Dynamic Programming/LongestIncreasingSubsequence.java

import java.util.Scanner;

/**
 *
 * @author Afrizal Fikri (https://github.com/icalF)
 *
 */
public class LongestIncreasingSubsequence {
    public static void main(String[] args) throws Exception {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        int ar[] = new int[n];
        for (int i = 0; i < n; i++) {
            ar[i] = sc.nextInt();
        }

        System.out.println(LIS(ar));
    }

    private static int upperBound(int[] ar, int l, int r, int key) {
        while (l < r-1) {
            int m = (l + r) / 2;
            if (ar[m] >= key)
                r = m;
            else
                l = m;
        }

        return r;
    }

    private static int LIS(int[] array) {
        int N = array.length;
        if (N == 0)
            return 0;
 
        int[] tail = new int[N];
        int length = 1; // always points empty slot in tail
     
        tail[0] = array[0];
        for (int i = 1; i < N; i++) {

            // new smallest value
            if (array[i] < tail[0])
                tail[0] = array[i];

            // array[i] extends largest subsequence
            else if (array[i] > tail[length-1])
                tail[length++] = array[i];

            // array[i] will become end candidate of an existing subsequence or
            // Throw away larger elements in all LIS, to make room for upcoming grater elements than array[i]
            // (and also, array[i] would have already appeared in one of LIS, identify the location and replace it)
            else
                tail[upperBound(tail, -1, length-1, array[i])] = array[i];
        }
     
        return length;
    }
}