Update travelling_salesman_problem.py

Author: OmMahajan29

dynamic_programming/travelling_salesman_problem.py

@@ -5,47 +5,48 @@
 
 def tsp(distances: list[list[int]]) -> int:
     """
-    Solves the Travelling Salesman Problem (TSP) using
+    Solves the Travelling Salesman Problem (TSP) using 
     dynamic programming and bitmasking.
     Args:
-        distances: A 2D list where distances[i][j] represents the
+        distances: 2D list where distances[i][j] is the 
         distance between city i and city j.
     Returns:
-        The minimum cost to complete the tour visiting all cities.
+        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]])
+    >>> 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 of visiting all cities."""
+        """Recursively calculates the minimum cost to visit all cities."""
         if mask == visited_all:
             return distances[city][0]  # Return to start
 
-        min_cost = float("inf")
+        min_cost = float('inf')  # Large value to compare against
         for next_city in range(n):
-            if not mask & (1 << next_city):  # If next_city is unvisited
+            if not mask & (1 << next_city):  # If unvisited
                 new_cost = distances[city][next_city] + visit(
                     next_city, mask | (1 << next_city)
                 )
                 min_cost = min(min_cost, new_cost)
-        return min_cost
+        return int(min_cost)  # Ensure returning an integer
 
-    return visit(0, 1)  # Start from city 0 with only city 0 visited
+    return visit(0, 1)  # Start from city 0 with city 0 visited
 
 
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()