# Implementation of Dijkstra’s Shortest Path Algorithm in C++

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

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]

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

Now the following source code implements the above example

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 | #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

Great work. Clear, concise code. Thank you

Thank you.It helps me a lot.

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

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

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

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

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

1 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 😉

hey 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

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

thank 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

Download 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

thank 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:) 🙂

Glad 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

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

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

Hi Bibek,

I 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 [email protected]. I will look at it and provide you the feedback. Thanks

Hi Bibek,

I 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

Can you show me the error you got ?

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

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

please help me to rectify this error

pl providr source code for dijkstarts

pl provide opengl source code for djkstarts

bro there are errors of spaces there in the program

press backspace and then tab then the errors will be corrected

Nice and simple implementation. Nice job.

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

This algorithm is not dijkstra because no heap is maintained

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

Thanks for the code! 🙂 could you explain how you would modify a graph to use this algorithm?

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

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

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

can you show me link to bellman ford algorhytm

Need Help!

How can we get an alternate path using this algorithm?

its Urgent.

Thank you for Dijkstra Code.

Ok bhai karta send….

i can't understand ur code hell!