NYOJ 1103 区域赛系列一多边形划分

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

题目大意：

输入一个数n，接下来有n组测试数据，接下来的n行每一个行为都是整数m（3 < = m＝18），求m边形分成m-2个三角形的不同分法有几种。

c++

#include<iostream>#include<cstdio>#include<cstring>using namespace std;int main(){    int a[20];    int t,T=1,n,i,j,b;    a[2]=a[3]=1;    for(i=3;i<20;i++)    {        a[i]=0;        b=i-1;        for(j=2;j<i;j++)        {            a[i]+=a[j]*a[b];            b--;        }    }    scanf("%d",&t);    while(t--)    {        scanf("%d",&n);        printf("Case #%d : %d\n",T++,a[n]);    }    return 0;}