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)));
}