Update travelling_salesman_problem.py

Author: OmMahajan29

dynamic_programming/travelling_salesman_problem.py

@@ -1,8 +1,6 @@
 #!/usr/bin/env python3
-
 from functools import lru_cache
 
-
 def tsp(distances: list[list[int]]) -> int:
     """
     Solves the Travelling Salesman Problem (TSP) using
@@ -16,25 +14,22 @@ def tsp(distances: list[list[int]]) -> int:
     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]])
-    ValueError: Distance cannot be 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]])
+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)
     def visit(city: int, mask: int) -> int:
         """Recursively calculates the minimum cost to visit all cities."""
         if mask == visited_all:
             return distances[city][0]  # Return to start
-
         min_cost = float("inf")  # Large value to compare against
         for next_city in range(n):
             if not mask & (1 << next_city):  # If unvisited
@@ -43,11 +38,8 @@ def visit(city: int, mask: int) -> int:
                 )
                 min_cost = min(min_cost, new_cost)
         return int(min_cost)  # Ensure returning an integer
-
     return visit(0, 1)  # Start from city 0 with city 0 visited
 
-
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()