How to find number of possible binary tree topological permutations?

Question

Given number of binary tree nodes (X) write method that returns the number of random permutations of binary trees with X nodes.

Examples:

X=1: 1

     o

X=2: 2

     o    o
   o        o

X=3: 5

        o    o          o     o        o
      o        o      o         o    o   o
    o            o      o     o

I ended up with :

    public static int numOfPerms(int numOfNodes) {
       if (numOfNodes<=2 && numOfNodes > 0) {
           return numOfNodes;
       }
       int res = 1;
       for (int i=1; i<=numOfNodes; i++) {
           res = res*(4*i-1)/(i+1);
       }
       return res;
    } 

I would appreciate sharing here better solutions.

Answer 1

Try this recursive method:

static int numOfPerms(int numOfNodes) {
    if (numOfNodes == 1) {
        return 1; 
    }

    numOfNodes = numOfNodes - 1;
    return ((numOfPerms(numOfNodes) * (2*numOfNodes+2) * 
            (2*numOfNodes+1))/((numOfNodes+1)*(numOfNodes+2)));
}