题目
Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
For example, Given n = 3, there are a total of 5 unique BST's.
1 3 3 2 1
\ / / / \ \
3 2 1 1 3 2
/ / \ \
2 1 2 3
分析及解答
public int numTrees(int n) {
//卡特兰数
long result = 1;//防止在计算过程中，超出整数int的范围。
for(int i = 0; i < n;i++){
result = result * (2*n - i)/(i+1);//避免在除的过程因为有不能整除而造成的数的损失。(也避免long超出范围)
}
int r = Integer.parseInt(String.valueOf(result/(n+1)));//将long转为int.
return r;
}
