用c++解决pipeline system consists of N transfer station, some of which are connected by pipelines. For each of M pipelines the numbers of stations A[i] and B[i], which are connected by this pipeline, and its profitability C[i] are known. A profitability of a pipeline is an amount of dollars, which will be daily yielded in taxes by transferring the gas through this pipeline. Each two stations are connected by not more than one pipeline. The system was built by Soviet engineers, who knew exactly, that the gas was transferred from Ukrainian gas fields to Siberia and not the reverse. That is why the pipelines are unidirectional, i.e. each pipeline allows gas transfer from the station number A[i] to the station number B[i] only. More over, if it is possible to transfer the gas from the station X to the station Y (perhaps, through some intermediate stations), then the reverse transfer from Y to X is impossible. It is known that the gas arrives to the starting station number S and should be dispatched to the buyers on the final station number F. The President ordered the Government to find a route (i.e. a linear sequence of stations which are connected by pipelines) to transfer the gas from the starting to the final station. A profitability of this route should be maximal. A profitability of a route is a total profitability of its pipelines. Unfortunately, the President did not consider that some pipelines ceased to exist long ago, and, as a result, the gas transfer between the starting and the final stations may appear to be impossible... Input The first line contains the integer numbers N (2 ≤ N ≤ 500) and M (0 ≤ M ≤ 124750). Each of the next M lines contains the integer numbers A[i], B[i] (1 ≤ A[i], B[i] ≤ N) and C[i] (1 ≤ C[i] ≤ 10000) for the corresponding pipeline. The last line contains the integer numbers S and F (1 ≤ S, F ≤ N; S ≠ F). Output If the desired route exists, you should output its profitability. Otherwise you should output "No solution".

这是一个经典的图论问题，可以使用Dijkstra算法或Bellman-Ford算法解决。以下是使用Dijkstra算法的步骤：

1. 定义一个数组dist，其中dist[i]表示从起点S到第i个站点的最大收益。

2. 初始化dist数组，将起点S的dist[S]赋值为0，其他点的dist[i]赋值为负无穷。

3. 定义一个优先队列pq，将起点S加入队列中。

4. 当pq非空时，取出队列中dist最小的站点u。

5. 对于每个与站点u相邻的站点v，如果通过从u到v的边可以获得更高的收益，则更新dist[v]为dist[u]+边(u,v)的收益，并将v加入队列pq中。

6. 重复步骤4和步骤5，直到队列pq为空。

7. 最终dist[F]即为最大收益。如果dist[F]为负无穷，则表示从起点S无法到达终点F，输出"No solution"。

以下是使用Dijkstra算法解决此问题的C++代码实现：

#include <iostream>
#include <vector>
#include <queue>
using namespace std;

const int INF = 0x3f3f3f3f;

int main()
{
    int n, m, s, f;
    cin >> n >> m;
    vector<vector<pair<int, int>>> g(n + 1);
    for (int i = 0; i < m; i++)
    {
        int a, b, c;
        cin >> a >> b >> c;
        g[a].push_back({b, c});
    }
    cin >> s >> f;
    vector<int> dist(n + 1, -INF);
    dist[s] = 0;
    priority_queue<pair<int, int>> pq;
    pq.push({0, s});
    while (!pq.empty())
    {
        int u = pq.top().second;
        pq.pop();
        for (auto p : g[u])
        {
            int v = p.first;
            int w = p.second;
            if (dist[v] < dist[u] + w)
            {
                dist[v] = dist[u] + w;
                pq.push({dist[v], v});
            }
        }
    }
    if (dist[f] == -INF)
        cout << "No solution" << endl;
    else
        cout << dist[f] << endl;
    return 0;
}