TSP_test

#include <iostream>
#include <vector>
#include <limits>
#include <queue>
#include <algorithm>

using namespace std;

const int INF = numeric_limits<int>::max();

struct Edge {
    int from, to, weight;
};

struct Node {
    vector<Edge> edges;
    int cost;
    int degree[100]; // Max |V| assumed to be 100
    int numEdges;

    Node() : cost(0), numEdges(0) {
        fill(degree, degree + 100, 0);
    }
};

int n; // number of vertices
int maxDegree;
int weightMatrix[100][100]; // Symmetric weight matrix

// Function to calculate the lower bound of the cost
int calculateLowerBound(Node& node) {
    // Here you can implement Prim's or Kruskal's algorithm to find the min spanning tree
    // For simplicity, let's return a dummy value
    return 0; // Replace this with actual logic
}

// Function to perform the branch and bound
void branchAndBound(Node& currentNode, int& bestCost) {
    // Check if we have a complete solution
    if (currentNode.numEdges == n - 1) {
        bestCost = min(bestCost, currentNode.cost);
        return;
    }

    for (int i = 0; i < n; ++i) {
        for (int j = i + 1; j < n; ++j) {
            // Check if we can add the edge (i, j)
            if (weightMatrix[i][j] != INF) {
                // Check degree constraint
                if (currentNode.degree[i] < maxDegree && currentNode.degree[j] < maxDegree) {
                    Node newNode = currentNode;
                    newNode.cost += weightMatrix[i][j];
                    newNode.edges.push_back({ i, j, weightMatrix[i][j] });
                    newNode.degree[i]++;
                    newNode.degree[j]++;
                    newNode.numEdges++;

                    int lowerBound = calculateLowerBound(newNode);
                    if (newNode.cost + lowerBound < bestCost) {
                        branchAndBound(newNode, bestCost);
                    }
                }
            }
        }
    }
}

int main() {
    // Initialize the weight matrix and maxDegree
    // For example, let's assume we have 4 vertices and a maximum degree of 2
    n = 4;
    maxDegree = 2;

    // Sample weight matrix (symmetric)
    weightMatrix[0][1] = 10;
    weightMatrix[0][2] = 15;
    weightMatrix[0][3] = 20;
    weightMatrix[1][2] = 35;
    weightMatrix[1][3] = 25;
    weightMatrix[2][3] = 30;

    // Fill the rest of the matrix with INF
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            if (i != j && weightMatrix[i][j] == 0) {
                weightMatrix[i][j] = INF;
            }
        }
    }

    Node initialNode;
    int bestCost = INF;

    branchAndBound(initialNode, bestCost);

    cout << "Minimum cost of the tree: " << bestCost << endl;

    return 0;
}