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


Answer: (D)

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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