import numpy as np

def traveling_salesman_edge_insertion(distance_matrix):
    """
    Solves the traveling salesman problem using the edge insertion technique.

    Args:
        distance_matrix: A numpy array representing the distances between cities.

    Returns:
        A list representing the optimal tour, and the total distance of the tour.
    """

    num_cities = distance_matrix.shape[0]

    # 1. Sort edges in ascending order (excluding zero distances)
    sorted_edges = np.argsort(distance_matrix[distance_matrix > 0])

    # 2. Initialize tour with the shortest edge
    tour = [np.unravel_index(sorted_edges[0], distance_matrix.shape)]

    # 3. Iterate until all edges have been processed and tour length stabilizes
    current_best_length = np.inf  # Track best achieved tour length
    improved_length = -1  # Flag for improvement in current iteration

    while improved_length < current_best_length:
        improved_length = current_best_length  # Reset improvement flag

        # Loop through remaining edges, starting from the second-shortest
        for i in range(1, len(sorted_edges)):
            edge_i, edge_j = np.unravel_index(sorted_edges[i], distance_matrix.shape)

            # Skip if either node is already in the tour (avoids cycles and repetitions)
            if not (edge_i in tour) and not (edge_j in tour):
                # Try inserting the edge at each possible position
                for k in range(len(tour) + 1):
                    new_tour = tour[:k] + [edge_j] + tour[k:]  # Insert edge_j at position k
                    new_length = calculate_path_length(distance_matrix, new_tour)

                    # If new tour length is shorter, update tour and flag improvement
                    if new_length < current_best_length:
                        tour = new_tour
                        current_best_length = new_length
                        improved_length = new_length
                        break  # Exit inner loop if improvement found

    return tour, current_best_length

# ... (rest of the code remains unchanged)

def calculate_path_length(distance_matrix, tour):
    """Calculates the total distance of a given tour."""
    total_distance = 0
    for i in range(len(tour) - 1):
        total_distance += distance_matrix[tour[i], tour[i + 1]]
    return total_distance

# Example usage
output_matrix = np.array([
    [0, 2, 9, 10, 12],
    [2, 0, 29, 8, 6],
    [5, 4, 0, 3, 9],
    [10, 15, 9, 0, 1],
    [7, 6, 9, 1, 0]
])

tour, total_distance = traveling_salesman_edge_insertion(output_matrix)

print("Tour:", tour)
print("Total distance:", total_distance)
by

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About Python

Python is a very popular general-purpose programming language which was created by Guido van Rossum, and released in 1991. It is very popular for web development and you can build almost anything like mobile apps, web apps, tools, data analytics, machine learning etc. It is designed to be simple and easy like english language. It's is highly productive and efficient making it a very popular language.

Tutorial & Syntax help

Loops

1. If-Else:

When ever you want to perform a set of operations based on a condition IF-ELSE is used.

if conditional-expression
    #code
elif conditional-expression
    #code
else:
    #code

Note:

Indentation is very important in Python, make sure the indentation is followed correctly

2. For:

For loop is used to iterate over arrays(list, tuple, set, dictionary) or strings.

Example:

mylist=("Iphone","Pixel","Samsung")
for i in mylist:
    print(i)

3. While:

While is also used to iterate a set of statements based on a condition. Usually while is preferred when number of iterations are not known in advance.

while condition  
    #code

Collections

There are four types of collections in Python.

1. List:

List is a collection which is ordered and can be changed. Lists are specified in square brackets.

Example:

mylist=["iPhone","Pixel","Samsung"]
print(mylist)

2. Tuple:

Tuple is a collection which is ordered and can not be changed. Tuples are specified in round brackets.

Example:

myTuple=("iPhone","Pixel","Samsung")
print(myTuple)

Below throws an error if you assign another value to tuple again.

myTuple=("iPhone","Pixel","Samsung")
print(myTuple)
myTuple[1]="onePlus"
print(myTuple)

3. Set:

Set is a collection which is unordered and unindexed. Sets are specified in curly brackets.

Example:

myset = {"iPhone","Pixel","Samsung"}
print(myset)

4. Dictionary:

Dictionary is a collection of key value pairs which is unordered, can be changed, and indexed. They are written in curly brackets with key - value pairs.

Example:

mydict = {
    "brand" :"iPhone",
    "model": "iPhone 11"
}
print(mydict)

Supported Libraries

Following are the libraries supported by OneCompiler's Python compiler

NameDescription
NumPyNumPy python library helps users to work on arrays with ease
SciPySciPy is a scientific computation library which depends on NumPy for convenient and fast N-dimensional array manipulation
SKLearn/Scikit-learnScikit-learn or Scikit-learn is the most useful library for machine learning in Python
PandasPandas is the most efficient Python library for data manipulation and analysis
DOcplexDOcplex is IBM Decision Optimization CPLEX Modeling for Python, is a library composed of Mathematical Programming Modeling and Constraint Programming Modeling