# GATE | GATE CS 2008 | Question 45

Dijkstra’s single source shortest path algorithm when run from vertex a in the below graph, computes the correct shortest path distance to (A) only vertex a
(B) only vertices a, e, f, g, h
(C) only vertices a, b, c, d
(D) all the vertices

Explanation: Dijkstra’s single source shortest path is not guaranteed to work for graphs with negative weight edges, but it works for the given graph.
Let us see…

```Let us run the 1st pass
b 1
b is minimum, so shortest distance to b is 1.

After 1st  pass, distances are
c 3, e -2.
e is minimum, so shortest distance to e is -2

After 2nd pass, distances are
c 3, f 0.
f is minimum, so shortest distance to f is 0

After 3rd pass, distances are
c 3, g 3.
Both are same, let us take g. so shortest distance to g is 3.

After 4th pass, distances are
c 3, h 5
c is minimum, so shortest distance to c is 3

After 5th pass, distances are
h  -2
h is minimum, so shortest distance to h is -2```
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