create a traveling salesman program with 50 nodes, in cpp

To create a Traveling Salesman Problem (TSP) solution with 50 nodes using C++, you can follow these steps. The TSP is a well-known optimization problem where a salesman must visit all cities exactly once and return to the starting city, minimizing the total travel distance.

We'll use a simple brute-force approach for small node counts due to its simplicity. For larger numbers of nodes (like 50), this approach will be inefficient because it has factorial time complexity. However, I'll demonstrate how you might set up the problem and implement the brute-force solution as a starting point:

1. Define the graph with distances between cities
2. Implement a function to calculate the total distance for a given path
3. Use recursion to find all permutations of paths and select the minimum one

Here's an example implementation in C++:

```cpp
#include <iostream>
#include <vector>
#include <algorithm>

// Number of nodes
const int N = 50;

// Function to compute the total distance of a path
int calculateDistance(const std::vector<std::vector<int>>& graph, const std::vector<int>& path) {
    int total_distance = 0;
    for (size_t i = 0; i < path.size() - 1; ++i) {
        total_distance += graph[path[i]][path[i + 1]];
    }
    // Return to starting point
    total_distance += graph[path.back()][path.front()];
    return total_distance;
}

// Recursive function to generate all permutations and find the shortest path
void tspUtil(const std::vector<std::vector<int>>& graph, std::vector<int>& path, bool* visited, int curr_pos, int n, int& min_cost) {
    // If all vertices are included in the path
    if (path.size() == n) {
        int currentCost = calculateDistance(graph, path);
        if (currentCost < min_cost) {
            min_cost = currentCost;
        }
        return;
    }

    for (int v = 0; v < n; v++) {
        // If this vertex is adjacent to the curr_pos and not visited
        if (!visited[v] && graph[curr_pos][v] != 0) {
            path.push_back(v);
            visited[v] = true;
            tspUtil(graph, path, visited, v, n, min_cost);
            visited[v] = false;
            path.pop_back();
        }
    }
}

// Function to solve TSP
int solveTSP(const std::vector<std::vector<int>>& graph) {
    int min_cost = INT_MAX; // Initialize minimum cost as infinity

    std::vector<int> path = {0}; // Start with the first vertex in the path
    bool* visited = new bool[N];
    for (int i = 0; i < N; ++i)
        visited[i] = false;

    visited[0] = true;
    tspUtil(graph, path, visited, 0, N, min_cost);
    delete[] visited;

    return min_cost;
}

int main() {
    // Create the graph with distances between cities
    std::vector<std::vector<int>> graph(N, std::vector<int>(N, 0));

    // Initialize your graph here with actual distances
    // For example:
    graph[0][1] = 10; // Distance from city 0 to city 1
    graph[1][0] = 10;
    graph[0][2] = 15;
    graph[2][0] = 15;
    // ... fill out the entire distance matrix ...

    std::cout << "The cost of the minimum path is: " << solveTSP(graph) << std::endl;

    return 0;
}
```

### Explanation:
1. **Graph Representation**: The graph is represented as a 2D vector where `graph[i][j]` denotes the distance between city i and j.
2. **calculateDistance Function**: This function computes the total travel cost for any given path.
3. **tspUtil Recursive Function**: It generates all permutations of paths and calculates their costs, updating the minimum cost found.
4. **solveTSP Function**: This initializes the first vertex in the path as visited and calls the recursive function to find the shortest path.

### Note:
This implementation uses a brute-force approach which is feasible only for small values of `N`. For larger values like 50 cities, more advanced algorithms such as dynamic programming, branch-and-bound, or heuristic methods (e.g., Genetic Algorithms) are required.