Update travelling_salesman_problem.py

Author: OmMahajan29

dynamic_programming/travelling_salesman_problem.py

@@ -1,55 +1,56 @@
 #!/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.
+        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]])
+
+>>> 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]])
+>>> 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]])  
+# 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)):
         raise ValueError("Distance cannot be negative")
 
-    # Create a memoization table
+    # Memoization table
     memo = [[-1] * (1 << n) for _ in range(n)]
-    visited_all = (1 << n) - 1
+    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 start
+            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 = 10**9  # Use a large integer instead of float('inf')
+
+        min_cost = float('inf')  # Use infinity for initial comparison
         for next_city in range(n):
-            if not mask & (1 << next_city):  # If 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)
         memo[city][mask] = min_cost  # Store result in the memoization table
         return min_cost
-
-    return visit(0, 1)  # Start from city 0 with city 0 visited
-
+    return visit(0, 1)  # Start from city 0 with only city 0 visited
 
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()