Algorithm-Analysis-Design-Lab/Traveling_Salesperson(branch&bound).cpp at main · Hazrat-Ali9/Algorithm-Analysis-Design-Lab · GitHub

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#include <bits/stdc++.h>
using namespace std;
const int N = 4;

int final_path[N+1];

bool visited[N];

int final_res = INT_MAX;

class tsp
{

    public:
    void copyToFinal(int curr_path[]);
    int firstMin(int adj[N][N], int i);
    int secondMin(int adj[N][N], int i);
    void TSPRec(int adj[N][N], int curr_bound, int curr_weight,
            int level, int curr_path[]);
    void TSP(int adj[N][N]);
};

void tsp::copyToFinal(int curr_path[])
{
    for (int i=0; i<N; i++)
        final_path[i] = curr_path[i];
    final_path[N] = curr_path[0];
}

int tsp::firstMin(int adj[N][N], int i)
{
    int min = INT_MAX;
    for (int k=0; k<N; k++)
        if (adj[i][k]<min && i != k)
            min = adj[i][k];
    return min;
}

int tsp::secondMin(int adj[N][N], int i)
{
    int first = INT_MAX, second = INT_MAX;
    for (int j=0; j<N; j++)
    {
        if (i == j)
            continue;

        if (adj[i][j] <= first)
        {
            second = first;
            first = adj[i][j];
        }
        else if (adj[i][j] <= second &&
                 adj[i][j] != first)
            second = adj[i][j];
    }
    return second;
}

void tsp::TSPRec(int adj[N][N], int curr_bound, int curr_weight,
            int level, int curr_path[])
{
    if (level==N)
    {
        if (adj[curr_path[level-1]][curr_path[0]] != 0)
        {
            int curr_res = curr_weight +
                    adj[curr_path[level-1]][curr_path[0]];

            if (curr_res < final_res)
            {
                copyToFinal(curr_path);
                final_res = curr_res;
            }
        }
        return;
    }

    for (int i=0; i<N; i++)
    {
        if (adj[curr_path[level-1]][i] != 0 &&
            visited[i] == false)
        {
            int temp = curr_bound;
            curr_weight += adj[curr_path[level-1]][i];

            if (level==1)
              curr_bound -= ((firstMin(adj, curr_path[level-1]) +
                             firstMin(adj, i))/2);
            else
              curr_bound -= ((secondMin(adj, curr_path[level-1]) +
                             firstMin(adj, i))/2);

            if (curr_bound + curr_weight < final_res)
            {
                curr_path[level] = i;
                visited[i] = true;

                TSPRec(adj, curr_bound, curr_weight, level+1,
                       curr_path);
            }

            curr_weight -= adj[curr_path[level-1]][i];
            curr_bound = temp;

            memset(visited, false, sizeof(visited));
            for (int j=0; j<=level-1; j++)
                visited[curr_path[j]] = true;
        }
    }
}

void tsp::TSP(int adj[N][N])
{
    int curr_path[N+1];

    int curr_bound = 0;
    memset(curr_path, -1, sizeof(curr_path));
    memset(visited, 0, sizeof(curr_path));

    for (int i=0; i<N; i++)
        curr_bound += (firstMin(adj, i) +
                       secondMin(adj, i));

    curr_bound = (curr_bound&1)? curr_bound/2 + 1 :
                                 curr_bound/2;

    visited[0] = true;
    curr_path[0] = 0;

    TSPRec(adj, curr_bound, 0, 1, curr_path);
}

int main()
{
    int adj[N][N] = { {0, 10, 15, 20},
        {10, 0, 35, 25},
        {15, 35, 0, 30},
        {20, 25, 30, 0}
    };

    tsp T;

    T.TSP(adj);

    printf("Minimum cost : %d\n", final_res);
    printf("Path Taken : ");
    for (int i=0; i<=N; i++)
        printf("%d ", final_path[i]);

    return 0;
}

/*OUTPUT
D:\Data\Downloads\DAA Codes>g++ tsp.cpp
D:\Data\Downloads\DAA Codes>a
Minimum cost : 80
Path Taken : 0 1 3 2 0
*/