Count Complete Tree Nodes

最新推荐文章于 2024-09-12 01:58:26 发布

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本文介绍了一种高效计算完全二叉树中节点数量的方法。通过获取树的高度及右子树的高度，判断最后一个节点的位置，并递归计算左右子树的节点数。此算法适用于所有完全二叉树。

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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.

1. Get the height of the tree : because it is a complete tree, we can get the height of it from it's leftmost branch. If the tree just has one node, the height is 0, if root==null, the height is -1.

2. Get the height of the right subtree, if the height of the right subtree just one less than that of the whole tree, then the last node on the last row should be at the right subtree， the number of nodes on the left subtree plus the root should be 2^h and recursively get the number of nodes on the right subtree. If the height of the right subtree is not one less than that of the whole tree, than the last node on the last row should be at the left subtree, the number of nodes on the right subtree plus the root should be 2^(h-1) and recursively get the number of the nodes on the left subtree.

/**
 * 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 h = height(root);
        
        return h < 0 ? 0 :
               height(root.right) == h-1 ? (1 << h) + countNodes(root.right)
                                         : (1 << h-1) + countNodes(root.left);
    }
    
    private int height(TreeNode root) {
        return root == null ? -1: height(root.left) + 1;
    }   
}