Unique Binary Search Trees

Posted 2020-06-13

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

 

 

 

 

//Sigma(左边的子树可能状态 * 右边子树可能状态) = 当前个数的nodes形成的BST总数。
class Solution {
public:
    int numTrees(int n) {
        int *m = new int[n + 1]();
        m[0] = 1;
        m[1] = 1;
        for (int i = 2; i <= n; i++)
        {
            for (int j = 0; j < i; j++)
            {
                m[i] += m[j] * m[i -1 - j];
            }
        }
        int result = m[n];
        delete m;
        return result;
    }
};