GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
67 views

asked in Algorithms by Active (1.2k points)   | 67 views
C, 1st statement false because if distance b/w  s-a is 1, a-b=1, b-t=1 & s-t=4; So shortest distance is s-a-b-t= 3; & if we add 1 in every edge so s-a-b-t=6 & s-t=5 .In this case shortest path is change.          2nd statement is true; take same data now double each edge so new distance s-a-b-t=6 & s-t=8; So shortest distance remain same.

2 Answers

+3 votes
Best answer

By using counter Example:

Here shortest path from s TO t is A to B and B to D. Let's increase edge weight of each edge by 3. Now the shortes path from s To t is A to D that is 7. So S1 is false.

if we multiply edge weights with same number the edge weights are increased in same ratio so No change in path but total weight has been changed.

So ans is option C.

 

answered by Veteran (21.6k points)  
selected by
Nice explanation @Gabbar..
+2 votes

 

Consider above graph,

S1)

Now suppose shortest path from S to A was S-B and then B-A. shortest path length = SB + BA = 5+5 =10

Now if we increase weight of each edge by 1, then new shortest path will be

shortest path length = min (SB + BA, SA)= min(6+6,11) =11

that means shortest path has changed. So S1 is wrong

S2)

Now even if we double the edge weight shortest path remains the same

shortest path length = min(SB + BA, SA) = min(10+10,20) = 20

that means shortest path is still S-B and then B-A

So S2 is correct

Hence answer should be C)

answered by Boss (7.4k points)  
Top Users Jan 2017
  1. Debashish Deka

    8126 Points

  2. sudsho

    5042 Points

  3. Habibkhan

    4706 Points

  4. Vijay Thakur

    4458 Points

  5. Bikram

    4348 Points

  6. saurabh rai

    4212 Points

  7. Arjun

    4010 Points

  8. santhoshdevulapally

    3722 Points

  9. GateSet

    3292 Points

  10. Sushant Gokhale

    3286 Points

Monthly Topper: Rs. 500 gift card

19,122 questions
24,033 answers
52,725 comments
20,276 users