Finished. Now comes extensive testing.

main.py

@@ -89,18 +89,21 @@ def invariants(width, pattern, constraints=None):
     invs = []
     for sol in solve2(width, pattern, constraints):
         exp = list(expand_solution(sol, width, pattern))
-        count += 1
         if len(invs) == 0:
             invs = exp
         else:
             for i, e in enumerate(exp):
                 if invs[i] != e:
                     invs[i] = -1
-    return count, invs
+    return invs
 
 def visual(constraints):
     "returns a visual representation of constraints"
-    return "".join({1:'\N{LEFT SEVEN EIGHTHS BLOCK}', 0:'.', -1:'?'}[x] for x in constraints)
+    return "".join({
+        1:'\N{FULL BLOCK}\N{LEFT SEVEN EIGHTHS BLOCK}',
+        0:'__',
+        -1:'??'
+    }[x] for x in constraints)
 
 class Board:
     """Board
@@ -119,17 +122,17 @@ class Board:
         for i in range(self.height):
             self.rows[i] = [-1] * self.width
 
-        print("rows:")
+        # print("rows:")
-        for y in range(self.height):
+        # for y in range(self.height):
-            n, c = invariants(self.width, self.row_patterns[y])
+        #     n, c = invariants(self.width, self.row_patterns[y])
-            print(n, self.row_patterns[y], visual(c))
+        #     print(n, self.row_patterns[y], visual(c))
 
-        print("cols:")
+        # print("cols:")
-        for x in range(self.height):
+        # for x in range(self.height):
-            n, c = invariants(self.width, self.col_patterns[x])
+        #     n, c = invariants(self.width, self.col_patterns[x])
-            print(n, self.col_patterns[x], visual(c))
+        #     print(n, self.col_patterns[x], visual(c))
 
-        print(self.row(0))
+        # print(self.row(0))
 
     def col(self, i):
         """a column"""
@@ -139,37 +142,121 @@ class Board:
         """a row"""
         return self.rows[i]
 
-    def solve(self):
+    def replace_row(self, i, row):
-        min_row_index = 0
+        self.rows[i] = row
-        min_row_count = 0
+
+    def replace_col(self, i , col):
         for y in range(self.height):
-            count = 0
+            self.rows[y][i] = col[y]
+
+
+    def compute_invariants(self):
+        while True:
+            changed = False
+
+            row_sols = [0] * self.height
+            col_sols = [0] * self.width
+
+            # rows
+            for y in range(self.height):
+                invs = None; count = 0
                 for sol in solve2(self.width, self.row_patterns[y], self.row(y)):
                     count += 1
-            if count < min_row_count:
+                    exp = list(expand_solution(sol, self.width, self.row_patterns[y]))
-                min_row_count = count
+                    if invs == None:
-                min_row_index = y
+                        invs = exp
+                    for i, e in enumerate(exp):
+                        if invs[i] != e:
+                            invs[i] = -1
+                if invs != None and self.row(y) != invs:
+                    self.replace_row(y, invs)
+                    changed = True
+                row_sols[y] = count
+
+            # columns
+            for x in range(self.width):
+                invs = None; count = 0
+                for sol in solve2(self.height, self.col_patterns[x], self.col(x)):
+                    count += 1
+                    exp = list(expand_solution(sol, self.height, self.col_patterns[x]))
+                    if invs == None:
+                        invs = exp
+                    for i, e in enumerate(exp):
+                        if invs[i] != e:
+                            invs[i] = -1
+                if invs != None and self.col(x) != invs:
+                    self.replace_col(x, invs)
+                    changed = True
+                col_sols[x] = count
+
+            if not changed:
+                break
+
+        return row_sols, col_sols
+
+    def solve(self, solved=lambda x: None, depth=0):
+        row_sols, col_sols = self.compute_invariants()
+        # if depth < 2:
+        #     print("depth:", depth)
+        #     print(self)
+        #     print("row_sols:", row_sols)
+        #     print("col_sols:", col_sols)
+
+        if min(row_sols) == 0 or min(col_sols) == 0:
+            return False
+
+        if max(row_sols) == 1:
+            print("solved")
+            solved(self)
+            return True
+
+        min_row, y = min((a,b) for b,a in enumerate(row_sols) if a > 1)
+        min_col, x = min((a,b) for b,a in enumerate(col_sols) if a > 1)
+
+        if min_row < min_col:
+            for sol in solve2(self.width, self.row_patterns[y], self.row(y)):
+                b = self.copy()
+                b.replace_row(y, expand_solution(sol, self.width, self.row_patterns[y]))
+                if b.solve(solved, depth + 1):
+                    return True 
+        else:
+            for sol in solve2(self.height, self.col_patterns[x], self.col(x)):
+                b = self.copy()
+                b.replace_col(x, expand_solution(sol, self.height, self.col_patterns[x]))
+                if b.solve(solved, depth + 1):
+                    return True
 
 
-        pass
+    def copy(self):
+        newboard = Board((self.col_patterns, self.row_patterns))
+        for i in range(self.height):
+            newboard.rows[i] = self.rows[i][:]
+        return newboard
+
+    def __str__(self):
+        s = ""
+        for y in range(self.height):
+            s += visual(self.rows[y])
+            s += "\n"
+        return s
 
 if __name__ == "__main__":
 
     def draw(solution, width, pattern):
         "draws a solution"
         for s, p in zip(solution, pattern):
-            print('.' * s, end="")
+            print('__' * s, end="")
-            print('\N{LEFT SEVEN EIGHTHS BLOCK}' * p, end="")
+            print('\N{FULL BLOCK}\N{LEFT SEVEN EIGHTHS BLOCK}' * p, end="")
         print('.' * (width - sum(solution) - sum(pattern)))
 
-    width = int(sys.argv[1])
+    # width = int(sys.argv[1])
-    pattern = tuple(int(x) for x in sys.argv[2].split())
+    # pattern = tuple(int(x) for x in sys.argv[2].split())
-    constraints = [-1] * width
+    # constraints = [-1] * width
-    try:
+    # try:
-        for i, c in enumerate(sys.argv[3]):
+    #     for i, c in enumerate(sys.argv[3]):
-            constraints[i] = {'1':1, '0':0, '?':-1}[c]
+    #         constraints[i] = {'1':1, '0':0, '?':-1}[c]
-    except:
+    # except:
-        constraints = [-1] * width
+    #     constraints = [-1] * width
 
     # for solution in solve1(width, pattern):
     #     e = expand_solution(solution, width, pattern)
@@ -182,18 +269,45 @@ if __name__ == "__main__":
         rows = [[int(y) for y in x.strip().split()] for x in rows]
         return rows
 
+    def parse_constraints(s, width):
+        constraints = [-1] * width
+        for i, c in enumerate(s):
+            constraints[i] = {'1':1, '0':0, '?':-1, '.':0, '\N{LEFT SEVEN EIGHTHS BLOCK}': 1}[c]
+        return constraints
 
-    b = Board((
+    # width = 15
-        parse("""1 1 1 1 1, 1 1 1, 1 1 1 1, 1 2, 1 1 1 1, 1 1 1, 1 1 1,
+    # pattern = (1, 1, 1, 2)
-                 3 1, 1 1, 1 2 6 1, 2 1, 2 3 1, 1 1, 1 1 3 1, 2 1 1"""),
+    # constraints = parse_constraints('????????010?', width)
-        parse("""1 2, 1 1 2, 2 1 1 1 1, 3 1, 1 1 1 1, 1 2 1, 1, 1 1 1 2,
+    # for sol in solve2(width, pattern, constraints):
-                 2 2 1 1, 1 1 1 1 1, 1 2 2, 2 2, 1 1 1 1 1, 1 1 1 1, 1 1""")
+    #     draw(sol, width, pattern)
-    ))
 
-    # c = Board((
+    # b = Board((
-    #     parse("""1 5 2, 1 1 2, 1 1 2 1 2, 2 2, 2 1 1 1, 1 1 1, 1 1, 1 1 1, 2 3 1 1,
+    #     parse("1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1"),
-    #              1 2 3 1 1, 1 3 1 1, 2 1 1 1, 1 1 1 2 1, 1 1 1 2 1, 2 1"""),
+    #     parse("1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1")
-    #     parse("""1 2 1 1, 1 1 4, 2 1, 1 1 1 1 2, 1 3 1 1, 1 2, 1 1 1 1 1 1,
-    #              1 1 1 1 1 2, 1 1 2, 1 2 1 1, 3 1 4, 1 4 1, 3, 3 1 1, 1 2 1""")
     # ))
+    # b.solve(print)
+
+    # b = Board((
+    #     parse("""1 1 1 1 1, 1 1 1, 1 1 1 1, 1 2, 1 1 1 1, 1 1 1, 1 1 1,
+    #              3 1, 1 1, 1 2 6 1, 2 1, 2 3 1, 1 1, 1 1 3 1, 2 1 1"""),
+    #     parse("""1 2, 1 1 2, 2 1 1 1 1, 3 1, 1 1 1 1, 1 2 1, 1, 1 1 1 2,
+    #              2 2 1 1, 1 1 1 1 1, 1 2 2, 2 2, 1 1 1 1 1, 1 1 1 1, 1 1""")
+    # ))
+    # b.solve(print)
+
+    # b = Board((
+    #     parse("""2 4, 1 1 3 1, 6, 3 3, 3 4, 1 3 2, 3 4 1, 3 5 1 1, 12,
+    #              5 3 3, 6 4, 2 3, 1 2 2, 3 4, 3 5"""),
+    #     parse("""1 6, 2 2 4 2, 3 5 2, 11, 1 6 1, 4 1 5, 5 3 3, 10 2, 1 7 1 1, 5 1 1 1,
+    #              1 3 1, 3, 3, 1 1, 3"""),
+    # ))
+    # b.solve()
+
+    c = Board((
+        parse("""1 5 2, 1 1 2, 1 1 2 1 2, 2 2, 2 1 1 1, 1 1 1, 1 1, 1 1 1, 2 3 1 1,
+                 1 2 3 1 1, 1 3 1 1, 2 1 1 1, 1 1 1 2 1, 1 1 1 2 1, 2 1"""),
+        parse("""1 2 1 1, 1 1 4, 2 1, 1 1 1 1 2, 1 3 1 1, 1 2, 1 1 1 1 1 1,
+                 1 1 1 1 1 2, 1 1 2, 1 2 1 1, 3 1 4, 1 4 1, 3, 3 1 1, 1 2 1""")
+    ))
+    c.solve(print)