Performance of Dijkstra's algorithm implementation

Question

Below is an implementation of Dijkstra\'s algorithm I wrote from the pseudocode in the Wikipedia article. For a graph with about 40 000 nodes and 80 000 edges, it takes 3 o

Answer 1

There are several things you can improve on this:

• implementing the priority queue with sort and erase adds a factor of |E| to the runtime - use the heap functions of the STL to get a log(N) insertion and removal into the queue.
• do not put all the nodes in the queue at once but only those where you have discovered a path (which may or may not be the optimal, as you can find an indirect path through nodes in the queue).
• creating objects for every node creates unneccessary memory fragmentation. If you care about squeezing out the last 5-10%, you could think about a solution to represent the incidence matrix and other information directly as arrays.

Answer 2

Use priority_queue.

My Dijkstra implementation:

struct edge
{
    int v,w;
    edge(int _w,int _v):w(_w),v(_v){}
};
vector<vector<edge> > g;
enum color {white,gray,black};
vector<int> dijkstra(int s)
{
    int n=g.size();
    vector<int> d(n,-1);
    vector<color> c(n,white);
    d[s]=0;
    c[s]=gray;
    priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > > q; // declare priority_queue
    q.push(make_pair(d[s],s)); //push starting vertex
    while(!q.empty())
    {
        int u=q.top().second;q.pop(); //pop vertex from queue
        if(c[u]==black)continue;
        c[u]=black; 
        for(int i=0;i<g[u].size();i++)
        {
            int v=g[u][i].v,w=g[u][i].w;
            if(c[v]==white) //new vertex found
            {
                d[v]=d[u]+w;
                c[v]=gray;
                q.push(make_pair(d[v],v)); //add vertex to queue
            }
            else if(c[v]==gray && d[v]>d[u]+w) //shorter path to gray vertex found
            {
                d[v]=d[u]+w;
                q.push(make_pair(d[v],v)); //push this vertex to queue
            }
        }
    }
    return d;
}