HDU 1134 卡特蘭數 大數乘法除法

Problem Description
This is a small but ancient game. You are supposed to write down the numbers 1, 2, 3, ... , 2n - 1, 2n consecutively in clockwise order on the ground to form a circle, and then, to draw some straight line segments to connect them into number pairs. Every number must be connected to exactly one another. And, no two segments are allowed to intersect.

It's still a simple game, isn't it? But after you've written down the 2n numbers, can you tell me in how many different ways can you connect the numbers into pairs? Life is harder, right?

Input
Each line of the input file will be a single positive number n, except the last line, which is a number -1. You may assume that 1 <= n <= 100.

Output
For each n, print in a single line the number of ways to connect the 2n numbers into pairs.

Sample Input
2
3
-1

Sample Output
2
5

  #include <stdio.h>  
#include <string.h>  
#include <iostream>  
using namespace std; 
int n; 
#define BASE 10000  
#define UNIT 4  
#define FORMAT "%04d"  
 
class BigNum{ 
public: 
    int a[20]; 
    int length; 
    BigNum(const int k){ //用小於BASE的k初始化大數  
        memset(a, 0, sizeof(a)); 
        a[0] = k; 
        length = 1; 
    } 
    BigNum(){ 
        memset(a, 0, sizeof(a)); 
        length = 0; 
    } 
    BigNum operator * (const BigNum & B){ 
        BigNum ans; 
        int i,j,up=0,num; 
        for(i=0; i<length; i++){ 
            up = 0; //每次循環都要初始化為0  
            for(j=0; j<B.length; j++){ 
                num = up + a[i] * B.a[j] + ans.a[i+j]; 
                up = num / BASE; 
                num = num % BASE; 
            //  cout << num << endl;  
                ans.a[i+j] = num; 
            } 
        //  cout << up << endl;  
            if(up > 0) 
                ans.a[i+j] = up; 
        } 
        ans.length = i+j; 
        while(ans.a[ans.length -1] == 0 && ans.length > 1) 
            ans.length--; 
        return ans; 
    } 
    BigNum operator /(const int & k) const{  // k < BASE, 對此題適用  
        BigNum ans; 
        int down=0,i,num; 
        for(i=length-1; i>=0; i--){ 
            num = ( (down * BASE) + a[i] ) / k; 
            down =  ( (down * BASE) + a[i] ) % k; 
            ans.a[i] = num; 
        } 
        ans.length = length; 
        while(ans.a[ans.length-1] == 0 && ans.length > 1) 
            ans.length -- ; 
        return ans; 
    } 
    void print(){ 
        printf("%d", a[length-1]); 
        for(int i=length-2; i>=0; i--) 
            printf(FORMAT,a[i]); 
    } 
}; 
 
//f(n) = C(2n,n)/(n+1)  
int main(){ 
    BigNum nums[101]; 
    nums[1] = BigNum(1); 
    nums[2] = BigNum(2); 
    nums[3] = BigNum(5); 
    for(int i=4; i<=100; i++){ 
        nums[i] = nums[i-1] * (4*i-2)/(i+1); 
    } 
    int n; 
    while(scanf("%d", &n), n>0){ 
        nums[n].print(); 
        printf("\n"); 
    } 
    return 0; 
} 

#include <stdio.h>
#include <string.h>
#include <iostream>
using namespace std;
int n;
#define BASE 10000
#define UNIT 4
#define FORMAT "%04d"

class BigNum{
public:
 int a[20];
 int length;
 BigNum(const int k){ //用小於BASE的k初始化大數
  memset(a, 0, sizeof(a));
  a[0] = k;
  length = 1;
 }
 BigNum(){
  memset(a, 0, sizeof(a));
  length = 0;
 }
 BigNum operator * (const BigNum & B){
  BigNum ans;
  int i,j,up=0,num;
  for(i=0; i<length; i++){
   up = 0; //每次循環都要初始化為0
   for(j=0; j<B.length; j++){
    num = up + a[i] * B.a[j] + ans.a[i+j];
    up = num / BASE;
    num = num % BASE;
   // cout << num << endl;
    ans.a[i+j] = num;
   }
  // cout << up << endl;
   if(up > 0)
    ans.a[i+j] = up;
  }
  ans.length = i+j;
  while(ans.a[ans.length -1] == 0 && ans.length > 1)
   ans.length--;
  return ans;
 }
 BigNum operator /(const int & k) const{  // k < BASE, 對此題適用
   BigNum ans;
  int down=0,i,num;
  for(i=length-1; i>=0; i--){
   num = ( (down * BASE) + a[i] ) / k;
   down =  ( (down * BASE) + a[i] ) % k;
   ans.a[i] = num;
  }
  ans.length = length;
  while(ans.a[ans.length-1] == 0 && ans.length > 1)
   ans.length -- ;
  return ans;
 }
 void print(){
  printf("%d", a[length-1]);
  for(int i=length-2; i>=0; i--)
   printf(FORMAT,a[i]);
 }
};

//f(n) = C(2n,n)/(n+1)
int main(){
 BigNum nums[101];
 nums[1] = BigNum(1);
 nums[2] = BigNum(2);
 nums[3] = BigNum(5);
 for(int i=4; i<=100; i++){
  nums[i] = nums[i-1] * (4*i-2)/(i+1);
 }
 int n;
 while(scanf("%d", &n), n>0){
  nums[n].print();
  printf("\n");
 }
 return 0;
}