nyoj-1103-区域赛系列一多边形划分

http://acm.nyist.net/JudgeOnline/problem.php?pid=1103

区域赛系列一多边形划分

时间限制：1000 ms  |  内存限制：65535 KB

难度：2

描述

Give you a convex（凸边形）, diagonal n-3 disjoint divided into n-2 triangles(直线), for different number of methods, such as n=5, there are 5 kinds of partition method, as shown in Figure

输入

The first line of the input is a n (1<=n<=1000), expressed n data set.
The next n lines each behavior an integer m (3<=m<=18), namely the convex edges.

输出

For each give m,, output how many classification methods.
example output: Case #a : b

样例输入

3 3 4 5

样例输出

Case #1 : 1 Case #2 : 2 Case #3 : 5 

提示

Catalan number

解题思路： 卡特兰数

1 #include <stdio.h>

 2 #include <string.h>
 3 
 4 int Catalan(int n)
 5 {
 6     if(n <= )
 7         return ;
 8 
 9     int *h = new int [n+]; //保存临时结果
     h[] = h[] = ;        //h(0)和h(1)
     for(int i = ; i <= n; i++)    //依次计算h(2),h(3)...h(n)
         {
             h[i] = ;
        for(int j = ; j < i; j++) //根据递归式计算 h(i)= h(0)*h(i-1)+h(1)*h(i-2) + ... + h(i-1)h(0)
             h[i] += (h[j] * h[i--j]);
     }
     int result = h[n]; //保存结果
     delete [] h;       //注意释放空间
     return result;
 }
 
 int main(){
     int c, x;
     int Case = ;
     scanf("%d", &c);
     while(c--){
         scanf("%d", &x);
         printf("Case #%d : %d\n", Case++, Catalan(x - ));
     }
     return ;
 }