confudes with Dijkstra's algorithm.

Question

I have tried to understand the question but I got really confused.

So starting from node 3, the distance to other nodes are

3 to 1 = 3

3 to 2 = 1

3 to 4 = 4

3 to 5 = 2

3 to 6 = 3

3 to 7 = 2

and the question asks what is the third node added to the set S.

What I think it should be is 2->5->7->1->6->4 therefore the answer should be (B.7)

but the actual answer is (A.5)

Where did I made a mistake with the question?

Answer 1

Here is how the algorithm works:

$$ \begin{array}{c|c} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline 3 & \infty & 1 & 0 & \infty & \infty & 9 & 2\\ \hline 2 & 3 & 1 & 0 & \infty & 2 & 6 & 2 \end{array} $$

So at the next step algorithm will choose $5$ because it's current distance is minimal ($5 < 7$ breaks the tie) and it's not in $S$.