GATE CSE
First time here? Checkout the FAQ!
x
+4 votes
114 views

asked in Algorithms by Active (1.4k points)   | 114 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

+5 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 (23.2k points)  
selected by
Nice explanation @Gabbar..
+3 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 (7.8k points)  


Top Users Aug 2017
  1. ABKUNDAN

    4658 Points

  2. Bikram

    4134 Points

  3. akash.dinkar12

    3144 Points

  4. rahul sharma 5

    2928 Points

  5. manu00x

    2682 Points

  6. makhdoom ghaya

    2390 Points

  7. just_bhavana

    2058 Points

  8. Tesla!

    1782 Points

  9. pawan kumarln

    1574 Points

  10. learner_geek

    1558 Points


24,892 questions
31,967 answers
74,213 comments
30,083 users