The following are some general rules for constructing Roman numerals:
I is 1, II is 2, and III is 3. VI is 6 (literally, “5 and 1”), VII is 7, and VIII is 8.
-I, X, C, and M) can be repeated up to three times. At 4, you need to subtract from the next highest fives character. You can’t represent 4 as IIII; instead, it is represented as IV (“1 less than 5”). The number 40 is written as XL (10 less than 50), 41 as XLI, 42 as XLII, 43 as XLIII, and then 44 as XLIV (10 less than 50, then 1 less than 5).
-9, you need to subtract from the next highest tens character: 8 is VIII, but 9 is IX (1 less than 10), not VIIII (since the I character can not be repeated four times). The number 90 is XC, 900 is CM.
-10 is always represented as X, never as VV. The number 100 is always C, never LL.
-DC is 600; CD is a completely different number (400, 100 less than 500). CI is 101; IC is not even a valid Roman numeral (because you can’t subtract 1 directly from 100; you would need to write it as XCIX, for 10 less than 100, then 1 less than 10).
+I is 1, II is 2, and III is 3. VI is 6 (literally, “5 and 1”), VII is 7, and VIII is 8.
+I, X, C, and M) can be repeated up to three times. At 4, you need to subtract from the next highest fives character. You can't represent 4 as IIII; instead, it is represented as IV (“1 less than 5”). 40 is written as XL (“10 less than 50”), 41 as XLI, 42 as XLII, 43 as XLIII, and then 44 as XLIV (“10 less than 50, then 1 less than 5”).
+9, you need to subtract from the next highest tens character: 8 is VIII, but 9 is IX (“1 less than 10”), not VIIII (since the I character can not be repeated four times). 90 is XC, 900 is CM.
+10 is always represented as X, never as VV. 100 is always C, never LL.
+DC is 600; CD is a completely different number (400, “100 less than 500”). CI is 101; IC is not even a valid Roman numeral (because you can't subtract 1 directly from 100; you would need to write it as XCIX, “10 less than 100, then 1 less than 10”).
What would it take to validate that an arbitrary string is a valid Roman numeral? Let’s take it one digit at a time. Since Roman numerals are always written highest to lowest, let’s start with the highest: the thousands place. For numbers 1000 and higher, the thousands are represented by a series of M characters.
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As you saw in Case Study: Roman Numerals, there are several simple rules for constructing a Roman numeral, using the letters M, D, C, L, X, V, and I. Let's review the rules:
-
I is 1, II is 2, and III is 3. VI is 6 (literally, “5 and 1”), VII is 7, and VIII is 8.
I, X, C, and M) can be repeated up to three times. At 4, you need to subtract from the next highest fives character. You can't represent 4 as IIII; instead, it is represented as IV (“1 less than 5”). 40 is written as XL (“10 less than 50”), 41 as XLI, 42 as XLII, 43 as XLIII, and then 44 as XLIV (“10 less than 50, then 1 less than 5”).
9, you need to subtract from the next highest tens character: 8 is VIII, but 9 is IX (“1 less than 10”), not VIIII (since the I character can not be repeated four times). 90 is XC, 900 is CM.
10 is always represented as X, never as VV. 100 is always C, never LL.
DC is 600; CD is a completely different number (400, “100 less than 500”). CI is 101; IC is not even a valid Roman numeral (because you can't subtract 1 directly from 100; you would need to write it as XCIX, “10 less than 100, then 1 less than 10”).
-Thus, one useful test would be to ensure that the from_roman() function should fail when you pass it a string with too many repeated numerals. How many is “too many” depends on the numeral.