NYOJ 1103 —— m划分为n个正整数的个数

多边形划分

时间限制：1000 ms  |  内存限制：65535 KB

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

 

#include <cstdio>
#include <iostream>

using namespace std;

int dp[20];

int f(int n)
{
    if(dp[n])    return dp[n];
    if(n == 2 || n == 3)    return 1;
    if(n == 4)    return 2;
    
    int ret = 0;
    for(int i=2; i<n; i++) {
        ret += f(i) * f(n-i+1);
    }        
    return dp[n] = ret;
}

int main ()
{
    int n, m;
    scanf("%d", &n);
    for(int kase=1; kase<=n; kase++) {
        scanf("%d", &m);
        printf("Case #%d : %d\n", kase, f(m));
    }
    
    return 0;
}