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make repeated rules uniform between chapters

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Mark Pilgrim
2009-09-25 23:55:35 -04:00
parent fe7a9611b9
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regular-expressions.html
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@@ -84,11 +84,12 @@ body{counter-reset:h1 5}
</ul>
<p>The following are some general rules for constructing Roman numerals:
<ul>
<li>Characters are additive. <code>I</code> is <code>1</code>, <code>II</code> is <code>2</code>, and <code>III</code> is <code>3</code>. <code>VI</code> is <code>6</code> (literally, &#8220;<code>5</code> and <code>1</code>&#8221;), <code>VII</code> is <code>7</code>, and <code>VIII</code> is <code>8</code>.
<li>The tens characters (<code>I</code>, <code>X</code>, <code>C</code>, and <code>M</code>) can be repeated up to three times. At <code>4</code>, you need to subtract from the next highest fives character. You can&#8217;t represent <code>4</code> as <code>IIII</code>; instead, it is represented as <code>IV</code> (&#8220;<code>1</code> less than <code>5</code>&#8221;). The number <code>40</code> is written as <code>XL</code> (<code>10</code> less than <code>50</code>), <code>41</code> as <code>XLI</code>, <code>42</code> as <code>XLII</code>, <code>43</code> as <code>XLIII</code>, and then <code>44</code> as <code>XLIV</code> (<code>10</code> less than <code>50</code>, then <code>1</code> less than <code>5</code>).
<li>Similarly, at <code>9</code>, you need to subtract from the next highest tens character: <code>8</code> is <code>VIII</code>, but <code>9</code> is <code>IX</code> (<code>1</code> less than <code>10</code>), not <code>VIIII</code> (since the <code>I</code> character can not be repeated four times). The number <code>90</code> is <code>XC</code>, <code>900</code> is <code>CM</code>.
<li>The fives characters can not be repeated. The number <code>10</code> is always represented as <code>X</code>, never as <code>VV</code>. The number <code>100</code> is always <code>C</code>, never <code>LL</code>.
<li>Roman numerals are always written highest to lowest, and read left to right, so the order of characters matters very much. <code>DC</code> is <code>600</code>; <code>CD</code> is a completely different number (<code>400</code>, <code>100</code> less than <code>500</code>). <code>CI</code> is <code>101</code>; <code>IC</code> is not even a valid Roman numeral (because you can&#8217;t subtract <code>1</code> directly from <code>100</code>; you would need to write it as <code>XCIX</code>, for <code>10</code> less than <code>100</code>, then <code>1</code> less than <code>10</code>).
<ol>
<li>Sometimes characters are additive. <code>I</code> is <code>1</code>, <code>II</code> is <code>2</code>, and <code>III</code> is <code>3</code>. <code>VI</code> is <code>6</code> (literally, &#8220;<code>5</code> and <code>1</code>&#8221;), <code>VII</code> is <code>7</code>, and <code>VIII</code> is <code>8</code>.
<li>The tens characters (<code>I</code>, <code>X</code>, <code>C</code>, and <code>M</code>) can be repeated up to three times. At <code>4</code>, you need to subtract from the next highest fives character. You can't represent <code>4</code> as <code>IIII</code>; instead, it is represented as <code>IV</code> (&#8220;<code>1</code> less than <code>5</code>&#8221;). <code>40</code> is written as <code>XL</code> (&#8220;<code>10</code> less than <code>50</code>&#8221;), <code>41</code> as <code>XLI</code>, <code>42</code> as <code>XLII</code>, <code>43</code> as <code>XLIII</code>, and then <code>44</code> as <code>XLIV</code> (&#8220;<code>10</code> less than <code>50</code>, then <code>1</code> less than <code>5</code>&#8221;).
<li>Sometimes characters are&hellip; the opposite of additive. By putting certain characters before others, you subtract from the final value. For example, at <code>9</code>, you need to subtract from the next highest tens character: <code>8</code> is <code>VIII</code>, but <code>9</code> is <code>IX</code> (&#8220;<code>1</code> less than <code>10</code>&#8221;), not <code>VIIII</code> (since the <code>I</code> character can not be repeated four times). <code>90</code> is <code>XC</code>, <code>900</code> is <code>CM</code>.
<li>The fives characters can not be repeated. <code>10</code> is always represented as <code>X</code>, never as <code>VV</code>. <code>100</code> is always <code>C</code>, never <code>LL</code>.
<li>Roman numerals are read left to right, so the order of characters matters very much. <code>DC</code> is <code>600</code>; <code>CD</code> is a completely different number (<code>400</code>, &#8220;<code>100</code> less than <code>500</code>&#8221;). <code>CI</code> is <code>101</code>; <code>IC</code> is not even a valid Roman numeral (because you can't subtract <code>1</code> directly from <code>100</code>; you would need to write it as <code>XCIX</code>, &#8220;<code>10</code> less than <code>100</code>, then <code>1</code> less than <code>10</code>&#8221;).
</ul>
<h3 id=thousands>Checking For Thousands</h3>
<p>What would it take to validate that an arbitrary string is a valid Roman numeral? Let&#8217;s take it one digit at a time. Since Roman numerals are always written highest to lowest, let&#8217;s start with the highest: the thousands place. For numbers 1000 and higher, the thousands are represented by a series of <code>M</code> characters.