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which is N here, the size of the array.Ģ. Define problem variables and decide the states: There is only one parameter on which the state of the problem depends i.e. What are the other elements of dynamic programming we need to figure out?ġ.

This means the implementation of our dynamic programming should be bottom-up. Well, the recursion approach above is top-down. This means we could improve the time complexity of our algorithm using Dynamic Programming. The height of the tree is the stack space used.Ĭreate a recursion tree for the above recursion.Īs you can clearly see in the recursion tree, there are overlapping subproblems and also holds an optimal substructure property. To confirm the space complexity in recursion, draw the recursion tree.What’s the order of elements in the array that is the worst-case for this problem?.

Can you see the overlapping subproblems in this case?.Is this recursion top-down or bottom-up?.Space Complexity: O(N), for stack space in recursion Critical ideas to think! Recurrence relation: T(N) = 1 + Sum j = 1 to N-1 (T(j)) Max_ans = max(max_ans, lis_ending_here(arr, i)) return max_ans Because a single number can be a subsequence too You need to find the length of the longest increasing subsequence that can be derived from the given array.Įxplanation: The longest increasing subsequence is int longest_increasing_subsequence(int arr, int N)

You are given an array A with N elements, write a program to find the longest increasing subsequence in the array.Īn increasing subsequence is a subsequence with its elements in increasing order. Problem Description: A subsequence is derived from an array by deleting a few of its elements and not changing the order of remaining elements. Level: Medium Asked In: Amazon, Facebook, Microsoft Understanding the Problem

Elements of programming interviews find celibrity