Create travelling_salesman_problem.py

dynamic_programming/travelling_salesman_problem.py

@@ -0,0 +1,55 @@
+#!/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
+    """
+    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")
+    # 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
+        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] = 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()