Longest Increasing Subsequence

/*
 * Problem : Find the LIS length.
 * Input   : n, then n integers.
 * Output  : The length.
 * Approach: Keep the smallest tails.
 * Time    : O(n log n)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static int solve(int[] a) {
        // Step 1: tails[i] = the smallest last value of an increasing subsequence with length i + 1.
        int[] tails = new int[a.length];
        int length = 0;

        for (int value : a) {
            // Step 2: Binary search for the first tail that is greater than or equal to the value.
            int low = 0;
            int high = length;
            while (low < high) {
                int mid = low + (high - low) / 2;
                if (tails[mid] < value) {
                    low = mid + 1;
                } else {
                    high = mid;
                }
            }

            // Step 3: Replace that tail with the value. If the value is bigger than all tails, the subsequence grows.
            tails[low] = value;
            if (low == length) {
                length++;
            }
        }
        return length;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = scanner.nextInt();
        }
        System.out.println(solve(a));
    }
}