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 <= 1)
 7         return 1;
 8 
 9     int *h = new int [n+1]; //保存临时结果
10     h[0] = h[1] = 1;        //h(0)和h(1)
11     for(int i = 2; i <= n; i++)    //依次计算h(2),h(3)...h(n)
12         {
13             h[i] = 0;
14        for(int j = 0; 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)
15             h[i] += (h[j] * h[i-1-j]);
16     }
17     int result = h[n]; //保存结果
18     delete [] h;       //注意释放空间
19     return result;
20 }
21 
22 int main(){
23     int c, x;
24     int Case = 1;
25     scanf("%d", &c);
26     while(c--){
27         scanf("%d", &x);
28         printf("Case #%d : %d\n", Case++, Catalan(x - 2));
29     }
30     return 0;
31 }