeatedly append the largest symbol that still fits and subtract its value. Putting the subtractive pairs in the table is the key idea, because it removes all special cases. Greedy is correct here because the Roman system is designed so that the largest-first choice always gives the standard form.

Roman → integer. Scan from left to right. Add each symbol's value, except subtract it when the next symbol is larger (the I in IV, the C in CM). An equivalent version scans right to left and subtracts any symbol smaller than the largest seen so far.

Telling them apart: a line that starts with a digit is an integer.

Complexity: O(length) per line. Every result has at most 15 characters (3888 = MMMDCCCLXXXVIII).

Follow-ups: validate input, rejecting forms like IIII, VX or IC (one approach: convert, convert back, and compare), and explain why 3999 is the usual limit: standard notation has no symbol above M.