traveling salesman problem dynamic programming

Question

I've written a code, that gives the least cost for an array, which stores length of paths from each city to each city. I used recursion in my code. User chooses the first city from which the salesman begins his tour. The salesman has to visit each city once and come back to city which he started from. My code gives the correct cost, but I have no idea how to get the path, which gives that least cost. Should I use some extra arrays? I don't know when to add a city to the path. Any help?

void Dynamic::dynamic(Array array)
{
    int start;
    size = array.getSize();
    s = size;
    path = new int[size+1];
    
    
    
    cout << "Which city we start from?" << endl;
    cin >> start;
    int* cities = new int[size];
    for (int i=0; i<size+1; i++)
    {
        cities[i] = i;
        
    }
    
    
    
    int cost = g(array, size-1, cities, start, start, s);
    
    cout<<"Minimum cost: " << cost << endl;
    cout << "Path:" <<endl;
    
    for (int i=size; i>=0; i--)
    {
        cout << path[i] << "\t";
    }
    
    cout << "\n";
    
}

int Dynamic::g(Array & array, int level, int* tab, int city, int start, int z)
{
    if (level>0)
    {
        

        int minimum = INF;
        
        
        int position;
        bool exists = false;
        int k = z;
    
        for (int i=0; i<z; i++)
        {
            
            if (tab[i] == city)
            {
                position = i;
                exists = true;
            }
        }
        
        int* tmp;
        
    if (exists == true)
    
    {
        k = z-1;
        tmp = new int [k];
        for (int i=0; i<position; i++)
        {
            tmp[i] = tab[i];
        }
    
        for (int i=position; i<k; i++)
        {
            tmp[i] = tab[i+1];
        }
    }
    
    else
    {
        tmp = new int [k];
        for (int i=0; i<k; i++)
        {
            tmp[i] = tab[i];
        }
    }
    
        
        for (int i=0; i<k; i++)
        {
        
        
            
            int c = array[city][tmp[i]];
        
            int* t = new int [k-1];
            for(int j=0; j<i; j++)
            {
                t[j] = tmp[j];
            }           
            
            for (int j=i; j<k-1; j++)
            {
                t[j] = tmp[j+1];
            }
        
            
            int a = g(array, level-1, t, tmp[i], start, k-1);
            
            int result = c + a;
            
            if (minimum> result)
            {
                minimum = result;
                
                
                
            }
            
            
        }
        
        return minimum;
    }
    
    if (level == 0)
    {
        
        return array[city][start];
    }
}

And what is `Array`? Have you created your own `std::vector` alternative? Why? And why do you pass it by value to your `dynamic` function? — Some programmer dude, Dec 07 '21 at 09:23
class array just reads a .txt file, which stores paths from each city to each city — czesiek, Dec 07 '21 at 09:24
first line is the number of cities, and in next lines i have costs to other cities. Array is like [number_of_cities][number_of_cities] cost from a city to the same city is 0. But my code avoids risk of going to the same city again. — czesiek, Dec 07 '21 at 09:32
@czesiek You've written code that leaks memory all over the place. Use `std::vector`, not `new[]` and `delete[]`. — PaulMcKenzie, Dec 07 '21 at 09:32
But when should I add the city to the path? I think I still don't understand the recursion properly. — czesiek, Dec 07 '21 at 09:37

traveling salesman problem dynamic programming

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