[LC] 300. Longest Increasing Subsequence

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(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

Time: O(N^2) 

class Solution {
    public int lengthOfLIS(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        int[] arr = new int[nums.length];
        int res = 0;
        for (int i = 0; i < nums.length; i++) {
            arr[i] = 1;
            for (int j = 0; j < i; j++) {
                if (nums[j] < nums[i]) {
                    // note which one + 1
                    arr[i] = Math.max(arr[i], arr[j] + 1);
                }
            }
            res = Math.max(res, arr[i]);
        }
        return res;
    }
}