day 7 optimization

instead of lists, construct a tower of nested generators. i think this
is equivalent to a recursive backtracking solution.

since the input doesn't contain 0 we can check for <goal in the
intermediate layers, and ==goal at the end.

day07/sol.py

@@ -6,38 +6,29 @@ def solve(file):
         goal = int(nums[0].rstrip(":"))
         nums = [int(x) for x in nums[1:]]
 
-        if viable(goal, nums):
+        if viable(goal, nums, lambda n,x: (n*x, n+x)):
             t += goal
-        elif viable2(goal, nums):
+        elif viable(goal, nums, lambda n,x: (n*x, n+x, int(str(n)+str(x)))):
             t2 += goal
     print(t)
     print(t+t2)
 
-def viable(goal, nums):
+def viable(goal, nums, combine):
     candidates = [nums[0]]
-    next = []
-    for x in nums[1:]:
-        for n in candidates:
-            for m in n*x, n+x:
-                if m <= goal:
-                    next.append(m)
-        next, candidates = candidates, next
-        next.clear()
-    #print(goal, nums, candidates, goal in candidates)
-    return goal in candidates
-
-def viable2(goal, nums):
-    candidates = [nums[0]]
-    next = []
-    for x in nums[1:]:
-        for n in candidates:
-            for m in n*x, n+x, int(str(n)+str(x)):
-                if m <= goal: #and m not in next:
-                    next.append(m)
-        next, candidates = candidates, next
-        next.clear()
-    print(goal, nums, len(candidates), goal in candidates)
-    return goal in candidates
+    for x in nums[1:-1]:
+        candidates = (lambda C, x: (
+            m
+            for n in C
+            for m in combine(n,x)
+            if m < goal
+        ))(candidates, x)
+    #candidates = list(candidates); print(len(candidates))
+    x = nums[-1]
+    for n in candidates:
+        for m in combine(n,x):
+            if m == goal:
+                return True
+    return False
 
 solve(open('sample1.in'))
 solve(open('input'))