NYOJ 1103 区域赛系列一多边形划分 （卡特兰数）

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

推荐博客：http://blog.csdn.net/zy691357966/article/details/40350961

#include <iostream>

using namespace std;

int main()
{
int n, m;
int a[21] = {1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420};

cin >> n;
for  (int i = 1; i <= n; i++){
cin >> m;
cout << "Case #" << i << " : " << a[m - 2] << endl;
}
return 0;
}