HDU1023 Train Problem II

传送门https://vjudge.net/problem/HDU-1023

解题思路：

大数和卡特兰数

实现代码：

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cstdlib>
using namespace std;

const int MAX=100;
const int BASE=10000;

void multiplay(int a[],int b){
    int arr=0;
    for(int i=MAX-1;i>=0;i--){
        arr+=a[i]*b;
        a[i]=arr%BASE;
        arr/=BASE;
    }
}
void divide(int a[],int b){
    int div=0;
    for(int i=0;i<MAX;i++){
        div=div*BASE+a[i];
        a[i]=div/b;
        div%=b;
    }
}

int main(){
    int a[101][MAX];

    memset(a[1],0,sizeof(a[1]));

    a[1][MAX-1]=1;
    for(int i=2;i<101;i++){
        memcpy(a[i],a[i-1],sizeof(a[i]));
        multiplay(a[i],4*i-2);
        divide(a[i],i+1);
    }
    int n;
    while(cin>>n){
        int i;
        for(i=0;i<MAX&&a[n][i]==0;i++);
        cout<<a[n][i++];
        for(;i<MAX;i++){
            printf("%04d",a[n][i]);
        }
        cout<<endl;
    }
    return 0;
}