21.满足条件的01序列 卡特兰数

 样例解释

转换成路径问题

 

 

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
ll qmi(ll a, ll b, ll p) {
    ll res = 1;
    while (b) {
        if (b & 1) {
            res = res * a % p;
        }
        a = a * a % p;
        b >>= 1;
    }
    return res;
}
int main() {
    int n;
    cin >> n;
    //C(2n, n) / (n + 1)
    int a = 2 * n, b = n;
    ll res = 1;
    for (int i = 1, j = a; i <= b; i++, j--) {
        res = res * j % mod;
        res = res * qmi(i, mod - 2, mod) % mod;
    }
    res = res * qmi(n + 1, mod - 2, mod) % mod;
    cout << res << endl;
    return 0;
}