LeetCode 96. Unique Binary Search Trees

Problem: https://leetcode.com/problems/unique-binary-search-trees/

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

Thought:

For bst of 1...n, it can be structured bu root i and left tree 1...i and right tree i+1....n, so dp is available

Code C++:

class Solution {
public:
int numTrees(int n) {
int *num = new int[n + 1];
for (int i = 0; i <= n; i++) {
num[i] = 0;
}

num[0] = 1;
num[1] = 1;

for (int i = 2; i <= n; i++) {
for (int j = 1; j <= i; j++) {
num[i] += num[j - 1] * num[i - j];
}
}

return num
;
}
};