Longest Increasing Subsequence

Problem

Given an integer array nums, return the length of the longest strictly increasing subsequence — a subsequence that keeps the original relative order but need not be contiguous.

Examples

Example 1

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

Output:4

[2,3,7,101].

Example 2

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

Output:4

Constraints

1 <= nums.length <= 2500

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How to approach it: the 1-D Dynamic Programming pattern

Break a problem into overlapping subproblems along a single dimension — like "the answer up to index i" — solve each one once, and reuse the result instead of recomputing it.

Look for this pattern when

A greedy or purely recursive approach recomputes the same subproblem repeatedly.
The problem asks for a count, a minimum/maximum, or a yes/no reachability over a sequence, where the answer at position `i` depends on answers at earlier positions.

Read the full 1-D Dynamic Programming guide →

Video walkthroughs

Original problem on LeetCode ↗