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Problem 89

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Roman numerals

For a number written in Roman numerals to be considered valid there are basic rules which must be followed. Even though the rules allow some numbers to be expressed in more than one way there is always a “best” way of writing a particular number.

For example, it would appear that there are at least six ways of writing the number sixteen:

IIIIIIIIIIIIIIII
VIIIIIIIIIII
VVIIIIII
XIIIIII
VVVI
XVI

However, according to the rules only XIIIIII and XVI are valid, and the last example is considered to be the most efficient, as it uses the least number of numerals.

The 11K text file, roman.txt (right click and ‘Save Link/Target As…’), contains one thousand numbers written in valid, but not necessarily minimal, Roman numerals; see About… Roman Numerals for the definitive rules for this problem.

Find the number of characters saved by writing each of these in their minimal form.

Note: You can assume that all the Roman numerals in the file contain no more than four consecutive identical units.

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罗马数字

要正确地用罗马数字表达一个数，必须遵循一些基本规则。尽管符合规则的写法有时会多于一种，但对每个数来说总是存在一种“最好的”写法。

例如，至少有六种写法可以表达十六这个数：

IIIIIIIIIIIIIIII
VIIIIIIIIIII
VVIIIIII
XIIIIII
VVVI
XVI

然而，根据规则，只有XIIIIII和XVI是合理的写法，而后一种因为使用了最少的数字而被认为是最有效的写法。

在文本文件roman.txt中包含了一千个合理的罗马数字写法，但并不都是最有效的写法；有关罗马数字的明确规则，可以参考“关于罗马数字”。

如果将这些数都写成最有效的写法，求所能节省的字符数。

注意：你可以假定文件中的所有罗马数字写法都不包含连续超过四个相同字符。

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