Dijkstra's Algorithm in C++

Dijkstra's Algorithm

Dijkstra's algorithm is a single source shortest path (sssp) algorithm. Like BFS, this famous graph searching algorithm is widely used in programming and problem solving, generally used to determine shortest tour in a weighted graph.

This algorithm is almost similar to standard BFS, but instead of using a Queue data structure, it uses a heap like data structure or a priority queue to maintain the weight order of nodes. Here is the algorithm and pseudo-code. You can also look into Introduction to Algorithms (by C.L.R.S).

Here is a short implementation of this algorithm in C++, I assumed that, all the edge-weights are positive, and the max possible distance is less than 2²⁰ which is set as INF macro and the graph supports MAX nodes starting from 1 to MAX-1, these macros needs to be set properly.

Input format:

N E // number of nodes and edges
E lines containing an edge (u, v, w) on each line
// edge(u, v, w) means weight of edge u-v is w
// u, v in range 1 to N
S // starting node

C++ code:

#include <cstdio>
#include <queue>
#include <vector>
using namespace std;

#define MAX 100001
#define INF (1<<20)
#define DEBUG if(0)
#define pii pair< int, int >
#define pb(x) push_back(x)

struct comp {
    bool operator() (const pii &a, const pii &b) {
        return a.second > b.second;
    }
};

priority_queue< pii, vector< pii >, comp > Q;
vector< pii > G[MAX];
int D[MAX];
bool F[MAX];

int main() {
    int i, u, v, w, sz, nodes, edges, starting;
    DEBUG freopen("in.txt","r", stdin);

    // create graph
    scanf("%d %d", &nodes, &edges);
    for(i=0; i<edges; i++) {
        scanf("%d %d %d", &u, &v, &w);
        G[u].pb(pii(v, w));
        G[v].pb(pii(u, w)); // for undirected
    }
    scanf("%d", &starting);

    // initialize graph
    for(i=1; i<=nodes; i++) D[i] = INF;
    D[starting] = 0;
    Q.push(pii(starting, 0));

    // dijkstra
    while(!Q.empty()) {
        u = Q.top().first;
        Q.pop();
        if(F[u]) continue;
        sz = G[u].size();
        DEBUG printf("visiting from %d:", u);
        for(i=0; i<sz; i++) {
            v = G[u][i].first;
            w = G[u][i].second;
            if(!F[v] && D[u]+w < D[v]) {
                DEBUG printf(" %d,", v);
                D[v] = D[u] + w;
                Q.push(pii(v, D[v]));
            }
        }
        DEBUG printf("\n");
        F[u] = 1; // done with u
    }

    // result
    for(i=1; i<=nodes; i++) printf("Node %d, min weight = %d\n", i, D[i]);
    return 0;
}

This is a straight forward implementation, according to the problem solving purpose, changes are to be made here and there.