What is the optimal time complexity of solving Longest Increasing Subsequence?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Longest Increasing Subsequence?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Longest Increasing Subsequence?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Longest Increasing Subsequence?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Longest Increasing Subsequence

Learn how to solve the 'Longest Increasing Subsequence' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given an integer array nums, return the length of the longest strictly increasing subsequence.

Write a function lengthOfLIS(nums: List[int]) -> int.

Constraints

•1 <= len(nums) <= 2500
•-10^4 <= nums[i] <= 10^4

Examples

Example 1

Input

nums = [10,9,2,5,3,7,101,18]

Output

Explanation

The longest increasing subsequence is [2,3,7,101], therefore the length is 4.

Example 2

Input

nums = [0,1,0,3,2,3]

Output

Explanation

The longest increasing subsequence is [0,1,2,3], length is 4.

Example 3

Input

nums = [7,7,7,7,7,7,7]

Output

Explanation

The longest increasing subsequence is [7], length is 1.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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