Description
Given n, how many structurally unique BST’s (binary search trees) that store values 1 … n?
Example:1
2
3
4
5
6
7
8
9
10Input: 3
Output: 5
Explanation:
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
Solution
Catelan1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17// C0 = 1;
// C(n + 1) = C(0)C(n) + C(1)C(n - 1)....
class Solution {
public int numTrees(int n) {
int[] Catelan = new int[n + 1];
Catelan[0] = 1;
for (int i = 1; i <= n; i++){
for (int j = 0; j < i; j++){
Catelan[i] += Catelan[j] * Catelan[i - j - 1];
}
}
return Catelan[n];
}
}