ncpc-2014 Catalan Square

Posted 2021-01-02 kuroko-ghh

Catalan Square

注意的是等于Cn+1

 

高精度卡特兰数

#include<bits/stdc++.h>
#define BASE 10000
#define MAX 100010
using namespace std;

struct BigInt{
    int num[MAX],len;

    BigInt(int _ = 0) {
        num[len = 1] = _;
    }
    BigInt operator +(const BigInt &a)const {
        BigInt re;
        re.len = max(len,a.len);
        int temp = 0;
        for(int i = 1; i <= a.len; ++i) {
            re.num[i] = temp + num[i] + a.num[i];
            temp = re.num[i] / BASE;
            re.num[i] %= BASE;
        }
        if(temp)    re.num[++re.len] = temp;
        return re;
    }
    BigInt operator *(int a)const {
        BigInt re;
        re.len = len;
        int temp = 0;
        for(int i = 1; i <= len; ++i) {
            re.num[i] = temp + num[i] * a;
            temp = re.num[i] / BASE;
            re.num[i] %= BASE;
        }
        while(temp) re.num[++re.len] = temp % BASE,temp /= BASE;
        return re;
    }
    BigInt operator /(int a)const {
        BigInt re;
        re.len = len;
        int temp = 0;
        for(int i = len; i; --i) {
            re.num[i] = (temp + num[i]) / a;
            temp = (temp + num[i]) % a * BASE;
        }
        while(!re.num[re.len])  --re.len;
        return re;
    }
};

int main()
{   
    //freopen("in.txt","r",stdin);
    int x;
    cin >> x;
    x=x+1;
    BigInt ans(1);
    for(int i = 2; i <= x; ++i)
        ans = ans * (4 * i - 2) / (i + 1);
    printf("%d",ans.num[ans.len]);
    for(int i = ans.len - 1; i; --i)
        printf("%04d",ans.num[i]);
    return 0;
}

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