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 = 0; c = getchar(), !isdigit(c); ) if(c == '-') f = 1;
    for(x = 0; isdigit(c); c = getchar()) x = x * 10 + c - '0';
    if(f) x = -x;
    return x;
}
template<typename Q> Q read() {
    static Q x; read(x); return x;
}

struct LL {
    const static int N = 300, base = 10;
    int da[N], n;
    
    void init(int n) {
        this->n = n;
        memset(da, 0, sizeof(da[0]) * n);
    }
    
    void clear_zero() {
        while(n && !da[n-1]) n--;
    }
    
    LL operator * (const int &rhs) const {
        static LL c;
        c.init(n + 3);
        for(int i = 0; i < c.n; i++) {
            if(i < n) c.da[i] += da[i] * rhs;
            c.da[i+1] += c.da[i] / base;
            c.da[i] %= base;
        }
        c.clear_zero();
        return c;
    }
    
    void print() const {
        if(n == 0) putchar('0');
        else for(int i = n - 1; i >= 0; i--) {
            putchar(da[i] + '0');
        }
    }
}res;

const int LIM = 1000, N = 500;

int mi[LIM+1], primes[N], tot;
bool flag[LIM+1];

void get_prime(int n) {
    for(int i = 2; i <= n; i++) {
        if(!flag[i]) primes[tot] = i, mi[i] = tot++;
        for(int j = 0; j < tot; j++) {
            int k = primes[j];
            if(i * k > n) break;
            flag[i * k] = 1;
            if(i % k == 0) break;
        }
    }
}

int num[N];

void add(int x, int sign) {
    for(int i = 0, k; k = primes[i], k * k <= x; i++) {
        while(x % k == 0) {
            num[i] += sign;
            x /= k;
        }
    }
    if(x ^ 1) 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 * 2);
    
    for(int i = n * 2; i > n; i--) add(i, 1);
    for(int i = n; i > 1; i--) add(i, -1);
    add(n + 1, -1);
    
    res.da[0] = res.n = 1;
    for(int i = 0; i < tot; i++) {
        while(num[i]--) res = res * primes[i];
    }
    
    res.print();
    
    return 0;
}