day 3 refactor + comments

day03/sol.py

@@ -1,15 +1,24 @@
 input = open("input")
 part1 = 0
 part2 = 0
+shift = [0] + [10**i for i in range(12)]
 for line in input:
-    cells = list(line.strip())
-    cells.reverse()
-    max = ["0"*i for i in range(12+1)]
-    for (k,c) in enumerate(cells):
+    digits = list(line.strip())
+    # max[n] is the value of the maximal n digit subsequence
+    max = [0] * 13
+    # iterate over the digits in least-significant to most-significant order.
+    # k is the number of digits already processed.
+    for (k,c) in enumerate(reversed(digits)):
+        c = int(c)
+        # the maximal n-digit subsequence we can make that starts with the
+        # current digit (c) is equal to the concatenation of c and the
+        # maximal (n-1)-digit subsequence.
+        # if that's more than the best value we've seen so far, update max[n].
+        # we have to update max in reverse order in order to avoid reusing digits.
         for i in reversed(range(1,min(k+2,len(max)))):
-            j = c+max[i-1]
-            if j > max[i]:
-                max[i] = j
+            joltage = c*shift[i] + max[i-1]
+            if joltage > max[i]:
+                max[i] = joltage
     #print(max[12])
     part1 += int(max[2])
     part2 += int(max[12])