HDU 1023 Train Problem II （大数卡特兰数）

Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4358    Accepted Submission(s): 2391

Problem Description

As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the trains can get out of the railway.

 

Input

The input contains several test cases. Each test cases consists of a number N(1<=N<=100). The input is terminated by the end of file.

 

Output

For each test case, you should output how many ways that all the trains can get out of the railway.

 

Sample Input

1 2 3 10

 

Sample Output

1 2 5 16796

Hint

The result will be very large, so you may not process it by 32-bit integers.

 

Author

Ignatius.L

 

 这题的意思就是和那个经典的出栈次序问题一模一样，就是卡特兰

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;

int a[110][110];    //大数卡特兰数
int b[110];         //卡特兰数的长度 

void Catalan(){     //求卡特兰数
    int i,j,len,carry,tmp;
    a[1][0]=b[1]=1;
    len=1;
    for(i=2;i<=100;i++){
        for(j=0;j<len;j++)      //乘法 
            a[i][j]=a[i-1][j]*(4*i-2);
        carry=0;
        for(j=0;j<len;j++){     //处理相乘结果
            tmp=carry+a[i][j];
            a[i][j]=tmp%10;
            carry=tmp/10;
        }
        while(carry){       //进位处理 
            a[i][len++]=carry%10;
            carry/=10;
        }
        //carry=0;
        for(j=len-1;j>=0;j--){  //除法 
            tmp=carry*10+a[i][j];
            a[i][j]=tmp/(i+1);
            carry=tmp%(i+1);
        }   
        while(!a[i][len-1])     //高位零处理
            len--;
        b[i]=len;
    }
}

int main(){

    //freopen("input.txt","r",stdin);

    int n;
    Catalan();
    while(~scanf("%d",&n)){
        for(int i=b[n]-1;i>=0;i--)
            printf("%d",a[n][i]);
        printf("
");
    }
    return 0;
}