Djikstra's Shortest path algorithm

Question

I am learning Djikstra's and i have prepared the code below based on slightly different idea than Djikstra. Now, In many of the websites, i have seen the use of Extract min and boolean array of visited edges. I have used none and my answer is also correct. Is there any test case or scenario where my algo won't work.

    import java.util.*;
    class ShortestPath2 {
        static int Ar[][];
        static int dist[];

        static int nodes;
        public static void djikstra(int source) {
            LinkedList < Integer > list = new LinkedList < Integer > ();
            dist[source] = 0;

            list.add(source);
            while (!list.isEmpty()) {
                source = list.removeFirst();

                for (int i = 0; i < nodes; i++) {
                    if (Ar[source][i] != 0) {

                        if (dist[i] > dist[source] + Ar[source][i]) {
                            dist[i] = Math.min(dist[i], dist[source] + Ar[source][i]);
                            list.add(i);
                        }
                    }
                }

            }
            System.out.println(Arrays.toString(dist));
        }

        public static void main(String[] args) {
            nodes = 9;

            Ar = new int[nodes][nodes];
            dist = new int[nodes];

            Arrays.fill(dist, Integer.MAX_VALUE);

            Ar = new int[][] {
                 {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}
            };

            djikstra(0);
        }
    }

You should probably post this on code review rather than stack overflow: http://codereview.stackexchange.com/ — John Coleman, Sep 30 '16 at 09:49
@JohnColeman They'll have a heart attack! OP: **please** learn how to format your code properly. This is unreadable. Does it even work properly? It looks like you're using a linked list to keep track of the visited nodes, but how does it reliably choose the shortest hop from the set of visited nodes at each iteration? In any case, a linked list is the wrong data structure for this job. If you use a min-heap, the code will run faster by several orders of magnitude on large data sets. — r3mainer, Sep 30 '16 at 09:51
@Tempux Ah, I see it now. And I'm getting a headache. I'm out of here... — r3mainer, Sep 30 '16 at 09:56
@squeamishossifrage I was taking at face value OP's claim that it worked but they wanted to know if any edge-case had been missed. If this is the case it seems like a code review problem. Perhaps they are mistaken that the code actually works. — John Coleman, Sep 30 '16 at 10:00
@squeamishossifrage to be fair, code being goddamn ugly is not a problem for Code Review, that's what we're here for. The only main requirement is that the OP reasonably believes their code works as intended, and they are actually looking for a general review of their implementation. Asking us to look for edge-cases is borderline. Would be better if OP just said, "My code does this thing, how could it be done better?" — Kaz, Sep 30 '16 at 10:09

Saeid · Accepted Answer · 2016-09-30T12:18:10.900

3

The whole idea behind Dijkstra algorithm is using the priority queue. You can't remove the priority queue from Dijkstra and still call it Dijkstra algorithm. What you have written is a BFS without checking for visited. Your code won't terminate if the graph has a negative cycle. Your code will find the shortest path on graph a without negative cycles but the complexity could become exponential. Because there is the possibility of revisiting the nodes over and over again (as a result of removing the visited list). If you add the visited list to your code, your code won't always find the shortest path because you aren't using priority queue. So you need both the priority queue and visited list in order to find the shortest path in linear time.

A --100---B --100-- I---100---O  // A-B, B-I, I-O weight : 100
|        / \       / \        |  // A-C, C-D, ... weight : 1
C-D-E-F-G   H-J-K-L   M-N-P-Q-R

As an example you can use the above graph to see how many times your code will revisit O.

edited Sep 30 '16 at 12:18

answered Sep 30 '16 at 10:41

Saeid

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What do u mean by Negative Cycle? As far as i know, Djikstra's Original Implementation don't account for negative weight. And it won't go to cycle because of : if(dist[i]>dist[source]+Ar[source][i]) { dist[i]=Math.min(dist[i],dist[source]+Ar[source][i]); list.add(i); } – waterbyte Sep 30 '16 at 11:31
Sorry for bad code editing, but I don't have a PC as of now and mobile editing is posing a lot of problem. – waterbyte Sep 30 '16 at 11:36
I don't see, why there is possibility of Entering a node again because Node is added onto the list only when a shorter path to it is found. And if there would be any Cycle to be formed, then the path to it would be larger and it won't be added to the list. – waterbyte Sep 30 '16 at 11:40
@Waterbyte Dijkstara doesn't give the correct shortest paths when there is negative edges in the graph, but it will terminate. Your code doesn't not terminate when there is a negative cycle. Infinite loop is considered a huge bug. – Saeid Sep 30 '16 at 12:13
@Waterbyte just look at the example I gave in the answer. First you go to B using *A-B* edge. But again there is shorter path to B from A using *C-D-E-F-G* so you visit *B* again. This can happen too many times with other nodes. – Saeid Sep 30 '16 at 12:15
So, Apart from visiting same node twice which don't affect the answer(as shortest path is still updated) and the special case of negative weight, it works right? And though, it visits node twice, Is it better than Djikstra's which uses Priority Queue and Boolean for Visited? – waterbyte Sep 30 '16 at 12:20
@Waterbyte Do your edges have weights? – Saeid Sep 30 '16 at 12:25
In my example, the array Values are weight. One thing to notice is that I was learning Djikstras from the GeeksforGeek website. So, the example is from there. After writing my own code which was different than Djikstra's, i compared the solution any found out that my Code Idea produces Correct result. I tried various examples and all time the correct answer was evaluated by my code. – waterbyte Sep 30 '16 at 12:27
1

@Waterbyte It is absolutely worse than Dijkstra. Because it is possible that you visit nodes many many times(not twice, just simulate your algorithm on the example graph). Your algorithm complexity is exponential. Dijkstra is linear. – Saeid Sep 30 '16 at 12:32
Yup, I got it. The complexity would be exponential.There would be too many updates. Thanks Tempux for clearing this out. – waterbyte Sep 30 '16 at 12:36

score 1 · Answer 2 · edited Jan 24 '18 at 07:54

Dijkstra's Original Implementation doesn't resolve the negative edge (but can detect it) and negative cycle problem.

To resolve this, we can use the Bellman Ford Algorithm.

It will give the correct shortest path even if there is a negative edge (but no negative cycle)
It can detect whether a negative cycle is there or not (but doesn't give the correct solution if a negative cycle is there, so better we terminate the code)

Djikstra's Shortest path algorithm

2 Answers2