Update travelling_salesman_problem.py

Author: OmMahajan29

dynamic_programming/travelling_salesman_problem.py

@@ -1,54 +1,55 @@
 #!/usr/bin/env python3
 
-from functools import lru_cache
-
-
 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]])
+    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]])
+    >>> 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
+        ...
+    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
+    memo = [[-1] * (1 << n) for _ in range(n)]
     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
+        if memo[city][mask] != -1:  # Return cached result if exists
+            return memo[city][mask]
+
+        min_cost = float('inf')  # Large value to compare against
         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)
-        return int(min_cost)  # Ensure returning an integer
-
+        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
-
-
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()