Dijkstra’s Shortest Path Algorithm is popular algorithm for finding shortest path between different nodes. The algorithm (Pseudo Code) is as follows

Now lets come to an example which further illustrates above algorithm. Consider a weighted graph

Now the following source code implements the above example

The output of above program is

procedure Dijkstra (G): weighted connected simple graph,

with all weights positive)

[G has vertices a = v0, v1, ..... , vn = z and weights w(v1, v2)

where w(vi, vj) = INFINITY if [vi, vj] is not an edge in G]

for i := 1 to n

L(vi) := INFINITY

L(a) := 0

S := NULL

[ the labels are now initialized so that the label of a is 0

and all other labels are INIFINITY, S is empty set]

while z is not belongs to S

begin

u := a vertex not in S with L(u) minimal

S := S U [u]

for all vertices u not in S

If L(u) + w(u,v) < L(v) then L(v) := L(u) + w(u,v)

[this adds a vertex to S with minimal label and updates the labels

vertices no in S]

end [L(z) = length of a shortest path from a to z]

with all weights positive)

[G has vertices a = v0, v1, ..... , vn = z and weights w(v1, v2)

where w(vi, vj) = INFINITY if [vi, vj] is not an edge in G]

for i := 1 to n

L(vi) := INFINITY

L(a) := 0

S := NULL

[ the labels are now initialized so that the label of a is 0

and all other labels are INIFINITY, S is empty set]

while z is not belongs to S

begin

u := a vertex not in S with L(u) minimal

S := S U [u]

for all vertices u not in S

If L(u) + w(u,v) < L(v) then L(v) := L(u) + w(u,v)

[this adds a vertex to S with minimal label and updates the labels

vertices no in S]

end [L(z) = length of a shortest path from a to z]

**Example:**Now lets come to an example which further illustrates above algorithm. Consider a weighted graph

Here a, b, c .. are nodes of the graph and the number between nodes are weights (distances) of the graph. Now we are going to find the shortest path between source (a) and remaining vertices. The adjacency matrix of the graph is

Now the following source code implements the above example

#include<iostream> #define INFINITY 999 using namespace std; class Dijkstra{ private: int adjMatrix[15][15]; int predecessor[15],distance[15]; bool mark[15]; //keep track of visited node int source; int numOfVertices; public: /* * Function read() reads No of vertices, Adjacency Matrix and source * Matrix from the user. The number of vertices must be greather than * zero, all members of Adjacency Matrix must be postive as distances * are always positive. The source vertex must also be positive from 0 * to noOfVertices - 1 */ void read(); /* * Function initialize initializes all the data members at the begining of * the execution. The distance between source to source is zero and all other * distances between source and vertices are infinity. The mark is initialized * to false and predecessor is initialized to -1 */ void initialize(); /* * Function getClosestUnmarkedNode returns the node which is nearest from the * Predecessor marked node. If the node is already marked as visited, then it search * for another node. */ int getClosestUnmarkedNode(); /* * Function calculateDistance calculates the minimum distances from the source node to * Other node. */ void calculateDistance(); /* * Function output prints the results */ void output(); void printPath(int); }; void Dijkstra::read(){ cout<<"Enter the number of vertices of the graph(should be > 0)\n"; cin>>numOfVertices; while(numOfVertices <= 0) { cout<<"Enter the number of vertices of the graph(should be > 0)\n"; cin>>numOfVertices; } cout<<"Enter the adjacency matrix for the graph\n"; cout<<"To enter infinity enter "<<INFINITY<<endl; for(int i=0;i<numOfVertices;i++) { cout<<"Enter the (+ve)weights for the row "<<i<<endl; for(int j=0;j<numOfVertices;j++) { cin>>adjMatrix[i][j]; while(adjMatrix[i][j]<0) { cout<<"Weights should be +ve. Enter the weight again\n"; cin>>adjMatrix[i][j]; } } } cout<<"Enter the source vertex\n"; cin>>source; while((source<0) && (source>numOfVertices-1)) { cout<<"Source vertex should be between 0 and"<<numOfVertices-1<<endl; cout<<"Enter the source vertex again\n"; cin>>source; } } void Dijkstra::initialize(){ for(int i=0;i<numOfVertices;i++) { mark[i] = false; predecessor[i] = -1; distance[i] = INFINITY; } distance[source]= 0; } int Dijkstra::getClosestUnmarkedNode(){ int minDistance = INFINITY; int closestUnmarkedNode; for(int i=0;i<numOfVertices;i++) { if((!mark[i]) && ( minDistance >= distance[i])) { minDistance = distance[i]; closestUnmarkedNode = i; } } return closestUnmarkedNode; } void Dijkstra::calculateDistance(){ initialize(); int minDistance = INFINITY; int closestUnmarkedNode; int count = 0; while(count < numOfVertices) { closestUnmarkedNode = getClosestUnmarkedNode(); mark[closestUnmarkedNode] = true; for(int i=0;i<numOfVertices;i++) { if((!mark[i]) && (adjMatrix[closestUnmarkedNode][i]>0) ) { if(distance[i] > distance[closestUnmarkedNode]+adjMatrix[closestUnmarkedNode][i]) { distance[i] = distance[closestUnmarkedNode]+adjMatrix[closestUnmarkedNode][i]; predecessor[i] = closestUnmarkedNode; } } } count++; } } void Dijkstra::printPath(int node){ if(node == source) cout<<(char)(node + 97)<<".."; else if(predecessor[node] == -1) cout<<"No path from “<<source<<”to "<<(char)(node + 97)<<endl; else { printPath(predecessor[node]); cout<<(char) (node + 97)<<".."; } } void Dijkstra::output(){ for(int i=0;i<numOfVertices;i++) { if(i == source) cout<<(char)(source + 97)<<".."<<source; else printPath(i); cout<<"->"<<distance[i]<<endl; } } int main(){ Dijkstra G; G.read(); G.calculateDistance(); G.output(); return 0; }

The output of above program is

Thank you. Love the way you have put comments to explain as to what are you up too. Thank you and keep posting codes with comments. They really help

ReplyDeleteGreat work. Clear, concise code. Thank you

ReplyDeleteThank you.It helps me a lot.

ReplyDeleteMay I asked you to post Bellman-Ford algorithm like this one.

ReplyDeleteOk i will post it after my exam :):)

DeleteThank You, but is it possible to get multiple shortest paths?

ReplyDeleteYep, there may be multiple shortest path between any two nodes. But above code only shows a single shortest path.

Deletecan you show me link to bellman ford algorhytm

DeleteHow would you impliment this code by reading in a file formatted like this:

ReplyDelete1 2 10

1 4 30

1 5 100

2 3 50

2 1 70

3 5 10

3 1 50

4 3 20

4 5 60

5 2 40

Q

the numbers (1-5) are the vertices and the third number in the line is the weight. the file length will be unspecified and Q terminates the file? Your code helps but im not sure how to convert to get this file format to work

Thanks ! great work and keep going, it was really helpful ;)

ReplyDeletehey i am using turbo c and getting lot of errors in the program ..which one do you think is the best compiler to run this progam

ReplyDeleteThis code may not work in Turbo C. This is compiled using GCC MinGW Compiler.

Deletethank you so much for your valuable reply Bibek..if you dont mind could you please tell me step by step instructions to run this program using GCC MinGW compiler. i am not able to do that please its a request

DeleteDownload the Code::Blocks binary from this link http://prdownload.berlios.de/codeblocks/codeblocks-12.11mingw-setup_user.exe. The GCC compiler is already embedded with this so just run the code and you will see the output

Deletethank you so much!! everything is working fine :) out of many other programs which i downloaded this is one giving the exact output as i wanted...happyyyyyyy:) :)

ReplyDeleteGlad to hear that. This program actually uses Adjacency matrix. you can modify it to entire a entire graph instead of matrix. If you find any bug then let me know

DeleteThanks for the code! :) could you explain how you would modify a graph to use this algorithm?

Deletethanks for program . God bless you , should i prefer using priority queue instead ?

ReplyDeleteYes Rohit you can use priority queue. Priority queue makes the program even faster

DeleteHi Bibek,

ReplyDeleteI am trying to implement Dijkstra's algorithm in C with the help of your code above. I tried the same but somehow I am not able to get the expected shortest path.

The modifications I have made are:

Instead of asking user input for the number of nodes and cost, I am giving an input file which has all these info. I also mention the source and destination node from which I want the code to find the shortest path. But somehow everytime it just says no path from "source" to "destination"

Will you be able to help me with this?

Thanks in advance for any help.

-Preethi

Hello Preethi, please send me your code at subedishankar2011@gmail.com. I will look at it and provide you the feedback. Thanks

DeleteHi Bibek,

ReplyDeleteI have mailed you my source files. Please do have a look at it.

Thanks

i am not able to run the above source code in dev c++ compiler.I got struck at line no 109.please help me

ReplyDeleteCan you show me the error you got ?

DeleteError:no'int Dijstra::getclosestUnmarkedNode()' member function declared in dijkstra

ReplyDeleteIn member function'void Dijkstra::calculate Distance()'

please help me to rectify this error

ReplyDeletebro there are errors of spaces there in the program

Deletepress backspace and then tab then the errors will be corrected

pl provide opengl source code for djkstarts

ReplyDeletepl providr source code for dijkstarts

ReplyDeleteNice and simple implementation. Nice job.

ReplyDeleteBut isn't the complexity n^2 instead of (m+n)logn?

This algorithm is not dijkstra because no heap is maintained

ReplyDeletethis would not work if it has a cycle. explain..d

ReplyDeletecan any one help me on find the shortest distance for all nodes by using Bellman-Ford algorithm cpp program

ReplyDeletehello can anyone help me pls?? getting a error in dis statement bool mark[15]; can anyone tell me pls

ReplyDeletehello can anyone help me with dis code?? getting a error with dis line bool mark[15]; pls anyone tell me

ReplyDelete