Roman to Integer

Roman to integer converts a Roman numeral to its value. Roman notation is mostly additive — symbols run largest to smallest and sum — with six subtractive exceptions like IV for 4 and CM for 900. Handling those six as special cases produces long conditional chains. The observation that removes them entirely: - A symbol is subtracted exactly when it is smaller than the symbol immediately after it, and added otherwise. In IV, the I precedes a larger V, so it subtracts. In VI, the I follows and adds. That one comparison covers all six subtractive pairs without naming any of them. So scan left to right, comparing each symbol with its successor, and add or subtract accordingly. The final symbol has no successor and is always added. An equivalent formulation scans right to left, adding when a symbol is at least as large as the previous one seen and subtracting otherwise. Some find this cleaner since it avoids looking ahead. A lookup table maps the seven symbols to their values, and the input is guaranteed valid, so no verification of malformed numerals is needed. The comparison must be strictly less than. Using <= would wrongly subtract in cases like II, where two equal symbols should both add. The constraints cap the input at 3999, so no symbol above M appears. Integer to Roman is the reverse direction, where the subtractive forms are placed in the lookup table as values in their own right — a neat symmetry with this problem's approach of not naming them at all. One pass gives O(n) time and O(1) space.

Roman numerals are additive except when a smaller symbol precedes a larger one, which signals subtraction. So a single left-to-right pass that compares each character to its neighbour handles every case — no lookup table of the six subtractive pairs needed.