GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
427 views

I was reading some of the notes (made easy and ACE)  and noticed that some teacher have taught that time complexity for Binary Knapsack O(2^(n/2)). which can not be reduced further. but What I have seen here that in worst case by using memoization we can reduce the time complexity upto O(n.W) where n is number of Object and W is capacity of knapsack.

What I am thinking that, Is it really Binary knapsack is NPC, Like Travelling Salesman problem because TSP tales O(n^2*2^n) times to calculate the tour by using dynamic method, which is efficient than o(n^n) of TSP brutforce techniques? Put some light, Am I missing something. Should I stop seeing those notes which people have posted over the internet. 

asked in Algorithms by Veteran (34.8k points) 11 82 292 | 427 views

1 Answer

+2 votes
Best answer

See AFAIK in DP we consider only the distinct function calls .So Using DP the complexity of Binary knapsack is O(nW).

But for the larger value of W the the complexity of Binary knapsack is O(2n). Because in 0/1 knapsack has very less repetition

So for the larger value W ,0/1 knapsack will generate n level complete binary tree So it will have  2n function calls and the time complexity

becomes O(2n). So it one of NP complete problem.

answered by Veteran (39k points) 25 107 343
selected by
@ManojK Can you explain more, What do you mean by larger value? and Why that O(nW) did not work in the larger value?

 for n=5, W=100000  Here w has larger value.

Here n is polynomial in length but length of  w not polynomial it  can anything.

When comparing this with the  brute force algo take O(2n), but depending on W, either the dynamic programming algorithm is more efficient or the brute force algorithm could be more efficient. (For example, for n=5, W=100000, brute force is preferable, but for n=30 and W=1000, the dynamic programming solution is preferable.)

@manojK sir, abhi samjha cheekylaugh

Related questions

0 votes
1 answer
1
asked in Algorithms by firki lama Active (1.1k points) 1 21 47 | 75 views
+1 vote
0 answers
2
asked in Algorithms by Akriti sood Veteran (14.8k points) 15 151 316 | 160 views
+1 vote
2 answers
3


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23398 Points

  2. Bikram

    17078 Points

  3. Habibkhan

    8264 Points

  4. srestha

    6296 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4978 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4348 Points

  9. sushmita

    3964 Points

  10. Rishi yadav

    3804 Points


Recent Badges

Notable Question KISHALAY DAS
Notable Question sh!va
Notable Question abhijeetbzu
Great Question jothee
Popular Question rahul sharma 5
Nice Question mohit kumar 5
Notable Question rishu_darkshadow
Nice Comment Pranay Datta 1
Copy Editor Shivansh Gupta
Nice Comment KULDEEP SINGH 2
27,324 questions
35,176 answers
84,108 comments
33,279 users