The possible number of binary search trees that can be created with N keys is given by the Nth catalan number. Why?

Question

This has been bothering me for a while. I know that given N keys to arrange in the form of a binary search tree, the possible number of trees that can be created correspond

Answer 1

Well here is the recursive solution to count the trees...

int countTrees(int numkeys){

if(numkeys > 1){
    int i =1;
    int sum=0;

    for(i = 1; i <= numkeys; i++){

        int lcount = countTrees(i-1);
        int rcount = countTrees(numkeys-i);
        sum += lcount*rcount;
    }
    return(sum);
}else
    return(1);
}