What is the Longest Increasing Subsequence pattern?

The Longest Increasing Subsequence is a common coding interview pattern in Dynamic Programming problems. It provides a structured approach to solving related algorithm challenges efficiently.

When should I use Longest Increasing Subsequence?

Use the Longest Increasing Subsequence pattern when you encounter problems matching its characteristics. Check the "When to Use" and "Clues" sections in the lesson for specific indicators.

Is Longest Increasing Subsequence asked in FAANG interviews?

Yes, Longest Increasing Subsequence is an essential pattern commonly tested in FAANG and top tech company technical interviews.

Dynamic Programming

Medium

Longest Increasing Subsequence

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

10 min read

Solve on LeetCode

Problem Understanding

A subsequence is derived by deleting some or no elements without changing the order.

Example: [10, 9, 2, 5, 3, 7, 101, 18]

One LIS: [2, 3, 7, 101]
Length: 4

Algorithm Strategy

We define dp[i] as the length of the LIS ending at index i.

Recurrence:
For each j < i, if nums[j] < nums[i], we can extend the subsequence ending at j.
dp[i] = max(dp[i], dp[j] + 1)

Base Case: dp[i] = 1 (subsequence of itself).

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