最长上升子序列-线性dp

重点
1. 尽量尝试用低维数来表示状态方程
2. a[i] 表示以i结尾的所有上升子序列的集合，属性是最大值

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1010;
int a[N];
int f[N];

int main() {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];

    for (int i = 1; i <= n; i++) {
        f[i] = 1;  // 只有i一个字符
        for (int j = 1; j < i; j++) {
            if (a[j] < a[i]) f[i] = max(f[i], f[j] + 1);
        }
    }
    int res = 0;
    for (int i = 1; i <= n; i++) res = max(res, f[i]);
    //cout << endl;
    cout << res << endl;

    return 0;
}