dijkstra 27s algorithm python

1//Dijkstra's Algorithm (Using priority queue)
2//Watch Striver graph series on youtube I learned from there
3#include<bits/stdc++.h>
4using namespace std;
5void addedge(vector<pair<int,int>>adj[],int u,int v,int w)
6{
7    adj[u].push_back(make_pair(v,w));
8    adj[v].push_back(make_pair(u,w));
9}
10void Dijkstra(vector<pair<int,int>>adj[],int source,int n)
11{
12    priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>> prior; //Min-Heap storing will store distance and node
13    vector<int>dist(n,INT_MAX);
14    dist[source]=0;
15    prior.push(make_pair(0,source));
16    while(!prior.empty())
17    {
18        int distance=prior.top().first;
19        int node=prior.top().second;
20        prior.pop();
21        for(auto it:adj[node])
22        {
23            int next_node=it.first;
24            int next_weight=it.second;
25            if(dist[next_node]>distance+next_weight)
26            {
27                dist[next_node]=dist[node]+next_weight;
28                prior.push(make_pair(dist[next_node],next_node));
29            }
30        }
31    }
32    for(int i=0;i<n;i++)
33    {
34        cout<<dist[i]<<" ";
35    }
36}
37int main()
38{
39    int vertex,edges;
40    cout<<"ENTER THE NUMBER OF VERTEX AND EDGES:"<<endl;
41    cin>>vertex>>edges;
42    vector<pair<int,int>>adj[vertex];
43    int a,b,w;
44    cout<<"ENTER THE LINK AND THEN WEIGHT:"<<endl;
45    for(int i=0;i<edges;i++)
46    {
47        cin>>a>>b>>w;
48        addedge(adj,a,b,w);
49    }
50    int source;
51    cout<<"ENTER THE SOURCE NODE FROM WHICH YOU WANT TO CALCULATE THE SHORTEST DISTANCE:"<<endl;
52    cin>>source;
53    Dijkstra(adj,source,vertex);
54    return 0;
55}
56

1//djikstra's algorithm using a weighted graph (STL)
2//code by Soumyadepp
3//insta: @soumyadepp
4//linkedinID: https://www.linkedin.com/in/soumyadeep-ghosh-90a1951b6/
5
6#include <bits/stdc++.h>
7#define ll long long
8using namespace std;
9
10//to find the closest unvisited vertex from the source
11//note that numbering of vertices starts from 1 here. Calculate accordingly
12ll minDist(ll dist[], ll n, bool visited[])
13{
14    ll min = INT_MAX;
15    ll minIndex = 0;
16    for (ll i = 1; i <= n; i++)
17    {
18        if (!visited[i] && dist[i] <= min)
19        {
20            min = dist[i];
21            minIndex = i;
22        }
23    }
24    return minIndex;
25}
26
27//djikstra's algorithm for single source shortest path
28void djikstra(vector<pair<ll, ll>> *g, ll n, ll src)
29{
30    bool visited[n + 1];
31    ll dist[n + 1];
32    for (ll i = 0; i <= n; i++)
33    {
34        dist[i] = INT_MAX;
35        visited[i] = false;
36    }
37
38    dist[src] = 0;
39
40    for (ll i = 0; i < n - 1; i++)
41    {
42        ll u = minDist(dist, n, visited);
43        visited[u] = true;
44        for (ll v = 0; v < g[u].size(); v++)
45        {
46            if (dist[u] + g[u][v].second < dist[g[u][v].first])
47            {
48                dist[g[u][v].first] = dist[u] + g[u][v].second;
49            }
50        }
51    }
52    cout << "VERTEX : DISTANCE" << endl;
53    for (ll i = 1; i <= n; i++)
54    {
55        if (dist[i] != INT_MAX)
56            cout << i << "         " << dist[i] << endl;
57        else
58            cout << i << "         "
59                 << "not reachable" << endl;
60    }
61    cout << endl;
62}
63
64int main()
65{
66    //to store the adjacency list which also contains the weight
67    vector<pair<ll, ll>> *graph;
68    ll n, e, x, y, w, src;
69    cout << "Enter number of vertices and edges in the graph" << endl;
70    cin >> n >> e;
71    graph = new vector<pair<ll, ll>>[n + 1];
72    cout << "Enter edges and weight" << endl;
73    for (ll i = 0; i < e; i++)
74    {
75        cin >> x >> y >> w;
76        //checking for invalid edges and negative weights.
77        if (x <= 0 || y <= 0 || w <= 0)
78        {
79            cout << "Invalid parameters. Exiting" << endl;
80            exit(-1);
81        }
82        graph[x].push_back(make_pair(y, w));
83        graph[y].push_back(make_pair(x, w));
84    }
85    cout << "Enter source from which you want to find shortest paths" << endl;
86    cin >> src;
87    if (src >= 1 && src <= n)
88        djikstra(graph, n, src);
89    else
90        cout << "Please enter a valid vertex as the source" << endl;
91    return 0;
92}
93
94//time complexity : O(ElogV)
95//space complexity: O(V)
96

1
2# Providing the graph
3n = int(input("Enter the number of vertices of the graph"))
4
5# using adjacency matrix representation 
6vertices = [[0, 0, 1, 1, 0, 0, 0],
7            [0, 0, 1, 0, 0, 1, 0],
8            [1, 1, 0, 1, 1, 0, 0],
9            [1, 0, 1, 0, 0, 0, 1],
10            [0, 0, 1, 0, 0, 1, 0],
11            [0, 1, 0, 0, 1, 0, 1],
12            [0, 0, 0, 1, 0, 1, 0]]
13
14edges = [[0, 0, 1, 2, 0, 0, 0],
15         [0, 0, 2, 0, 0, 3, 0],
16         [1, 2, 0, 1, 3, 0, 0],
17         [2, 0, 1, 0, 0, 0, 1],
18         [0, 0, 3, 0, 0, 2, 0],
19         [0, 3, 0, 0, 2, 0, 1],
20         [0, 0, 0, 1, 0, 1, 0]]
21
22# Find which vertex is to be visited next
23def to_be_visited():
24    global visited_and_distance
25    v = -10
26    for index in range(num_of_vertices):
27        if visited_and_distance[index][0] == 0 \
28            and (v < 0 or visited_and_distance[index][1] <=
29                 visited_and_distance[v][1]):
30            v = index
31    return v
32
33
34num_of_vertices = len(vertices[0])
35
36visited_and_distance = [[0, 0]]
37for i in range(num_of_vertices-1):
38    visited_and_distance.append([0, sys.maxsize])
39
40for vertex in range(num_of_vertices):
41
42    # Find next vertex to be visited
43    to_visit = to_be_visited()
44    for neighbor_index in range(num_of_vertices):
45
46        # Updating new distances
47        if vertices[to_visit][neighbor_index] == 1 and 
48                visited_and_distance[neighbor_index][0] == 0:
49            new_distance = visited_and_distance[to_visit][1] 
50                + edges[to_visit][neighbor_index]
51            if visited_and_distance[neighbor_index][1] > new_distance:
52                visited_and_distance[neighbor_index][1] = new_distance
53        
54        visited_and_distance[to_visit][0] = 1
55
56i = 0
57
58# Printing the distance
59for distance in visited_and_distance:
60    print("Distance of ", chr(ord('a') + i),
61          " from source vertex: ", distance[1])
62    i = i + 1

1function Dijkstra(Graph, source):
2       dist[source]  := 0                     // Distance from source to source is set to 0
3       for each vertex v in Graph:            // Initializations
4           if v ≠ source
5               dist[v]  := infinity           // Unknown distance function from source to each node set to infinity
6           add v to Q                         // All nodes initially in Q
7
8      while Q is not empty:                  // The main loop
9          v := vertex in Q with min dist[v]  // In the first run-through, this vertex is the source node
10          remove v from Q 
11
12          for each neighbor u of v:           // where neighbor u has not yet been removed from Q.
13              alt := dist[v] + length(v, u)
14              if alt < dist[u]:               // A shorter path to u has been found
15                  dist[u]  := alt            // Update distance of u 
16
17      return dist[]
18  end function
19

1import sys
2
3class Vertex:
4    def __init__(self, node):
5        self.id = node
6        self.adjacent = {}
7        # Set distance to infinity for all nodes
8        self.distance = sys.maxint
9        # Mark all nodes unvisited        
10        self.visited = False  
11        # Predecessor
12        self.previous = None
13
14    def add_neighbor(self, neighbor, weight=0):
15        self.adjacent[neighbor] = weight
16
17    def get_connections(self):
18        return self.adjacent.keys()  
19
20    def get_id(self):
21        return self.id
22
23    def get_weight(self, neighbor):
24        return self.adjacent[neighbor]
25
26    def set_distance(self, dist):
27        self.distance = dist
28
29    def get_distance(self):
30        return self.distance
31
32    def set_previous(self, prev):
33        self.previous = prev
34
35    def set_visited(self):
36        self.visited = True
37
38    def __str__(self):
39        return str(self.id) + ' adjacent: ' + str([x.id for x in self.adjacent])
40
41class Graph:
42    def __init__(self):
43        self.vert_dict = {}
44        self.num_vertices = 0
45
46    def __iter__(self):
47        return iter(self.vert_dict.values())
48
49    def add_vertex(self, node):
50        self.num_vertices = self.num_vertices + 1
51        new_vertex = Vertex(node)
52        self.vert_dict[node] = new_vertex
53        return new_vertex
54
55    def get_vertex(self, n):
56        if n in self.vert_dict:
57            return self.vert_dict[n]
58        else:
59            return None
60
61    def add_edge(self, frm, to, cost = 0):
62        if frm not in self.vert_dict:
63            self.add_vertex(frm)
64        if to not in self.vert_dict:
65            self.add_vertex(to)
66
67        self.vert_dict[frm].add_neighbor(self.vert_dict[to], cost)
68        self.vert_dict[to].add_neighbor(self.vert_dict[frm], cost)
69
70    def get_vertices(self):
71        return self.vert_dict.keys()
72
73    def set_previous(self, current):
74        self.previous = current
75
76    def get_previous(self, current):
77        return self.previous
78
79def shortest(v, path):
80    ''' make shortest path from v.previous'''
81    if v.previous:
82        path.append(v.previous.get_id())
83        shortest(v.previous, path)
84    return
85
86import heapq
87
88def dijkstra(aGraph, start, target):
89    print '''Dijkstra's shortest path'''
90    # Set the distance for the start node to zero 
91    start.set_distance(0)
92
93    # Put tuple pair into the priority queue
94    unvisited_queue = [(v.get_distance(),v) for v in aGraph]
95    heapq.heapify(unvisited_queue)
96
97    while len(unvisited_queue):
98        # Pops a vertex with the smallest distance 
99        uv = heapq.heappop(unvisited_queue)
100        current = uv[1]
101        current.set_visited()
102
103        #for next in v.adjacent:
104        for next in current.adjacent:
105            # if visited, skip
106            if next.visited:
107                continue
108            new_dist = current.get_distance() + current.get_weight(next)
109            
110            if new_dist < next.get_distance():
111                next.set_distance(new_dist)
112                next.set_previous(current)
113                print 'updated : current = %s next = %s new_dist = %s' \
114                        %(current.get_id(), next.get_id(), next.get_distance())
115            else:
116                print 'not updated : current = %s next = %s new_dist = %s' \
117                        %(current.get_id(), next.get_id(), next.get_distance())
118
119        # Rebuild heap
120        # 1. Pop every item
121        while len(unvisited_queue):
122            heapq.heappop(unvisited_queue)
123        # 2. Put all vertices not visited into the queue
124        unvisited_queue = [(v.get_distance(),v) for v in aGraph if not v.visited]
125        heapq.heapify(unvisited_queue)
126    
127if __name__ == '__main__':
128
129    g = Graph()
130
131    g.add_vertex('a')
132    g.add_vertex('b')
133    g.add_vertex('c')
134    g.add_vertex('d')
135    g.add_vertex('e')
136    g.add_vertex('f')
137
138    g.add_edge('a', 'b', 7)  
139    g.add_edge('a', 'c', 9)
140    g.add_edge('a', 'f', 14)
141    g.add_edge('b', 'c', 10)
142    g.add_edge('b', 'd', 15)
143    g.add_edge('c', 'd', 11)
144    g.add_edge('c', 'f', 2)
145    g.add_edge('d', 'e', 6)
146    g.add_edge('e', 'f', 9)
147
148    print 'Graph data:'
149    for v in g:
150        for w in v.get_connections():
151            vid = v.get_id()
152            wid = w.get_id()
153            print '( %s , %s, %3d)'  % ( vid, wid, v.get_weight(w))
154
155    dijkstra(g, g.get_vertex('a'), g.get_vertex('e')) 
156
157    target = g.get_vertex('e')
158    path = [target.get_id()]
159    shortest(target, path)
160    print 'The shortest path : %s' %(path[::-1])
161