Update travelling_salesman_problem.py

dynamic_programming/travelling_salesman_problem.py

@@ -2,33 +2,28 @@
 
 from functools import lru_cache
 
-
 def tsp(distances: list[list[int]]) -> int:
     """
-    Solves the Travelling Salesman Problem (TSP) using dynamic programming and bitmasking.
-
+    Solves the Travelling Salesman Problem (TSP) using 
+    dynamic programming and bitmasking.
     Args:
-        distances: A 2D list where distances[i][j] represents the distance between city i and city j.
-
+        distances: A 2D list where distances[i][j] represents the 
+        distance between city i and city j.
     Returns:
         The minimum cost to complete the tour visiting all cities.
-
     Raises:
         ValueError: If any distance is negative.
 
     >>> tsp([[0, 10, 15, 20], [10, 0, 35, 25], [15, 35, 0, 30], [20, 25, 30, 0]])
     80
     >>> tsp([[0, 29, 20, 21], [29, 0, 15, 17], [20, 15, 0, 28], [21, 17, 28, 0]])
     69
-    >>> tsp([[0, 10, -15, 20], [10, 0, 35, 25], [15, 35, 0, 30], [20, 25, 30, 0]])  # doctest: +ELLIPSIS
-    Traceback (most recent call last):
-        ...
+    >>> tsp([[0, 10, -15, 20], [10, 0, 35, 25], [15, 35, 0, 30], [20, 25, 30, 0]])
     ValueError: Distance cannot be negative
     """
     n = len(distances)
     if any(distances[i][j] < 0 for i in range(n) for j in range(n)):
         raise ValueError("Distance cannot be negative")
-
     visited_all = (1 << n) - 1
 
     @lru_cache(None)
@@ -45,11 +40,7 @@ def visit(city: int, mask: int) -> int:
                 )
                 min_cost = min(min_cost, new_cost)
         return min_cost
-
     return visit(0, 1)  # Start from city 0 with only city 0 visited
-
-
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()