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?

Solution:

Using dynamic programming and binary search, a[i] for the min last value of increasing subsequence of length i.

class Solution {
    public int lengthOfLIS(int[] nums) {
        int[] a = new int[nums.length];
        int max_len = 0;
        for (int i = 0; i < nums.length; i++) {            
            int index = Arrays.binarySearch(a,0,max_len,nums[i]);            
            if (index < 0) {
                int p = -index-1;
                a[p] = nums[i];
                if (p == max_len) max_len++;
            }
        }
        return max_len;
    }
}