bzoj2822: [AHOI2012]树屋阶梯

咦，这里有好多东西https://en.wikipedia.org/wiki/Catalan_number

每个矩形最多贡献一个拐角

枚举左上角的点和那个拐角是一个矩形

 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<algorithm>
 #include<iostream>

 using namespace std;

 void setIO(const string& s) {
     freopen((s + ".in").c_str(), "r", stdin);
     freopen((s + ".out").c_str(), "w", stdout);
 }
 template<typename Q> Q read(Q& x) {
     static char c, f;
     for(f = ; c = getchar(), !isdigit(c); ) if(c == '-') f = ;
     for(x = ; isdigit(c); c = getchar()) x = x *  + c - '';
     if(f) x = -x;
     return x;
 }
 template<typename Q> Q read() {
     static Q x; read(x); return x;
 }

 struct LL {
     const static int N = , base = ;
     int da[N], n;

     void init(int n) {
         this->n = n;
         memset(da, , sizeof(da[]) * n);
     }

     void clear_zero() {
         while(n && !da[n-]) n--;
     }

     LL operator * (const int &rhs) const {
         static LL c;
         c.init(n + );
         for(int i = ; i < c.n; i++) {
             if(i < n) c.da[i] += da[i] * rhs;
             c.da[i+] += c.da[i] / base;
             c.da[i] %= base;
         }
         c.clear_zero();
         return c;
     }

     void print() const {
         if(n == ) putchar('');
         else for(int i = n - ; i >= ; i--) {
             putchar(da[i] + '');
         }
     }
 }res;

 const int LIM = , N = ;

 int mi[LIM+], primes[N], tot;
 bool flag[LIM+];

 void get_prime(int n) {
     for(int i = ; i <= n; i++) {
         if(!flag[i]) primes[tot] = i, mi[i] = tot++;
         for(int j = ; j < tot; j++) {
             int k = primes[j];
             if(i * k > n) break;
             flag[i * k] = ;
             if(i % k == ) break;
         }
     }
 }

 int num[N];

 void add(int x, int sign) {
     for(int i = , k; k = primes[i], k * k <= x; i++) {
         while(x % k == ) {
             num[i] += sign;
             x /= k;
         }
     }
     if(x ^ ) num[mi[x]] += sign;
 }
 int main() {
 #ifdef DEBUG
     freopen("in.txt", "r", stdin);
     freopen("out.txt", "w", stdout);
 #endif

     int n; scanf("%d", &n);
     get_prime(n * );

     for(int i = n * ; i > n; i--) add(i, );
     for(int i = n; i > ; i--) add(i, -);
     add(n + , -);

     res.da[] = res.n = ;
     for(int i = ; i < tot; i++) {
         while(num[i]--) res = res * primes[i];
     }

     res.print();

     return ;
 }