GPT-4 Conversation #1100459969792458802

[agile quail]

write c++ code for multistage graph

[radiant quail]

A multistage graph is a directed graph where nodes can be divided into stages (or layers) such that the edges of the graph emerge from one stage and terminate on the next stage. For example, in a 4-stage graph, nodes are divided into 4 sets (stages) and there are directed edges from the nodes in stage 1 to the nodes in stage 2, from stage 2 to stage 3, and from stage 3 to stage 4.

Here's a simple C++ code implementing the forward dynamic approach to find the shortest path in a multistage graph:

#include <iostream>
#include <vector>
#include <climits>

using namespace std;

const int INF = INT_MAX;

int shortestPath(vector<vector<int>> &graph, int stages) {
    int n = graph.size();
    vector<int> cost(n, INF);
    vector<int> path(stages);

    cost[n-1] = 0;

    for (int stage = stages - 2; stage >= 0; stage--) {
        for (int i = 1; i < n - 1; i++) {
            if (graph[stage][i] != INF) {
                int min_cost = INF;
                for (int k = i + 1; k < n; k++) {
                    if (graph[i][k] != INF && graph[i][k] + cost[k] < min_cost) {
                        min_cost = graph[i][k] + cost[k];
                        path[stage + 1] = k;
                    }
                }

                cost[i] = min_cost;
            }
        }
    }

    path[0] = 1;
    path[stages - 1] = n - 1;

    cout << "Shortest path: ";
    for (int i = 0; i < stages; i++) {
        cout << path[i] << " ";
    }
    cout << "\nCost: " << cost[1] << endl;

    return cost[1];
}

int main() {
    int stages = 4;

    vector<vector<int>> graph = {
        {INF,   1,   2, INF, INF, INF, INF, INF},
        {INF, INF, INF,   3,   4, INF, INF, INF},
        {INF, INF, INF, INF, INF,   5,   1, INF},
        {INF, INF, INF, INF, INF, INF, INF,   6},
        {INF, INF, INF, INF, INF, INF, INF,   4},
        {INF, INF, INF, INF, INF, INF, INF,   7},
        {INF, INF, INF, INF, INF, INF, INF,   5},
        {INF, INF, INF, INF, INF, INF, INF, INF}
    };