222. Count Complete Tree Nodes

222. Count Complete Tree Nodes

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.

 

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/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
  public int countNodes(TreeNode root) {
    int leftDepth = leftDepth(root);
    int rightDepth = rightDepth(root);

    if (leftDepth == rightDepth)
      return (1 << leftDepth) - 1; // a fully complete binary tree has 2^depth - 1 nodes
    else
      return 1 + countNodes(root.left) + countNodes(root.right);
  }

  private int rightDepth(TreeNode root) {
    int dep = 0;
    while (root != null) {
      root = root.right;
      ++dep;
    }
    return dep;
  }

  private int leftDepth(TreeNode root) {
    int dep = 0;
    while (root != null) {
      root = root.left;
      ++dep;
    }
    return dep;
  }
}