Increase speed by removing symetrical solutions

magic_hexagon.py

@@ -7,21 +7,23 @@
 FLOORS = 3
 ROWS_NB = 2*FLOORS-1
 CELLS_NB = 3*FLOORS*(FLOORS-1)+1
-NUMBERS = list(range(1, CELLS_NB+1))
+NUMBERS = range(1, CELLS_NB+1)
 LINE_SUM = sum(range(1, CELLS_NB+1)) // ROWS_NB
 
 # Algo global variables
 assert FLOORS == 3
 BOARD_INDEXES_STR = """
-    00.  01.  02.
-  11.  12.  13.  03.
-10.  17.  18.  14.  04.
-  09.  16.  15.  05.
-    08.  07.  06.
+    00.  01.  03.
+  02.  13.  14.  05.
+04.  12.  18.  15.  06.
+  11.  17.  16.  07.
+    10.  09.  08.
 """
-X_LINES = [[0, 1, 2], [11, 12, 13, 3], [10, 17, 18, 14, 4], [9, 16, 15, 5], [8, 7, 6]]
-Y_LINES = [[0, 11, 10], [1, 12, 17, 9], [2, 13, 18, 16, 8], [3, 14, 15, 7], [4, 5, 6]]
-Z_LINES = [[10, 9, 8], [11, 17, 16, 7], [0, 12, 18, 15, 6], [1, 13, 14, 5], [2, 3, 4]]
+# Modified snail
+X_LINES = [[0, 1, 3], [2, 13, 14, 5], [4, 12, 18, 15, 6], [11, 17, 16, 7], [10, 9, 8]]
+Y_LINES = [[0, 2, 4], [1, 13, 12, 11], [3, 14, 18, 17, 10], [5, 15, 16, 9], [6, 7, 8]]
+Z_LINES = [[4, 11, 10], [2, 12, 17, 9], [0, 13, 18, 16, 8], [1, 14, 15, 7], [3, 5, 6]]
+
 LINES_ENDED_BY_STEP = [
     [
         line
@@ -30,6 +32,8 @@
     ] for i in range(19)
 ]
 CORNERS_EXCEPT_FIRST = {2, 4, 6, 8, 10}
+FIRST_SIDE = 1
+LAST_SIDE = 2
 
 
 def display_board(board: List[int]):
@@ -47,6 +51,7 @@ def look_for_solutions_(
 
         # Cache
         corners_tested: Set[int],
+        first_side_test: Set[int],
         start_time: float,
 ) -> None:
     """Look for solutions given board state and step to start from
@@ -63,16 +68,20 @@ def look_for_solutions_(
         start_time i the time in secs when the search has started
     """
     if not remaining_numbers:
-        print(f'Solution found in {time() - start_time}s:')
+        print(f'Solution found in {(time() - start_time)*1000:.1f}ms')
         display_board(board)
         return
 
     for _ in range(CELLS_NB-step):
         # If step is on corner and number has already been tested as a corner, skip it
         # # Avoid rotations this way
-        number = remaining_numbers.pop()
-        if number in corners_tested and step in CORNERS_EXCEPT_FIRST:
-            remaining_numbers.appendleft(number)
+        number = remaining_numbers.popleft()
+        if step in CORNERS_EXCEPT_FIRST and number in corners_tested:
+            remaining_numbers.append(number)
+            continue
+        # Remove symetrical solutions
+        if step == LAST_SIDE and number in first_side_test:
+            remaining_numbers.append(number)
             continue
 
         # Add number to board and get next remaining numbers
@@ -93,14 +102,18 @@ def look_for_solutions_(
                 remaining_numbers,
                 step+1,
                 corners_tested=corners_tested,
+                first_side_test=first_side_test,
                 start_time=start_time,
             )
 
         # Add the removed number for the next iteration
-        remaining_numbers.appendleft(number)
+        remaining_numbers.append(number)
         # Number has been fully explored as first corner
         if step == 0:
             corners_tested.add(number)
+            first_side_test=set()
+        if step == FIRST_SIDE:
+            first_side_test.add(number)
 
     return
 
@@ -112,9 +125,10 @@ def look_for_solutions():
         remaining_numbers=deque(NUMBERS),
         step=0,
         corners_tested=set(),
+        first_side_test=set(),
         start_time=start,
     )
-    print(f'Full run ended in {time()-start}s')
+    print(f'Full run ended in {(time() - start)*1000:.1f}ms')
 
 
 if __name__ == '__main__':