Open In App

C / C++ Program for Dijkstra’s shortest path algorithm | Greedy Algo-7

Last Updated : 09 Oct, 2023
Improve
Improve
Like Article
Like
Save
Share
Report

Problem Statement: Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph.

What is Dijkstra’s Algorithm?

Dijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree. Like Prim’s MST, we generate an SPT (shortest path tree) with a given source as the root. We maintain two sets, one set contains vertices included in the shortest path tree, other set includes vertices not yet included in the shortest path tree. At every step of the algorithm, we find a vertex that is in the other set (set of not yet included) and has a minimum distance from the source.

Below are the detailed steps used in Dijkstra’s algorithm to find the shortest path from a single source vertex to all other vertices in the given graph. 

Algorithm

  1. Create a set sptSet (shortest path tree set) that keeps track of vertices included in the shortest path tree, i.e., whose minimum distance from the source is calculated and finalized. Initially, this set is empty. 
  2. Assign a distance value to all vertices in the input graph. Initialize all distance values as INFINITE. Assign the distance value as 0 for the source vertex so that it is picked first. 
  3. While sptSet doesn’t include all vertices 
    1. Pick a vertex u which is not there in sptSet and has minimum distance value. 
    2. Include u to sptSet
    3. Update the distance value of all adjacent vertices of u. To update the distance values, iterate through all adjacent vertices. For every adjacent vertex v, if the sum of the distance value of u (from source) and weight of edge u-v, is less than the distance value of v, then update the distance value of v. 

C++ Program for Dijkstra’s Single Source Shortest Path Algorithm

C++




// A C++ program for Dijkstra's single source shortest path
// algorithm. The program is for adjacency matrix
// representation of the graph
 
#include <limits.h>
#include <stdio.h>
 
// Number of vertices in the graph
#define V 9
 
// A utility function to find the vertex with minimum
// distance value, from the set of vertices not yet included
// in shortest path tree
int minDistance(int dist[], bool sptSet[])
{
    // Initialize min value
    int min = INT_MAX, min_index;
 
    for (int v = 0; v < V; v++)
        if (sptSet[v] == false && dist[v] <= min)
            min = dist[v], min_index = v;
 
    return min_index;
}
 
// A utility function to print the constructed distance
// array
void printSolution(int dist[], int n)
{
    printf("Vertex   Distance from Source\n");
    for (int i = 0; i < V; i++)
        printf("\t%d \t\t\t\t %d\n", i, dist[i]);
}
 
// Function that implements Dijkstra's single source
// shortest path algorithm for a graph represented using
// adjacency matrix representation
void dijkstra(int graph[V][V], int src)
{
    int dist[V]; // The output array.  dist[i] will hold the
                 // shortest
    // distance from src to i
 
    bool sptSet[V]; // sptSet[i] will be true if vertex i is
                    // included in shortest
    // path tree or shortest distance from src to i is
    // finalized
 
    // Initialize all distances as INFINITE and stpSet[] as
    // false
    for (int i = 0; i < V; i++)
        dist[i] = INT_MAX, sptSet[i] = false;
 
    // Distance of source vertex from itself is always 0
    dist[src] = 0;
 
    // Find shortest path for all vertices
    for (int count = 0; count < V - 1; count++) {
        // Pick the minimum distance vertex from the set of
        // vertices not yet processed. u is always equal to
        // src in the first iteration.
        int u = minDistance(dist, sptSet);
 
        // Mark the picked vertex as processed
        sptSet[u] = true;
 
        // Update dist value of the adjacent vertices of the
        // picked vertex.
        for (int v = 0; v < V; v++)
 
            // Update dist[v] only if is not in sptSet,
            // there is an edge from u to v, and total
            // weight of path from src to  v through u is
            // smaller than current value of dist[v]
            if (!sptSet[v] && graph[u][v]
                && dist[u] != INT_MAX
                && dist[u] + graph[u][v] < dist[v])
                dist[v] = dist[u] + graph[u][v];
    }
 
    // print the constructed distance array
    printSolution(dist, V);
}
 
// driver program to test above function
int main()
{
    /* Let us create the example graph discussed above */
    int graph[V][V] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
                        { 4, 0, 8, 0, 0, 0, 0, 11, 0 },
                        { 0, 8, 0, 7, 0, 4, 0, 0, 2 },
                        { 0, 0, 7, 0, 9, 14, 0, 0, 0 },
                        { 0, 0, 0, 9, 0, 10, 0, 0, 0 },
                        { 0, 0, 4, 14, 10, 0, 2, 0, 0 },
                        { 0, 0, 0, 0, 0, 2, 0, 1, 6 },
                        { 8, 11, 0, 0, 0, 0, 1, 0, 7 },
                        { 0, 0, 2, 0, 0, 0, 6, 7, 0 } };
 
    dijkstra(graph, 0);
 
    return 0;
}


Output

Vertex   Distance from Source
    0                  0
    1                  4
    2                  12
    3                  19
    4                  21
    5                  11
    6                  9
    7                  8
    8                  14

Complexity Analysis

Time Complexity: The time complexity of Dijkstra’s algorithm is O(V^2). This is because the algorithm uses two nested loops to traverse the graph and find the shortest path from the source node to all other nodes.

Space Complexity: The space complexity of Dijkstra’s algorithm is O(V), where V is the number of vertices in the graph. This is because the algorithm uses an array of size V to store the distances from the source node to all other nodes.

Please refer complete article on Dijkstra’s shortest path algorithm | Greedy Algo-7 for more details!



Previous Article
Next Article

Similar Reads

Java Program for Dijkstra's shortest path algorithm | Greedy Algo-7
Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph. Dijkstra's algorithm is very similar to Prim's algorithm for minimum spanning tree. Like Prim's MST, we generate a SPT (shortest path tree) with given source as root. We maintain two sets, one set contains vertices included in shortes
5 min read
Python Program for Dijkstra's shortest path algorithm | Greedy Algo-7
Given a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph.Dijkstra's algorithm is very similar to Prim's algorithm for minimum spanning tree. Like Prim's MST, we generate an SPT (shortest path tree) with a given source as root. We maintain two sets, one set contains vertices included in t
4 min read
C# Program for Dijkstra's shortest path algorithm | Greedy Algo-7
Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph. Dijkstra's algorithm is very similar to Prim's algorithm for minimum spanning tree. Like Prim's MST, we generate a SPT (shortest path tree) with given source as root. We maintain two sets, one set contains vertices included in shortes
5 min read
Dijkstra’s Algorithm for Adjacency List Representation | Greedy Algo-8
We recommend reading the following two posts as a prerequisite for this post. Greedy Algorithms | Set 7 (Dijkstra’s shortest path algorithm) Graph and its representations We have discussed Dijkstra's algorithm and its implementation for adjacency matrix representation of graphs. The time complexity for the matrix representation is O(V^2). In this p
21 min read
Dijkstra's shortest path algorithm in Java using PriorityQueue
Dijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree. Like Prim’s MST, we generate a SPT (shortest path tree) with a given source as a root. We maintain two sets, one set contains vertices included in the shortest-path tree, other set includes vertices not yet included in the shortest-path tree. At every step of the al
5 min read
Applications of Dijkstra's shortest path algorithm
Dijkstra’s algorithm is one of the most popular algorithms for solving many single-source shortest path problems having non-negative edge weight in the graphs i.e., it is to find the shortest distance between two vertices on a graph. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. Dijkstra’s Algori
4 min read
Dijkstra’s shortest path algorithm using set in STL
Given a graph and a source vertex in graph, find shortest paths from source to all vertices in the given graph. Input : Source = 0Output : Vertex Distance from Source 0 0 1 4 2 12 3 19 4 21 5 11 6 9 7 8 8 14We have discussed Dijkstra's shortest Path implementations. Dijkstra’s Algorithm for Adjacency Matrix Representation (In C/C++ with time comple
13 min read
Shortest path in a directed graph by Dijkstra’s algorithm
Given a directed graph and a source vertex in the graph, the task is to find the shortest distance and path from source to target vertex in the given graph where edges are weighted (non-negative) and directed from parent vertex to source vertices. Approach: Mark all vertices unvisited. Create a set of all unvisited vertices.Assign zero distance val
15 min read
Printing Paths in Dijkstra's Shortest Path Algorithm
Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph.We have discussed Dijkstra's Shortest Path algorithm in the below posts.  Dijkstra’s shortest path for adjacency matrix representationDijkstra’s shortest path for adjacency list representationThe implementations discussed above
15 min read
Dijkstra's Shortest Path Algorithm using priority_queue of STL
Given a graph and a source vertex in graph, find shortest paths from source to all vertices in the given graph. Input : Source = 0Output : Vertex Distance from Source 0 0 1 4 2 12 3 19 4 21 5 11 6 9 7 8 8 14We have discussed Dijkstra’s shortest Path implementations. Dijkstra’s Algorithm for Adjacency Matrix Representation (In C/C++ with time comple
34 min read
Article Tags :