300. Longest Increasing Subsequence

Leetcode Binary Search Dynamic Programming

Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

Input: [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.

Note:

There may be more than one LIS combination, it is only necessary for you to return the length.
Your algorithm should run in $O(n^2)$ complexity.
Follow up: Could you improve it to $O(n \log n)$ time complexity?