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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

答案

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


Unique Binary Search Trees