Update travelling_salesman_problem.py

Author: OmMahajan29

dynamic_programming/travelling_salesman_problem.py

@@ -1,30 +1,31 @@
 #!/usr/bin/env python3
 
-
 def tsp(distances: list[list[int]]) -> int:
     """
-        Solves the Travelling Salesman Problem (TSP)
-        using dynamic programming and bitmasking.
-
-        Args:
-            distances: 2D list where distances[i][j]
-            is the distance between city i and city j.
-
-        Returns:
-            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):
-            ...
-        ValueError: Distance cannot be negative
+    Solves the Travelling Salesman Problem (TSP)
+    using dynamic programming and bitmasking.
+
+    Args:
+        distances: 2D list where distances[i][j]
+        is the distance between city i and city j.
+
+    Returns:
+        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):
+        ...
+    ValueError: Distance cannot be negative
     """
     n = len(distances)
     if any(distances[i][j] < 0 for i in range(n) for j in range(n)):
@@ -40,21 +41,16 @@ def visit(city: int, mask: int) -> int:
             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(
                     next_city, mask | (1 << next_city)
                 )
                 min_cost = min(min_cost, new_cost)
-        memo[city][mask] = min_cost  # Store result in the memoization table
-        return min_cost
-
-    return visit(0, 1)  # Start from city 0 with only city 0 visited
-
-
+        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
-
     doctest.testmod()