Create traveling_salesman.py

src/python/traveling_salesman.py

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+from itertools import permutations
+
+def calculate_total_distance(path, distances):
+    """
+    Calculate the total distance of a path through cities.
+
+    Args:
+        path (list of int): A list representing the order of cities to visit.
+        distances (list of lists of int): A distance matrix between cities.
+
+    Returns:
+        int: The total distance of the path.
+
+    Example:
+    >>> distances = [[0, 2, 9, 10], [1, 0, 6, 4], [15, 7, 0, 8], [6, 3, 12, 0]]
+    >>> calculate_total_distance([0, 1, 2, 3, 0], distances)
+    21
+    """
+    total_distance = 0
+    for i in range(len(path) - 1):
+        total_distance += distances[path[i]][path[i + 1]]
+    total_distance += distances[path[-1]][path[0]]
+    return total_distance
+
+def traveling_salesman_bruteforce(distances):
+    """
+    Find the shortest path through cities using brute force.
+
+    Args:
+        distances (list of lists of int): A distance matrix between cities.
+
+    Returns:
+        tuple: A tuple containing the shortest path (list of int) and the shortest distance (int).
+
+    Example:
+    >>> distances = [[0, 2, 9, 10], [1, 0, 6, 4], [15, 7, 0, 8], [6, 3, 12, 0]]
+    >>> traveling_salesman_bruteforce(distances)
+    ([0, 1, 3, 2], 21)
+    """
+    num_cities = len(distances)
+    all_cities = list(range(num_cities))
+    shortest_path = None
+    shortest_distance = float('inf')
+
+    for path in permutations(all_cities):
+        distance = calculate_total_distance(path, distances)
+        if distance < shortest_distance:
+            shortest_distance = distance
+            shortest_path = path
+
+    return shortest_path, shortest_distance
+
+def create_distance_matrix(num_cities):
+    """
+    Create a distance matrix for a given number of cities.
+
+    Args:
+        num_cities (int): The number of cities.
+
+    Returns:
+        list of lists of int: A distance matrix between cities.
+
+    Example:
+    >>> create_distance_matrix(4)
+    [[0, 2, 9, 10], [2, 0, 6, 4], [9, 6, 0, 8], [10, 4, 8, 0]]
+    """
+    distances = []
+    for i in range(num_cities):
+        row = []
+        for j in range(num_cities):
+            if i == j:
+                row.append(0)
+            elif j > i:
+                distance = int(input(f"Enter distance between City {i + 1} and City {j + 1}: "))
+                row.append(distance)
+            else:
+                row.append(distances[j][i])
+        distances.append(row)
+    return distances
+
+def print_distance_matrix(distances):
+    """
+    Print the distance matrix.
+
+    Args:
+        distances (list of lists of int): A distance matrix between cities.
+
+    Example:
+    >>> distances = [[0, 2, 9, 10], [1, 0, 6, 4], [15, 7, 0, 8], [6, 3, 12, 0]]
+    >>> print_distance_matrix(distances)
+    Distance Matrix:
+    [0, 2, 9, 10]
+    [2, 0, 6, 4]
+    [9, 6, 0, 8]
+    [10, 4, 8, 0]
+    """
+    print("Distance Matrix:")
+    for row in distances:
+        print(row)
+
+def print_city_path(path):
+    """
+    Print the shortest path through cities.
+
+    Args:
+        path (list of int): A list representing the order of cities to visit.
+
+    Example:
+    >>> print_city_path([0, 1, 3, 2])
+    Shortest Path: City 1 -> City 2 -> City 4 -> City 3
+    """
+    city_path = [f"City {city + 1}" for city in path]
+    print("Shortest Path:", " -> ".join(city_path))
+
+def main_menu():
+    """
+    Display a menu for the traveling salesman problem and handle user input.
+
+    Example:
+    >>> # This function interacts with the user, so no specific doctests are provided.
+    >>> # You can run this function manually to test the menu functionality.
+    >>> main_menu()
+    """
+    while True:
+        print("\nMenu:")
+        print("1. Create a distance matrix")
+        print("2. Find the shortest path")
+        print("3. Exit")
+
+        choice = input("Enter your choice: ")
+
+        if choice == '1':
+            num_cities = int(input("Enter the number of cities: "))
+            distances = create_distance_matrix(num_cities)
+            print_distance_matrix(distances)
+        elif choice == '2':
+            if 'distances' in locals():
+                shortest_path, shortest_distance = traveling_salesman_bruteforce(distances)
+                print_city_path(shortest_path)
+                print("Shortest Distance:", shortest_distance)
+            else:
+                print("Please create a distance matrix first.")
+        elif choice == '3':
+            print("Goodbye!")
+            break
+        else:
+            print("Invalid choice. Please select a valid option.")
+
+if __name__ == "__main__":
+    main_menu()