Question

link

A perfect binary tree, i.e. each node in the tree is either a leaf node, or has two children, and all leaf nodes are on the same level. Each node has an index in depth-first order. 

      0
    /   \
  1      4
 / \    / \
2   3  5   6

Given the index (k) of a particular node, calculate its level.

Solution

This is a magical solution. It divides the tree in the middle with number k decrease by 1 each time.

Beautiful, and hard to understand.

Code

not written by me.

public int countLevel(TreeNode root, int k, int n) {
    int level = 0;
    while (k != 0) {
        k--;
        n = (n - 1) / 2;
        k = k % n;
        level++;
    }
    return level + 1;
}