[NOI 2018]冒泡排序

题意：求所有字典序大于给定序列且满足条件的排列个数之和。

思路：

考虑dp即可，打表出卡特兰数优化，直接dp可以44...

#include <bits/stdc++.h>
using namespace std ;
#define int long long
const int mod = 998244353ull;
inline int pow(int x,int y) {
    int ret = 1;
    while(y) {
        if(y & 1) ret = ret * x % mod;
        x = x * x % mod;
        y >>= 1;
    }
    return ret;
}
const   int maxn = 6e6+10;
int fac[maxn<<1];
int ifac[maxn<<1];
inline int C (int x,int y) {
    return fac[x] * ifac[y] % mod * ifac[x - y] % mod;
}

inline int calc(int x,int y) {
    if(x < y) {
        return 0;
    }
    
    int d = (x << 1) - y;
    int res = C(d,x);
    if(x != y) {
        res = (res - C(d,x + 1))%mod;
    }
    return res;
}

inline void init() {
    fac[0] = 1;
    for(int i = 1;i <= maxn; ++i) {
        fac[i] = fac[i - 1] * i % mod;
    }
    ifac[maxn] = pow(fac[maxn],mod - 2);
    for(int i = maxn;i >= 1; --i) {
        ifac[i - 1] = ifac[i] * i % mod;
    }
}
int p[maxn];
int T,n;
bool vis[maxn];
signed main () {
    ios::sync_with_stdio(false);
    init();
    cin >> T;
    while(T--) {
        cin >> n;
        for(int i = 1;i <= n; ++i) {
            cin >> p[i];
        }
        memset(vis,0,sizeof(vis));
        int mx = 0;
        int mn = 1;
        int res = 0;
        int cnt = 0;
        for(int i = 1;i < n; ++i,cnt --) {
            if(p[i] > mx) {
                cnt += p[i] - mx;
            }
            mx = max(mx,p[i]);
            vis[p[i]] = 1;
            while(vis[mn] == 1) {
                mn++;
            }
            res += calc(n - i + 1,cnt + 1);
            res %= mod;
            if(mx > p[i] && p[i] > mn) break;
        }
        cout<<(res + mod) % mod <<endl;
    }
    return 0;
}