Longest Increasing Subsequence, DP solution

Problem is here: https://leetcode.com/problems/longest-increasing-subsequence/description/:

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?

The solution below is the N^2. Use DP for it: keep track of the best sequence for all elements 0..i-1 using O(n) space. Then it is an easy O(n) time check for element i. Code is below, cheers, Marcelo.

public class Solution
{
public int LengthOfLIS(int[] nums)
{
if (nums == null || nums.Length == 0) return 0;

int[] longest = new int[nums.Length];

int retVal = 1;
longest[0] = 1;
for (int i = 1; i < longest.Length; i++)
{
longest[i] = 1;
for (int j = 0; j < i; j++)
longest[i] = nums[i] > nums[j] ? Math.Max(longest[i], longest[j] + 1) : longest[i];
retVal = Math.Max(longest[i], retVal);
}

return retVal;
}
}