Longest Increasing Subsequence in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Longest Increasing Subsequence (LIS) in a sequence of numbers?

The Longest Increasing Subsequence is the longest sequence of numbers from the original sequence where each number is strictly greater than the previous one, but the numbers do not need to be consecutive in the original sequence.

intermediate

What is the time complexity of the classic dynamic programming approach to find LIS?

The classic dynamic programming approach to find LIS has a time complexity of O(n²), where n is the length of the input sequence.

beginner

In the LIS problem, what does the dp array represent in the dynamic programming solution?

In the dynamic programming solution, dp[i] represents the length of the longest increasing subsequence that ends at index i.

advanced

What is the purpose of using binary search in the optimized LIS algorithm?

Binary search is used in the optimized LIS algorithm to efficiently find the position to replace elements in a temporary array that helps track the smallest possible tail values of increasing subsequences, reducing time complexity to O(n log n).

beginner

Can the Longest Increasing Subsequence be non-contiguous in the original sequence?

Yes, the Longest Increasing Subsequence can skip elements and does not need to be contiguous in the original sequence, only the order must be maintained.

What does the Longest Increasing Subsequence represent?

A The longest sequence of consecutive numbers

B The longest decreasing sequence

C The longest sequence of increasing numbers in order, not necessarily contiguous

D The sum of all increasing numbers

LIS is the longest sequence where each number is bigger than the previous, but numbers can be non-contiguous.

What is the time complexity of the classic dynamic programming LIS solution?

A O(n log n)

B O(n²)

C O(n)

D O(log n)

The classic DP approach uses nested loops, resulting in O(n²) time complexity.

In the DP solution, what does dp[i] store?

A Length of LIS ending at index i

B Length of LIS starting at index i

C Maximum number in the sequence

D Index of the smallest element

dp[i] stores the length of the longest increasing subsequence that ends exactly at position i.

Which technique reduces LIS time complexity to O(n log n)?

A Binary Search

B Recursion

C Brute Force

D Sorting

Binary search helps efficiently update the temporary array tracking subsequence tails.

Is the LIS always a contiguous subsequence?

A Yes, always contiguous

B Only if all elements are unique

C Only if sorted

D No, can skip elements

LIS can skip elements but must keep the original order.

Explain how the dynamic programming approach finds the Longest Increasing Subsequence.

Think about how you build solutions for smaller parts to solve the whole.

Describe the optimized method to find LIS using binary search and why it is faster.

Focus on how binary search helps quickly update subsequence tails.