Dijkstra algorithm with Adjacency lists

Question

So I have been trying to implement the Dijkstra Algorithm for shortest path in a directed graph using adjacency lists, but for I don't know what reason, it doesn't print out the results (prints the minimum distance as 0 to all nodes).

The code I wrote is:

#include <fstream>
#include <functional>
#include <climits>
#include <vector>
#include <queue>
#include <list>

using namespace std;

struct node {
    int vertex;
    int weight;
    node(int v, int w) : vertex(v), weight(w) { };
    node() { }
};

class CompareGreater {
    public:
        bool const operator()(node &nodeX, node &nodeY) {
            return (nodeX.weight > nodeY.weight) ;
        }
};

vector< list<node> > adj;
vector<int> weights;
priority_queue<node, vector<node>, CompareGreater> Q;

int nrVertices, nrEdges;

void readData();
void Dijkstra(node);
void writeData();

int main(int argc, char *argv[]) {

    readData();
    Dijkstra(node(1, 0));
    writeData();

    return 0;
}

void readData() {
    fstream in("dijkstra.in", ios::in);

    int nodeX, nodeY, weight;

    in >> nrVertices >> nrEdges;

    adj.resize(nrVertices+1);
    weights.resize(nrVertices+1);

    for (int i = 1; i <= nrVertices; ++i) {
        weights.push_back(INT_MAX);
    }

    for (int i = 1; i <= nrEdges; ++i) {
        in >> nodeX >> nodeY >> weight;
        adj[nodeX].push_back(node(nodeY, weight));
    }

    in.close();
}

void Dijkstra(node startNode) {
    node currentNode;

    weights[startNode.vertex] = 0;
    Q.push(startNode);

    while (!Q.empty()) {
        currentNode = Q.top();
        Q.pop();

        if (currentNode.weight <= weights[currentNode.vertex]) {
            for (list<node>::iterator it = adj[currentNode.vertex].begin(); it != adj[currentNode.vertex].end(); ++it) {
                if (weights[it->vertex] > weights[currentNode.vertex] + it->weight) {
                    weights[it->vertex] = weights[currentNode.vertex] + it->weight;
                    Q.push(node((it->vertex), weights[it->vertex]));
                }
            }
        }
    }
}

void writeData() {
    fstream out("dijkstra.out", ios::out);

    weights.resize(nrVertices+1);
    for (vector<int>::iterator it = weights.begin()+1; it != weights.end(); ++it) {
        out << (*it) << " ";
    }

    out.close();
}

The input data was:

5 7
1 2 10
1 3 2
1 5 100
2 4 3
3 2 5
4 3 15
4 5 5

It means there are 5 nodes, 7 arcs (directed edges), and the arcs exist from node 1 to 2 with the cost of 10, from 1 to 3 with the cost of 2, and so on.

However, the output is wrong. I have no idea where the program might fail. I took the main idea from here: http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=standardTemplateLibrary2#dijkstra1 (At the end it gives the idea for Dijkstra's Algorithm using a priority_queue).

Thanks in advance.

Raul

Answer 1

The problem is in the line

weights.resize(nrVertices+1);

in readData(). This sets up a vector with nrVertices+1 elements of value 0. Later on, you append the actual values you want to this vector using weights.push_back(INT_MAX);.

In the actual Dijkstra algorithm, all interesting weights are thus 0, instead of the INT_MAX you want.

Replace the line with

weights.resize(1);

(just to make sure that the index 1 really refers to the first element - you seem to use 1 as the first index instead of 0), and it might work.