Solve a row with constraints

main.py

@@ -3,13 +3,12 @@
 from itertools import combinations_with_replacement
 
 
-def row_solutions(width, pattern):
+def solve1(width, pattern):
     """
     This yields a tuple for each possible layout of
     pattern inside the row. The tuple elements are the
-    amount of cells that must be inserted before each
-    block in pattern. The tuple doesn't include the
-    number of cells at the end of the row since that's
+    gaps before each block in pattern.
+    The tuple doesn't include the last gap, since that's
     just: width - sum(sol) - sum(pattern) 
     """
     spaces = width - (sum(pattern) + len(pattern) - 1)
@@ -31,7 +30,7 @@ def expand_solution(solution, width, pattern):
 
 def matches(expanded_solution, constraints):
     """
-    solution is a tuple of spaces, the output of row_solutions
+    solution is a tuple of spaces, the output of solve1
     constraints is a tuple of values from 1, 0 and -1, that
     mean:
          0 -> OFF
@@ -46,6 +45,41 @@ def matches(expanded_solution, constraints):
     return True
 
 
+def solve2(width, pattern, constraints=None):
+    """
+    @width: int
+    @pattern: sequence of ints
+    @constraints: optional list of length width containing 1,0,-1 as elements
+
+    Does the same as solve1, but takes constraints
+    in consideration to be faster than solve1 + matches 
+    """
+    
+    if len(pattern) == 0:
+        return tuple()
+
+    if constraints is None:
+        constraints = [-1] * width
+    
+    p = pattern[0]
+
+    # the first gap can go from 0 to the following, inclusive
+    maxgap = width - sum(pattern[1:]) - (len(pattern) - 1) - p
+
+    for gap in range(maxgap + 1):
+        e = expand_solution((gap,), gap + p + 1, (p,))
+        if not matches(e, constraints[:gap + p + 1]):
+            continue
+        if len(pattern) == 1:
+            yield (gap,)
+            continue
+        subwidth = width - gap - p - 1
+        subpattern = pattern[1:]
+        subconstraints = constraints[-subwidth:] 
+        for s in solve2(subwidth, subpattern, subconstraints):
+            yield (gap,s[0]+1) + s[1:]
+
+
 if __name__ == "__main__":
     
     import sys
@@ -53,7 +87,7 @@ if __name__ == "__main__":
     def draw(solution, width, pattern):
         for s,p in zip(solution, pattern):
             print('.' * s, end="")
-            print('\N{FULL BLOCK}' * p, end="")
+            print('\N{LEFT SEVEN EIGHTHS BLOCK}' * p, end="")
         print('.' * (width - sum(solution) - sum(pattern)))
 
     width = int(sys.argv[1])
@@ -63,10 +97,12 @@ if __name__ == "__main__":
         for i,c in enumerate(sys.argv[3]):
             constraints[i]= {'1':1, '0':0, '?':-1}[c]
     except:
-        print(sys.exc_info())
         constraints = [-1] * width
 
-    for solution in row_solutions(width, pattern):
-        e = expand_solution(solution, width, pattern)
-        if matches(e, constraints):
-            draw(solution, width, pattern)
+    # for solution in solve1(width, pattern):
+    #     e = expand_solution(solution, width, pattern)
+    #     if matches(e, constraints):
+    #         draw(solution, width, pattern)
+
+    for sol in solve2(width, pattern, constraints):
+        draw(sol, width, pattern)