Hello Codeforces. I have just recently joined a contest at my school. In that contest, there was a problem requiring counting the number of shortest paths from a vertex s to every other vertex in a directed weighted graph. I have implemented my idea and tested it a bit so I had a strong belief that my code was correct. In the end, it turned out that the code was wrong. The contest gave me only one submission for each problem so I didn't have a chance to fix it during the contest. I have tried to find my mistakes in the code at home but I found nothing. Here is the code similar to what I submitted during the contest.

void Dijkstra (int s)
{
    // dist[i] is the minimum distance from s to i
    // num[i] is the number of shortest paths from s to i
    for (int i=1; i<=n; i++)
    {
        dist[i]=inf;
        num[i]=0;
    }
    dist[s]=0;
    priority_queue<pair<int,int>, vector<pair<int,int> >, greater<pair<int,int> > > pq;
    pq.push({0,s});
    num[s]=1;
    while (!pq.empty())
    {
        pair<int,int> tmp=pq.top();
        pq.pop();
        int u=tmp.second;
        for (auto g:adj[u])
        {
            // v is the adjacent vertex with u
            // w is the weight of the edge u-v
            int v=g.second;
            int w=g.first;
            if (dist[v]==dist[u]+w)
            {
                num[v]+=num[u];
            }
            if (dist[v]>dist[u]+w)
            {
                dist[v]=dist[u]+w;
                num[v]=num[u];
                pq.push({dist[v],v});
            }
        }
    }
}

Can anyone help me point out the mistake in the algorithm or maybe this was not the incorrect part in my initial code? I would be so grateful if you can provide a link to another problem that also requires counting the number of shortest paths so that I can test the code by myself. Thanks for reading and have a good day.