[LeetCode 300] Longest Increasing Subsequence

Problem

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

A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, [3,6,2,7] is a subsequence of the array [0,3,1,6,2,2,7].

Example 1:

Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
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: 4

Example 3:

Input: nums = [7,7,7,7,7,7,7]
Output: 1

Constraints:

1 <= nums.length <= 2500
-10^4 <= nums[i] <= 10^4

Follow up:

Can you come up with an algorithm that runs in O(n log(n)) time complexity?

Thoughts

Bottom up dynamic programming

TypeScript

function lengthOfLIS(nums: number[]): number {
    const LIS: number[] = Array(nums.length).fill(1);
    
    // move backward
    for(let i = nums.length - 1; i >= 0; i--){
        // check all the following values
        for(let j = i + 1; j < nums.length; j++){
            // dynamic programming condition
            if(nums[i] < nums[j]){
                LIS[i] = Math.max(LIS[i], 1 + LIS[j])
            }
        }
    }
    
    return Math.max(...LIS)
};

Reference

https://leetcode.com/problems/longest-increasing-subsequence/

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