Data Structure Questions and Answers-Longest Increasing Subsequence

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Data Structure Questions and Answers-Longest Increasing Subsequence

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Question 1 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
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 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
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 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
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 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
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 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
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
Question 5 Explanation: 
Each array element individually forms a longest increasing subsequence and so, the length of the longest increasing subsequence is 1. So, the number of increasing subsequences with the longest length is 6.

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