Extract Kth Character From The Rope Tree

Extract Kth Character From The Rope Tree - Problem

You are given the root of a binary tree and an integer k. Besides the left and right children, every node of this tree has two other properties:

A string node.val containing only lowercase English letters (possibly empty)
A non-negative integer node.len

There are two types of nodes in this tree:

Leaf: These nodes have no children, node.len = 0, and node.val is some non-empty string.
Internal: These nodes have at least one child (also at most two children), node.len > 0, and node.val is an empty string.

The tree described above is called a Rope binary tree. Now we define S[node] recursively as follows:

If node is some leaf node, S[node] = node.val
Otherwise if node is some internal node, S[node] = concat(S[node.left], S[node.right]) and S[node].length = node.len

Return the k-th character of the string S[root].

Note: If s and p are two strings, concat(s, p) is a string obtained by concatenating p to s. For example, concat("ab", "zz") = "abzz".

Input & Output

Example 1 — Basic Rope Tree

$ Input: root = [10,4,"world","hell","o "], k = 6

› Output: " "

💡 Note: The rope represents "hello world". The 6th character (1-indexed) is the space character between "hello" and "world".

Example 2 — Simple Leaf

$ Input: root = ["abc"], k = 2

› Output: "b"

💡 Note: Single leaf node with "abc". The 2nd character is 'b'.

Example 3 — Larger Tree

$ Input: root = [12,6,"hello","prog","ram"], k = 8

› Output: "h"

💡 Note: The rope represents "program" + "hello" = "programhello". The 8th character is 'h' from "hello".

Constraints

The sum of node.val.length over all leaf nodes ≤ 10⁴
1 ≤ k ≤ S[root].length
node.val contains only lowercase English letters
The tree has at most 1000 nodes

Visualization

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Asked in

G Google 15 f Facebook 12 a Amazon 8

The key insight is to use the length information in internal nodes to navigate efficiently without constructing the entire string. The optimal approach uses DFS with length-based navigation to find the k-th character in O(h) time where h is tree height. Time: O(h), Space: O(h).

Common Approaches

✓ Union Find

⏱️ Time: N/A Space: N/A

Build Complete String

⏱️ Time: O(n) Space: O(n)

Traverse the entire tree using DFS to build the complete string by concatenating all leaf values in order, then access the k-th character directly.

Optimized DFS Navigation

⏱️ Time: O(h) Space: O(h)

Use the length property of internal nodes to determine which subtree contains the k-th character, avoiding unnecessary string construction.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Smart Actions

💡 Explanation

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