JavaAlgorithms/DynamicProgramming/LongestIncreasingSubsequence.java

package DynamicProgramming;

import java.util.Scanner;

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

    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));
    sc.close();
  }

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

    // always points empty slot in tail
    int length = 1;

    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;
  }
}