LeetCode 300: Longest Increasing Subsequence, Deriving Sequence DP from Ending at i

Tue, 22 Sep 2026 00:00:00 +0800

Problem

Input and Output

Input: an integer array nums
Output: return the length of the longest strictly increasing subsequence in nums
A subsequence preserves the relative order of the original array, but it does not need to be contiguous, so elements may be skipped
If the selected indices are i_1 < i_2 < ... < i_k, they must also satisfy nums[i_1] < nums[i_2] < ... < nums[i_k]
The subsequence is non-empty, so at least one element must be selected
Constraints: 1 <= nums.length <= 2500, -10^4 <= nums[i] <= 10^4

Examples

Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
Explanation: [2,5,7,101] is a strictly increasing subsequence of length 4; its elements do not need to be contiguous in the original array.

Input: nums = [0,1,0,3,2,3]
Output: 4
Explanation: [0,1,2,3] has length 4; [0,1,3] is also valid, but shorter.

This article uses Python only. We start with the local question “how long can a subsequence ending at each position be?” and gradually turn it into a runnable solution.

Sequence DP on Jeanphilo Blog

LeetCode 300: Longest Increasing Subsequence, Deriving Sequence DP from Ending at i

Problem

Input and Output

Examples