1. 推導公式

2.卡特蘭數列程式設計實現

方法一:

func numTrees(n int) int {
	if 0 == n || 1 == n {
		return 1
	}
	G := make([]int, 0)
	G = append(G, 1)
	G = append(G, 1)
	for i:=2; i<=n; i++ {
		temp := 0
		for j:=1; j <=i; j++ {
			temp += G[j-1] * G[i-j]
		}
		G = append(G, temp)
	}
	return G[n]
}

方法二：

// f(n) = f(n-1)*f(0) + f(n-2)*f(1) + ... + f(n-i)*f(i-1) + ... + f(0)*f(n-1)
// f(n) = C(2n,n)/(n+1)
// f(n)=f(n-1)*(4*n-2)/(n+1);
// 上面該公式是卡特蘭數, 相關推導公司見wiki: https://blog.csdn.net/hemeinvyiqiluoben/article/details/11320419
func numTrees(n int) int {
	if 0 == n || 1 == n {
		return 1
	}
	res := 1
	for i:=2; i <=n; i++ {
		res = res * (4 * i - 2) / (i + 1)
	}
	return res
}