Make a c++11 Dijkstra Implementation return shortest Path

A C++11 implementation of the Dijkstra Algorithm by Michal Forisek does compute the shortest distance quite fast & elegantly with not too much code. But how can I return the path too ?

struct edge { int to, length; };

int dijkstra(const vector< vector<edge> > &graph, int source, int target) {
    vector<int> min_distance( graph.size(), INT_MAX );
    min_distance[ source ] = 0;
    set< pair<int,int> > active_vertices;
    active_vertices.insert( {0,source} );

    while (!active_vertices.empty()) {
        int where = active_vertices.begin()->second;
        if (where == target) return min_distance[where];
        active_vertices.erase( active_vertices.begin() );
        for (auto ed : graph[where]) 
            if (min_distance[ed.to] > min_distance[where] + ed.length) {
                active_vertices.erase( { min_distance[ed.to], ed.to } );
                min_distance[ed.to] = min_distance[where] + ed.length;
                active_vertices.insert( { min_distance[ed.to], ed.to } );
            }
    }
    return INT_MAX;
}