how does dijkstra's algorithm work code example

Example 1: dijkstra's algorithm python

import sys

class Vertex:
    def __init__(self, node):
        self.id = node
        self.adjacent = {}
        # Set distance to infinity for all nodes
        self.distance = sys.maxint
        # Mark all nodes unvisited        
        self.visited = False  
        # Predecessor
        self.previous = None

    def add_neighbor(self, neighbor, weight=0):
        self.adjacent[neighbor] = weight

    def get_connections(self):
        return self.adjacent.keys()  

    def get_id(self):
        return self.id

    def get_weight(self, neighbor):
        return self.adjacent[neighbor]

    def set_distance(self, dist):
        self.distance = dist

    def get_distance(self):
        return self.distance

    def set_previous(self, prev):
        self.previous = prev

    def set_visited(self):
        self.visited = True

    def __str__(self):
        return str(self.id) + ' adjacent: ' + str([x.id for x in self.adjacent])

class Graph:
    def __init__(self):
        self.vert_dict = {}
        self.num_vertices = 0

    def __iter__(self):
        return iter(self.vert_dict.values())

    def add_vertex(self, node):
        self.num_vertices = self.num_vertices + 1
        new_vertex = Vertex(node)
        self.vert_dict[node] = new_vertex
        return new_vertex

    def get_vertex(self, n):
        if n in self.vert_dict:
            return self.vert_dict[n]
        else:
            return None

    def add_edge(self, frm, to, cost = 0):
        if frm not in self.vert_dict:
            self.add_vertex(frm)
        if to not in self.vert_dict:
            self.add_vertex(to)

        self.vert_dict[frm].add_neighbor(self.vert_dict[to], cost)
        self.vert_dict[to].add_neighbor(self.vert_dict[frm], cost)

    def get_vertices(self):
        return self.vert_dict.keys()

    def set_previous(self, current):
        self.previous = current

    def get_previous(self, current):
        return self.previous

def shortest(v, path):
    ''' make shortest path from v.previous'''
    if v.previous:
        path.append(v.previous.get_id())
        shortest(v.previous, path)
    return

import heapq

def dijkstra(aGraph, start, target):
    print '''Dijkstra's shortest path'''
    # Set the distance for the start node to zero 
    start.set_distance(0)

    # Put tuple pair into the priority queue
    unvisited_queue = [(v.get_distance(),v) for v in aGraph]
    heapq.heapify(unvisited_queue)

    while len(unvisited_queue):
        # Pops a vertex with the smallest distance 
        uv = heapq.heappop(unvisited_queue)
        current = uv[1]
        current.set_visited()

        #for next in v.adjacent:
        for next in current.adjacent:
            # if visited, skip
            if next.visited:
                continue
            new_dist = current.get_distance() + current.get_weight(next)
            
            if new_dist < next.get_distance():
                next.set_distance(new_dist)
                next.set_previous(current)
                print 'updated : current = %s next = %s new_dist = %s' \
                        %(current.get_id(), next.get_id(), next.get_distance())
            else:
                print 'not updated : current = %s next = %s new_dist = %s' \
                        %(current.get_id(), next.get_id(), next.get_distance())

        # Rebuild heap
        # 1. Pop every item
        while len(unvisited_queue):
            heapq.heappop(unvisited_queue)
        # 2. Put all vertices not visited into the queue
        unvisited_queue = [(v.get_distance(),v) for v in aGraph if not v.visited]
        heapq.heapify(unvisited_queue)
    
if __name__ == '__main__':

    g = Graph()

    g.add_vertex('a')
    g.add_vertex('b')
    g.add_vertex('c')
    g.add_vertex('d')
    g.add_vertex('e')
    g.add_vertex('f')

    g.add_edge('a', 'b', 7)  
    g.add_edge('a', 'c', 9)
    g.add_edge('a', 'f', 14)
    g.add_edge('b', 'c', 10)
    g.add_edge('b', 'd', 15)
    g.add_edge('c', 'd', 11)
    g.add_edge('c', 'f', 2)
    g.add_edge('d', 'e', 6)
    g.add_edge('e', 'f', 9)

    print 'Graph data:'
    for v in g:
        for w in v.get_connections():
            vid = v.get_id()
            wid = w.get_id()
            print '( %s , %s, %3d)'  % ( vid, wid, v.get_weight(w))

    dijkstra(g, g.get_vertex('a'), g.get_vertex('e')) 

    target = g.get_vertex('e')
    path = [target.get_id()]
    shortest(target, path)
    print 'The shortest path : %s' %(path[::-1])

Example 2: dijkstra algorithm

//djikstra's algorithm using a weighted graph (STL)
//code by Soumyadepp
//insta: @soumyadepp
//linkedinID: https://www.linkedin.com/in/soumyadeep-ghosh-90a1951b6/

#include <bits/stdc++.h>
#define ll long long
using namespace std;

//to find the closest unvisited vertex from the source
//note that numbering of vertices starts from 1 here. Calculate accordingly
ll minDist(ll dist[], ll n, bool visited[])
{
    ll min = INT_MAX;
    ll minIndex = 0;
    for (ll i = 1; i <= n; i++)
    {
        if (!visited[i] && dist[i] <= min)
        {
            min = dist[i];
            minIndex = i;
        }
    }
    return minIndex;
}

//djikstra's algorithm for single source shortest path
void djikstra(vector<pair<ll, ll>> *g, ll n, ll src)
{
    bool visited[n + 1];
    ll dist[n + 1];
    for (ll i = 0; i <= n; i++)
    {
        dist[i] = INT_MAX;
        visited[i] = false;
    }

    dist[src] = 0;

    for (ll i = 0; i < n - 1; i++)
    {
        ll u = minDist(dist, n, visited);
        visited[u] = true;
        for (ll v = 0; v < g[u].size(); v++)
        {
            if (dist[u] + g[u][v].second < dist[g[u][v].first])
            {
                dist[g[u][v].first] = dist[u] + g[u][v].second;
            }
        }
    }
    cout << "VERTEX : DISTANCE" << endl;
    for (ll i = 1; i <= n; i++)
    {
        if (dist[i] != INT_MAX)
            cout << i << "         " << dist[i] << endl;
        else
            cout << i << "         "
                 << "not reachable" << endl;
    }
    cout << endl;
}

int main()
{
    //to store the adjacency list which also contains the weight
    vector<pair<ll, ll>> *graph;
    ll n, e, x, y, w, src;
    cout << "Enter number of vertices and edges in the graph" << endl;
    cin >> n >> e;
    graph = new vector<pair<ll, ll>>[n + 1];
    cout << "Enter edges and weight" << endl;
    for (ll i = 0; i < e; i++)
    {
        cin >> x >> y >> w;
        //checking for invalid edges and negative weights.
        if (x <= 0 || y <= 0 || w <= 0)
        {
            cout << "Invalid parameters. Exiting" << endl;
            exit(-1);
        }
        graph[x].push_back(make_pair(y, w));
        graph[y].push_back(make_pair(x, w));
    }
    cout << "Enter source from which you want to find shortest paths" << endl;
    cin >> src;
    if (src >= 1 && src <= n)
        djikstra(graph, n, src);
    else
        cout << "Please enter a valid vertex as the source" << endl;
    return 0;
}

//time complexity : O(ElogV)
//space complexity: O(V)

Example 3: dijkstra's algorithm python

import sys


class Vertex:
    def __init__(self, node):
        self.id = node
        self.adjacent = {}
        # Set distance to infinity for all nodes
        self.distance = sys.maxsize
        # Mark all nodes unvisited
        self.visited = False
        # Predecessor
        self.previous = None

    def __lt__(self, other):
        return self.distance < other.distance

    def add_neighbor(self, neighbor, weight=0):
        self.adjacent[neighbor] = weight

    def get_connections(self):
        return self.adjacent.keys()

    def get_id(self):
        return self.id

    def get_weight(self, neighbor):
        return self.adjacent[neighbor]

    def set_distance(self, dist):
        self.distance = dist

    def get_distance(self):
        return self.distance

    def set_previous(self, prev):
        self.previous = prev

    def set_visited(self):
        self.visited = True

    def __str__(self):
        return str(self.id) + ' adjacent: ' + str([x.id for x in self.adjacent])


class Graph:
    def __init__(self):
        self.vert_dict = {}
        self.num_vertices = 0

    def __iter__(self):
        return iter(self.vert_dict.values())

    def add_vertex(self, node):
        self.num_vertices = self.num_vertices + 1
        new_vertex = Vertex(node)
        self.vert_dict[node] = new_vertex
        return new_vertex

    def get_vertex(self, n):
        if n in self.vert_dict:
            return self.vert_dict[n]
        else:
            return None

    def add_edge(self, frm, to, cost=0):
        if frm not in self.vert_dict:
            self.add_vertex(frm)
        if to not in self.vert_dict:
            self.add_vertex(to)

        self.vert_dict[frm].add_neighbor(self.vert_dict[to], cost)
        self.vert_dict[to].add_neighbor(self.vert_dict[frm], cost)

    def get_vertices(self):
        return self.vert_dict.keys()

    def set_previous(self, current):
        self.previous = current

    def get_previous(self, current):
        return self.previous


def shortest(v, path):
    ''' make shortest path from v.previous'''
    if v.previous:
        path.append(v.previous.get_id())
        shortest(v.previous, path)
    return


import heapq


def dijkstra(aGraph, start, target):
    print('''Dijkstra's shortest path''')
    # Set the distance for the start node to zero
    start.set_distance(0)

    # Put tuple pair into the priority queue
    unvisited_queue = [(v.get_distance(), v) for v in aGraph]
    heapq.heapify(unvisited_queue)

    while len(unvisited_queue):
        # Pops a vertex with the smallest distance
        uv = heapq.heappop(unvisited_queue)
        current = uv[1]
        current.set_visited()

        # for next in v.adjacent:
        for next in current.adjacent:
            # if visited, skip
            if next.visited:
                continue
            new_dist = current.get_distance() + current.get_weight(next)

            if new_dist < next.get_distance():
                next.set_distance(new_dist)
                next.set_previous(current)
                print('updated : current = %s next = %s new_dist = %s' \
                      % (current.get_id(), next.get_id(), next.get_distance()))
            else:
                print('not updated : current = %s next = %s new_dist = %s' \
                      % (current.get_id(), next.get_id(), next.get_distance()))

        # Rebuild heap
        # 1. Pop every item
        while len(unvisited_queue):
            heapq.heappop(unvisited_queue)
        # 2. Put all vertices not visited into the queue
        unvisited_queue = [(v.get_distance(), v) for v in aGraph if not v.visited]
        heapq.heapify(unvisited_queue)


if __name__ == '__main__':

    g = Graph()

    g.add_vertex('a')
    g.add_vertex('b')
    g.add_vertex('c')
    g.add_vertex('d')
    g.add_vertex('e')
    g.add_vertex('f')

    g.add_edge('a', 'b', 7)
    g.add_edge('a', 'c', 9)
    g.add_edge('a', 'f', 14)
    g.add_edge('b', 'c', 10)
    g.add_edge('b', 'd', 15)
    g.add_edge('c', 'd', 11)
    g.add_edge('c', 'f', 2)
    g.add_edge('d', 'e', 6)
    g.add_edge('e', 'f', 9)

    print('Graph data:')
    for v in g:
        for w in v.get_connections():
            vid = v.get_id()
            wid = w.get_id()
            print('( %s , %s, %3d)' % (vid, wid, v.get_weight(w)))

    dijkstra(g, g.get_vertex('a'), g.get_vertex('e'))

    target = g.get_vertex('e')
    path = [target.get_id()]
    shortest(target, path)
    print('The shortest path : %s' % (path[::-1]))