Problem 089

e089.py

@@ -0,0 +1,85 @@
+"""Develop a method to express Roman numerals in minimal form.
+
+The rules for writing Roman numerals allow for many ways of writing each number (see FAQ: Roman Numerals). However, there is always a "best" way of writing a particular number.
+
+For example, the following represent all of the legitimate ways of writing the number sixteen:
+    IIIIIIIIIIIIIIII
+    VIIIIIIIIIII
+    VVIIIIII
+    XIIIIII
+    VVVI
+    XVI
+
+The last example being considered the most efficient, as it uses the least number of numerals.
+
+The 11K text file, roman.txt (p089/roman.txt), contains one thousand numbers written in valid, but not necessarily minimal, Roman numerals; that is, they are arranged in descending units and obey the subtractive pair rule (see FAQ 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.
+"""
+
+ROMAN_NUMERALS = {
+    'I': 1,
+    'V': 5,
+    'X': 10,
+    'L': 50,
+    'C': 100,
+    'D': 500,
+    'M': 1000
+}
+
+
+def roman_to_decimal(s):
+    # Read in roman digits in reverse
+    last = None
+    total = 0
+    for c in s[::-1]:
+        val = ROMAN_NUMERALS[c]
+        if last and val < last:
+            total = total - val
+        else:
+            total = total + val
+            last = val
+    return total
+
+def decimal_to_roman(n):
+    roman = ''
+    lookup = dict([(v, k) for (k, v) in ROMAN_NUMERALS.iteritems()])
+    values = sorted(ROMAN_NUMERALS.values())
+    total = 0
+    subtracted = False
+    for i in xrange(len(values)):
+        val = values[i]
+        if val == max(values):
+            count = n // val
+            roman = (lookup[val] * count) + roman
+        else:
+            nn = (n - total) % values[i + 1]
+            count = nn // val
+            if count > 3:
+                roman = lookup[val] + lookup[values[i + 2]] + roman
+                subtracted = True
+            else:
+                if count and subtracted:
+                    count = count - 1
+                subtracted = False
+                roman = (lookup[val] * count) + roman
+            total = total + nn
+    return roman
+
+def main():
+    saved = 0
+    with open('p089/roman.txt', 'r') as f:
+        while True:
+            line = f.readline()
+            if not line:
+                break
+            old = line.strip()
+            new = decimal_to_roman(roman_to_decimal(old))
+            print roman_to_decimal(old), old, new
+            saved = saved + (len(old) - len(new))
+    print 'Saved:', saved
+
+if __name__ == '__main__':
+    main()