CountCompleteTreeNodes.java

/**
 * Given a complete binary tree, count the number of nodes.
 *
 * Definition of a complete binary tree from Wikipedia:
 *
 * In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last
 * level are as far left as possible. It can have between 1 and 2h nodes inclusive at the last level h.
 *
 * Tags: Tree, Binary Search
 *
 * Similar Problems: (E) Closest Binary Search Tree Value
 */
public class CountCompleteTreeNodes {

    public int countNodes(TreeNode root) {
        if (root == null) {
            return 0;
        }
        int leftHeight = fullTreeHeight(root.left);
        int rightHeight = fullTreeHeight(root.right);

        if (leftHeight == rightHeight) {
            return (1 << leftHeight) + countNodes(root.right);
        } else {
            return (1 << rightHeight) + countNodes(root.left);
        }
    }

    private int fullTreeHeight(TreeNode root) {
        if (root == null) return 0;
        int res = 0;
        while (root != null) {
            root = root.left;
            res++;
        }
        return res;
    }

    public class TreeNode {

        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }

}