A - Train Problem II ( 火车和卡特兰数 )

Posted 2020-09-30 山杉三

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. 

InputThe 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. 
OutputFor 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.

 1 #include <iostream>
 2 #include <string.h>
 3 using namespace std;
 4 
 5 const int MAX = 305;
 6 int a[MAX][MAX];
 7 
 8 
 9 void chengf(int x,int i)
10 {
11     int temp = 0;;
12     for(int j = 300;j >=0;j--)
13     {
14         temp = a[i-1][j]*x + temp;
15         a[i][j] = temp % 10;
16         temp = temp / 10;
17 
18     }
19 }
20 
21 void chuf(int x,int i)
22 {
23     int temp = 0;
24     for(int j = 0;j <=300;j++)
25     {
26         temp = temp *10 + a[i][j];
27         a[i][j] = temp / x;
28         temp = temp %x;
29     }
30 }
31 
32 void DP()
33 {
34     memset(a,0,sizeof(a));
35     a[1][300] = 1;
36     for(int i = 2;i <= 100;i++)
37     {
38         int temp = 4*i - 2;
39         chengf(temp,i);
40         temp = i + 1;
41         chuf(temp,i);
42     }
43 }
44 
45 int main()
46 {
47    int n;
48    DP();
49    while(cin>>n)
50    {
51        int temp = 0;
52         for(int i = 0;i <= 300;i++)
53         {
54             if(a[n][i]!=0)
55             {
56                 temp = i;
57                 break;
58             }
59         }
60         for(int i = temp;i <=300;i++)
61             cout<<a[n][i];
62         cout<<endl;
63 
64    }
65 
66     return 0;
67 }