最长上升子序列
朴素版
O(n²)

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

优化版
O(nlogn)

vector<int> stk;
stk.push_back(a[0]);
for (int i = 1; i < n; i++)
{
    if (a[i] > stk.back())
    {
        stk.push_back(a[i]);
    }
    else
    {
        *lower_bound(stk.begin(), stk.end(), a[i]) = a[i];
    }
}
cout << stk.size() << endl;

最长公共子序列
O(nm)

char a[N], b[M];
int f[N][M];

cin >> n >> m >> a + 1 >> b + 1;
for (int i = 1; i <= n; i++)
{
    for (int j = 1; j <= m; j++)
    {
        f[i][j] = max(f[i - 1][j], f[i][j - 1]);
        if (a[i] == b[j])
        {
            f[i][j] = max(f[i][j], f[i - 1][j - 1] + 1);
        }
    }
}
cout << f[n][m] << endl;

最长公共上升子序列
O(n²)

int a[N], b[N], f[N][N];

for (int i = 1; i <= n; i++)
{
    int maxv = 1;
    for (int j = 1; j <= n; j++)
    {
        f[i][j] = f[i - 1][j];
        if (a[i] == b[j])
        {
            f[i][j] = max(f[i][j], maxv);
        }
        if (a[i] > b[j])
        {
            maxv = max(maxv, f[i - 1][j] + 1);
        }
    }
}
int res = 0;
for (int i = 1; i <= n; i++)
{
    res = max(res, f[n][i]);
}
cout << res << endl;