hdu 1023 Train Problem II 这题运用到大数相乘+大数相除+卡特兰数

Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 6454    Accepted Submission(s): 3514

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

12310

 

Sample Output

12516796
Hint
The result will be very large, so you may not process it by 32-bit integers.
 

 卡特兰数：百度百科

代码：

#include <stdio.h>int cat[110][100] ;int main(){int n ;cat[0][0] = cat[1][0] = 1 ;cat[0][1] = cat[1][1] = 1 ;for(int i = 2 ; i <= 100 ; ++i){for(int j = 1 ; j <= cat[i-1][0] ; ++j){cat[i][j] = cat[i-1][j]*(4*i-2) ;}int temp = 0 , len = 1;for(len = 1 ; len <= cat[i-1][0] ; ++len){cat[i][len] += temp ;temp = cat[i][len]/10 ;cat[i][len] %= 10 ; }while(temp != 0){cat[i][len++] += temp%10 ;temp /= 10 ;}for(int j = len-1 , r = 0; j > 0 ; --j){temp = r*10+cat[i][j] ;r = temp%(i+1) ;cat[i][j] = temp/(i+1) ;}while(cat[i][len] == 0){--len ;}cat[i][0] = len ;}while(~scanf("%d",&n)){for(int i = cat[n][0] ; i > 0 ; --i)printf("%d",cat[n][i]) ;puts("") ;}return 0 ;}

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