二叉树--给定节点个数求不同的二叉搜索树的个数

96. Unique Binary Search Trees

Medium

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

Example:

Input: 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

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