类似于单调栈的思想

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

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

        //数组模拟单调栈，idx指向栈顶元素
        //idx==-1说明栈为空
        int[] f = new int[n];
        int idx = -1;

        //考虑数组a中的每个元素，将其加入栈中，始终保持栈中元素严格单调递增
        for (int i = 0; i < n; i++) {
            //栈为空或者当前a中元素大于栈顶元素，直接进栈
            if (idx == -1 || a[i] > f[idx]) {
                f[++idx] = a[i];
            } else {    //用a[i]更新栈中元素，替换栈中第一个大于等于a[i]的元素为a[i]
                int l = 0, r = idx;
                while (l < r) {
                    int mid = l + r >> 1;
                    if (f[mid] < a[i]) l = mid + 1;
                    else r = mid;
                }
                f[l] = a[i];
            }
        }

        System.out.println(idx + 1);
    }
}