Count Complete Tree Nodes

最新推荐文章于 2024-09-12 01:58:26 发布

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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。通过递归地计算树的高度，并利用高度信息来减少不必要的节点遍历，该算法能够在O(log n)^2的时间复杂度内完成计算。

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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.

public class Solution {
    int height(TreeNode root) {
        return root == null ? -1 : 1 + height(root.left);
    }
    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);
    }
}

https://leetcode.com/discuss/38930/concise-java-solutions-o-log-n-2