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; } }