Time Complexity Analysis for Non-ovarlapping Subproblem Recursive Solution

Question

Here I am just putting python code.

  Rec(Arr,N,K,X) :
     if(X==0 and K==0):
         return 1
     elif(X<=0 or K<=0 or N<0):
        return 0
     else :
         return Rec(Arr,N-1,K,X)+Rec(Arr,N,K-1,X-Arr[N])

Provided that all element of Arr are distinct,this conclude that all sub problems are non-overlapping(just took an small case, do it manually)

Please Evaluate Time Complexity in terms of N,K,X. Thanks for reading this question...

What is wrong with my queation..everyone just downvoting it..can anyone point out issue? — Ramesh Chandra, May 12 '16 at 10:21
At what complexity did you arrive? And why do you think it's incorrect? — Cristiano Sousa, May 12 '16 at 11:08
@cristiano-sousa I thought as O(N*K)..I know that is wrong because I got TLE provided that N<=50 && K<=10. THANKS to #takoika..But I didnt understand his solution..but It gave me a hint that this solution will not work, i had to search for more optimized solution — Ramesh Chandra, May 12 '16 at 14:42

takoika · Accepted Answer · 2016-05-12T11:13:56.567

0

Basically this problem is regarded as depth first search of a binary tree whose height is bounded by max(N,K). So order of time complexity is bounded by 2^max(N,K). And then X and Arr might reduce this time complexity. But it is unclear because it depend on the values of Arr and X. (For example if Arr=[inf,...,inf], the time complexity will be N.)

edited May 12 '16 at 11:13

answered May 12 '16 at 10:56

takoika

363
2
10

Could you please explain little more ? – Ramesh Chandra May 12 '16 at 14:46
Assume due X it never exit..worst case..than – Ramesh Chandra May 12 '16 at 14:56
2^max(N,K) is upper bound without X and Arr. – takoika May 12 '16 at 16:42

Time Complexity Analysis for Non-ovarlapping Subproblem Recursive Solution

1 Answers1