HDU 1023 Train Problem II （打表求解卡特兰数）

快来打我* 2022-07-28 04:06 26阅读 0赞

HDU 1023 Train Problem Ⅱ：[http://acm.hdu.edu.cn/showproblem.php?pid=1023][http_acm.hdu.edu.cn_showproblem.php_pid_1023]

题面：

**Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)  
Total Submission(s): 7629 Accepted Submission(s): 4110**

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.

题目大意及分析：

由于此题为非降路径问题，且观察样例，即要计算卡特兰数，由于数据比较大，所以要利用打表的方法。

注意此题所给提示为32位int不能存下，但是64位longlong也不能存下，大数打表还是比较可靠的。

代码实现：//该代码算是卡特兰数打表的模板了

#include <iostream>
    #include <cstdio>
    
    using namespace std;
    
    int a[105][100];
    void Catal() //卡特兰数打表
    {
        int i,j,yu,len;
        a[2][0]=1;
        a[2][1]=2;
        a[1][0]=1;
        a[1][1]=1;
        len=1;
        for(i=3;i<101;i++)
        {
            yu=0;
            for(j=1;j<=len;j++)
            {
                int t=(a[i-1][j])*(4*i-2)+yu;
                yu=t/10;
                a[i][j]=t%10;
            }
            while(yu)
            {
                a[i][++len]=yu%10;
                yu/=10;
            }
            for(j=len;j>=1;j--)
            {
                int t=a[i][j]+yu*10;
                a[i][j]=t/(i+1);
                yu=t%(i+1);
            }
            while(!a[i][len])
            {
                len--;
            }
            a[i][0]=len;
        }
    }
    
    int main()
    {
        Catal();
        int n;
        while(scanf("%d",&n)!=EOF)
        {
            for(int i=a[n][0];i>0;i--)
            {
                printf("%d",a[n][i]);
            }
            printf("\n");
        }
        return 0;
    }

[http_acm.hdu.edu.cn_showproblem.php_pid_1023]: http://http://acm.hdu.edu.cn/showproblem.php?pid=1023