[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

dynamic_programming/travelling_salesman_problem.py

@@ -1,5 +1,6 @@
 #!/usr/bin/env python3
 
+
 def tsp(distances: list[list[int]]) -> int:
     """
     Solves the Travelling Salesman Problem (TSP)
@@ -8,7 +9,7 @@ def tsp(distances: list[list[int]]) -> int:
         distances: 2D list where distances[i][j]
         is the distance between city i and city j.
     Returns:
-        Minimum cost to complete the 
+        Minimum cost to complete the
         tour visiting all cities.
     Raises:
         ValueError: If any distance is negative.
@@ -31,14 +32,15 @@ def tsp(distances: list[list[int]]) -> int:
     # Memoization table
     memo = [[-1] * (1 << n) for _ in range(n)]
     visited_all = (1 << n) - 1  # All cities visited mask
+
     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 the starting city
 
         if memo[city][mask] != -1:  # Return cached result if exists
             return memo[city][mask]
-        min_cost = float('inf')  # Use infinity for initial comparison
+        min_cost = float("inf")  # Use infinity for initial comparison
         for next_city in range(n):
             if not (mask & (1 << next_city)):  # If unvisited
                 new_cost = distances[city][next_city] + visit(
@@ -47,9 +49,13 @@ def visit(city: int, mask: int) -> int:
                 min_cost = min(min_cost, new_cost)
         memo[city][mask] = int(min_cost)  # Store result as an integer
         return memo[city][mask]  # Return the cached result
+
     return visit(0, 1)  # Start from city 0 with city 0 visited
+
+
 if __name__ == "__main__":
     import doctest
+
     try:
         doctest.testmod()
     except Exception as e: