App6_MST_Kruskal.py

# this MST approach (Kruskal's algorithm)

import math

def euclidean_distance(x1, y1, x2, y2):
    return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

def orienteering_problem_kruskal(input_file, output_file):
    # Read input from the file
    with open(input_file, 'r') as file:
        lines = file.readlines()

    # Parse the input
    Tmax, P = map(int, lines[0].split())
    points = []
    for line in lines[1:]:
        x, y, score = map(float, line.split())
        points.append((x, y, score))

    # Calculate the distance matrix
    n = len(points)
    distance_matrix = [[0] * n for _ in range(n)]
    for i in range(n):
        for j in range(i+1, n):  # Utilize symmetry of the distance matrix
            dist = euclidean_distance(
                points[i][0], points[i][1], points[j][0], points[j][1])
            distance_matrix[i][j] = dist
            distance_matrix[j][i] = dist

    # Create the edges list with "score - cost" values
    edges = []
    for i in range(n):
        for j in range(i+1, n):
            edge_score = points[j][2] - distance_matrix[i][j]
            edges.append((i, j, edge_score))

    # Sort the edges list by the "score - cost" value in descending order
    edges.sort(key=lambda x: x[2], reverse=True)

    # Initialize the parent array for Union-Find
    parent = [i for i in range(n)]

    # Find the parent of a node using Union-Find algorithm
    def find_parent(node):
        if parent[node] == node:
            return node
        parent[node] = find_parent(parent[node])
        return parent[node]

    # Perform Kruskal's algorithm
    mst = []
    total_profit = 0
    total_cost = 0
    edge_count = 0
    for edge in edges:
        u, v, _ = edge
        parent_u = find_parent(u)
        parent_v = find_parent(v)
        if parent_u != parent_v and total_cost + distance_matrix[u][v] <= Tmax:
            parent[parent_u] = parent_v
            mst.append(edge)
            total_profit += points[v][2]
            total_cost += distance_matrix[u][v]
            edge_count += 1
            if edge_count == n - 1:
                break

    # Write the output to the file
    with open(output_file, 'w') as file:
        file.write("MST Edges:\n")
        for edge in mst:
            file.write(f"{edge[0]+1} - {edge[1]+1}\n")
        file.write("\n")
        file.write(f"Total Profit: {total_profit}\n")
        file.write(f"Total Cost: {total_cost}")

    print("MST Edges:")
    for edge in mst:
        print(f"{edge[0]+1} - {edge[1]+1}")
    print(f"Total Profit: {total_profit}")
    print(f"Total Cost: {total_cost}")

# Usage example
input_file = 'Dataset/set_64_1_80.txt'
output_file = 'Results/set_64_1_80_App6.txt'
orienteering_problem_kruskal(input_file, output_file)