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Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?

Example:

Input: 3Output: 5Explanation: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

Approach #1: DP. [C++]

class Solution {public:    int numTrees(int n) {        vector
    
      nums(n+1);        nums[0] = 1;        nums[1] = 1;                for (int i = 2; i <= n; ++i) {            for (int j = 0; j <= i-1; ++j) {                nums[i] += nums[j] * nums[i-1-j];            }        }                return nums[n];    }};
    

Analysis:

status: nums[n] represent that there have n nodes the result of BST's number.

init: nums[1] = 1, nums[0] = 1;

function: ∑(nums[j] * nums[i-1-j]);

result: nums[n]