How many number of binary tree possible for N number of nodes?

Question

Is there any formula.

Comments

Do we need to consider the node value.

Answer 1

It will be 2n!/(n+1)!n!

See the following code

int countTrees(int numKeys) {

  if (numKeys <=1) {
    return(1);
  }
  else {
    // there will be one value at the root, with whatever remains on the left and right each forming their own subtrees.
    // Iterate through all the values that could be the root...
    int sum = 0;
    int left, right, root;

    for (root=1; root<=numKeys; root++) {
      left = countTrees(root - 1);
      right = countTrees(numKeys - root);

      // number of possible trees with this root == left*right
      sum += left*right;
    }

    return(sum);
  }
}