0

LIS :The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest

Eg:

0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15

A longest increasing subsequence is 0, 2, 6, 9, 13, 15.

I can develop LIS using different ways like Dynamic programming and memorization techniques but, with a particular case where I like to implement LIS using recursion with time complexity of O(N^2).

As of I think using recursion we cannot implement algorithms with time complexity O(N^2).(Please correct me)

However i got this algorithm from google

Algorithm  LIS(A,n,x)
1: if n = 0 then
2:   return 0
3: m   LIS(A; n -1; x)
4: if A[n] < x then
5:   m =max(m; 1 + LIS(A; n-1;A[n]))
6: print(m)

Is this algorithm O(N^2)?

Can you please explain?

Krishna Chikkala
  • 91
  • 1
  • 10
  • Why do you need O(N^2)? O(N) recursive adaptation can be implemented. Just make method return position and length of found sequence. – Basilevs Nov 06 '14 at 03:49

1 Answers1

1

This Algorithm Prints Maximum in a array First Argument (A) is the array, Second Argument (n) is the index of item that now checks for max and third Argument (x) is maximum in that time. in worst case you have a sorted array and in every check (if A[n] < x then) you have to update third Argument with max that means at most you have to check all of array.

the algorithm take a max from index n to n-1 and check that with max from n to n-2 and check that with max in n to n-3 index and it continues to check with n to 1 to get max item.

that means it is O(n+(n-1)+(n-2)+...+2+1) = O(n^2)

pic

Sorry about Pic Quality :)

dev-masih
  • 4,188
  • 3
  • 33
  • 55
  • "This Algorithm Prints Maximum in a array First Argument (A) is the array" - what do you mean by it? let me be more specific This algorithm will generate size of largest increasing sub sequence form a random set of numbers (A) of size n and we use x to keep track of the large number and keep update it for each recursion. sorry if you are clear with the ques. my second question: O(nx(n-1)x(n-2)x...x2x1) = O(n^2) here you are multiplying each iteration, which gives n! but not sum of first n natural numbers please can you be more specific with the second question. Thanks in Advance. – Krishna Chikkala Nov 06 '14 at 03:33