hdu 1023 Train Problem II 高精训练

Train Problem II

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1106 Accepted Submission(s): 654

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

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

练习高精度的不错选择！

……经典的卡塔兰数列。

Catalan数的组合公式为 Cn=C(2n,n) / (n+1);

递推公式为 h(n ) = h(n-1)*(4*n-2) / (n+1)

#include<iostream>
using namespace std;
int a[101][101]={0};
int main()
{
    int n,i,j,len,r,temp,t;
    int b[101];
    a[1][0] = 1;
    len = 1;
    b[1] = 1;
    for(i=2;i<=100;i++)
    {
        t = i-1;
        for(j=0;j<len;j++) //乘法
            a[i][j] = a[i-1][j]*(4*t+2);
        for(r=j=0;j<len;j++)  //处理相乘结果
        {
            temp = a[i][j] + r;
            a[i][j] = temp % 10;
            r = temp / 10;
        }
        while(r) //进位处理
        {
            a[i][len++] = r % 10;
            r /= 10;
        }

        for(j=len-1,r=0;j>=0;j--) //除法
        {
            temp = r*10 + a[i][j];
            a[i][j] = temp/(t+2);
            r = temp%(t+2);
        }
        while(!a[i][len-1]) //高位零处理
            len --;
        b[i] = len;
    }
    while(cin>>n)
    {          for(j=b
-1;j>=0;j--)
            printf("%d",a
[j]);
        printf("/n");
    }
    return 0;
}