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www/statics/euler/Euler_Problem-089_explanation.md

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+I don't know why this problem has such a high number.
+
+We simply parse all the roman numbers in the file and create minimal roman literals from them.
+Then we simply sum all the length-differences together.
+
+And it wasn't really hard to write algorithms for these two conversions. Both are pretty straight forward.
+(And for number->roman we didn't even have to go the whole way, we only need the *length* of the result)
+
+For the conversion roman->number we first search for the length of the roman literal.
+Then we go backwards through the letters and get the value of each letter (cached by the array in line one).
+If the value of the letter is greater than the last value we increment the total value (by the letter value),
+otherwise we decrement it.
+I found it easier to traverse the number backwards because we can cache the value of the last digit and do the algorithm this way with less `g` calls.
+
+For the conversion number->optimal_roman_length i found this nice formula:
+
+~~~
+(n/1000) + R[(N%1000)/100] + R[(N%100)/10] + R[N%10]
+
+// n is our number
+// R is defined as an array with { 0, 1, 2, 3, 2, 1, 2, 3, 4, 2 }
+~~~