Task: Dijkstra's algorithm


C++: #include <iostream>
#include <vector>
#include <string>
#include <list>

#include <limits> 

#include <set>
#include <utility> 
#include <algorithm>
#include <iterator>


typedef int vertex_t;
typedef double weight_t;

const weight_t max_weight = std::numeric_limits<double>::infinity();

struct neighbor {
    vertex_t target;
    weight_t weight;
    neighbor(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};

typedef std::vector<std::vector<neighbor> > adjacency_list_t;


void DijkstraComputePaths(vertex_t source,
                          const adjacency_list_t &adjacency_list,
                          std::vector<weight_t> &min_distance,
                          std::vector<vertex_t> &previous)
{
    int n = adjacency_list.size();
    min_distance.clear();
    min_distance.resize(n, max_weight);
    min_distance[source] = 0;
    previous.clear();
    previous.resize(n, -1);
    std::set<std::pair<weight_t, vertex_t> > vertex_queue;
    vertex_queue.insert(std::make_pair(min_distance[source], source));

    while (!vertex_queue.empty()) 
    {
        weight_t dist = vertex_queue.begin()->first;
        vertex_t u = vertex_queue.begin()->second;
        vertex_queue.erase(vertex_queue.begin());

        
	const std::vector<neighbor> &neighbors = adjacency_list[u];
        for (std::vector<neighbor>::const_iterator neighbor_iter = neighbors.begin();
             neighbor_iter != neighbors.end();
             neighbor_iter++)
        {
            vertex_t v = neighbor_iter->target;
            weight_t weight = neighbor_iter->weight;
            weight_t distance_through_u = dist + weight;
	    if (distance_through_u < min_distance[v]) {
	        vertex_queue.erase(std::make_pair(min_distance[v], v));

	        min_distance[v] = distance_through_u;
	        previous[v] = u;
	        vertex_queue.insert(std::make_pair(min_distance[v], v));

	    }

        }
    }
}


std::list<vertex_t> DijkstraGetShortestPathTo(
    vertex_t vertex, const std::vector<vertex_t> &previous)
{
    std::list<vertex_t> path;
    for ( ; vertex != -1; vertex = previous[vertex])
        path.push_front(vertex);
    return path;
}


int main()
{
    
    adjacency_list_t adjacency_list(6);
    
    adjacency_list[0].push_back(neighbor(1, 7));
    adjacency_list[0].push_back(neighbor(2, 9));
    adjacency_list[0].push_back(neighbor(5, 14));
    
    adjacency_list[1].push_back(neighbor(0, 7));
    adjacency_list[1].push_back(neighbor(2, 10));
    adjacency_list[1].push_back(neighbor(3, 15));
    
    adjacency_list[2].push_back(neighbor(0, 9));
    adjacency_list[2].push_back(neighbor(1, 10));
    adjacency_list[2].push_back(neighbor(3, 11));
    adjacency_list[2].push_back(neighbor(5, 2));
    
    adjacency_list[3].push_back(neighbor(1, 15));
    adjacency_list[3].push_back(neighbor(2, 11));
    adjacency_list[3].push_back(neighbor(4, 6));
    
    adjacency_list[4].push_back(neighbor(3, 6));
    adjacency_list[4].push_back(neighbor(5, 9));
    
    adjacency_list[5].push_back(neighbor(0, 14));
    adjacency_list[5].push_back(neighbor(2, 2));
    adjacency_list[5].push_back(neighbor(4, 9));

    std::vector<weight_t> min_distance;
    std::vector<vertex_t> previous;
    DijkstraComputePaths(0, adjacency_list, min_distance, previous);
    std::cout << "Distance from 0 to 4: " << min_distance[4] << std::endl;
    std::list<vertex_t> path = DijkstraGetShortestPathTo(4, previous);
    std::cout << "Path : ";
    std::copy(path.begin(), path.end(), std::ostream_iterator<vertex_t>(std::cout, " "));
    std::cout << std::endl;

    return 0;
}






Python: from collections import namedtuple, deque
from pprint import pprint as pp
 
 
inf = float('inf')
Edge = namedtuple('Edge', ['start', 'end', 'cost'])
 
class Graph():
    def __init__(self, edges):
        self.edges = [Edge(*edge) for edge in edges]
        
        self.vertices = {e.start for e in self.edges} | {e.end for e in self.edges}
 
    def dijkstra(self, source, dest):
        assert source in self.vertices
        dist = {vertex: inf for vertex in self.vertices}
        previous = {vertex: None for vertex in self.vertices}
        dist[source] = 0
        q = self.vertices.copy()
        neighbours = {vertex: set() for vertex in self.vertices}
        for start, end, cost in self.edges:
            neighbours[start].add((end, cost))
            neighbours[end].add((start, cost))

        
 
        while q:
            
            u = min(q, key=lambda vertex: dist[vertex])
            q.remove(u)
            if dist[u] == inf or u == dest:
                break
            for v, cost in neighbours[u]:
                alt = dist[u] + cost
                if alt < dist[v]:                                  
                    dist[v] = alt
                    previous[v] = u
        
        s, u = deque(), dest
        while previous[u]:
            s.appendleft(u)
            u = previous[u]
        s.appendleft(u)
        return s
 
 
graph = Graph([("a", "b", 7),  ("a", "c", 9),  ("a", "f", 14), ("b", "c", 10),
               ("b", "d", 15), ("c", "d", 11), ("c", "f", 2),  ("d", "e", 6),
               ("e", "f", 9)])
pp(graph.dijkstra("a", "e"))