300. longest increasing subsequence

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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?

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