How to determine the longest increasing subsequence using dynamic programming?

Question

I have a set of integers. I want to find the longest increasing subsequence of that set using dynamic programming.

Answer 1

This is a Java implementation in O(n^2). I just did not use Binary Search to find the smallest element in S, which is >= than X. I just used a for loop. Using Binary Search would make the complexity at O(n logn)

public static void olis(int[] seq){

    int[] memo = new int[seq.length];

    memo[0] = seq[0];
    int pos = 0;

    for (int i=1; i= x){
                        memo[j] = x;
                        break;
                    }
                }
            }
            //just to print every step
            System.out.println(Arrays.toString(memo));
    }

    //the final array with the LIS
    System.out.println(Arrays.toString(memo));
    System.out.println("The length of lis is " + (pos + 1));

}