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 is a total of 5 unique BST ' s.

   1         3     3      2      1    \//      /\           3     2     1      1   3      2    /     /       \                    2     1         2                 3

intNumtrees (intN) {int*result =malloc((n +1)*sizeof(int)); if(n = =0|| n = =1)        return 1; if(n = =2)        return 2; result[0] = result[1] =1; result[2] =2;  for(inti =3; I <= N; i++)    {        intTMP =0; Result[i]=0;  for(intj =1; J <= I/2; J + +) TMP+ = Result[j-1] * Result[i-J]; Result[i]= tmp *2; if(I-(I/2) *2) Result[i]+ = Result[i/2] * Result[i/2]; }    returnresult[n];}

• Select a value in the sequence as the root node, Saozi the right subtree, and can have the product of the remaining number permutations, respectively
• Because the left and right sides select the same number, you can separate both sides of the calculation
• When opening up space, it is necessary to open up n+1, and array of [n] Correspondence

Unique Binary Search Trees