# Data Structure Questions and Answers-Longest Increasing Subsequence

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 Question 1
The longest increasing subsequence problem is a problem to find the length of a subsequence from a sequence of array elements such that the subsequence is sorted in increasing order and it's length is maximum. This problem can be solved using .....
 A Recursion B Dynamic programming C Brute force D All of the mentioned

Question 1 Explanation:
The longest increasing subsequence problem can be solved using all of the mentioned methods.

 Question 2
Find the longest increasing subsequence for the given sequence:

{10, -10, 12, 9, 10, 15, 13, 14}

 A {10, 12, 15} B {10, 12, 13, 14} C {-10, 12, 13, 14} D {-10, 9, 10, 13, 14}

Question 2 Explanation:
The longest increasing subsequence is {-10, 9, 10, 13, 14}.

 Question 3
Find the length of the longest increasing subsequence for the given sequence:

{-10, 24, -9, 35, -21, 55, -41, 76, 84}

 A 5 B 4 C 3 D 6

Question 3 Explanation:
The longest increasing subsequence is {-10, 24, 35, 55, 76, 84} and it's length is 6.

 Question 4
For any given sequence, there will ALWAYS be a unique increasing subsequence with the longest length.
 A True B False

Question 4 Explanation:
For a given sequence, it is possible that there is more than one subsequence with the longest length.

Consider, the following sequence: {10, 11, 12, 1, 2, 3}:

There are two longest increasing subsequences: {1, 2, 3} and {10, 11, 12}.

 Question 5
The number of increasing subsequences with the longest length for the given sequence are:

{10, 9, 8, 7, 6, 5}

 A 3 B 4 C 5 D 6