K-ary Tree Practice Question 7

Duration: 2 min

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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment demonstrates the solution to a specific problem involving full k-ary trees. The instructor begins by presenting a question asking for the value of k given that a full k-ary tree contains 121 total nodes and 30 internal nodes. The core of the lesson involves applying fundamental tree properties to derive a formula for calculating the branching factor k. The instructor explicitly writes down the given variables, I = 30 and n = 121, on the screen. He then introduces the standard formula for total edges in any tree structure, which is n - 1. By combining this with the property that each internal node in a full k-ary tree contributes exactly k edges, he establishes the equation kI = n - 1. Substituting the known values into this relationship yields k * 30 = 120. The final step involves simple algebraic division to isolate k, resulting in the answer 4.

Chapters

  1. 0:00 – 1:35 00:00-01:35

    The instructor solves a problem to find k in a full k-ary tree with 121 nodes and 30 internal nodes. He lists I = 30 and n = 121, then writes the formula Total edges = n - 1. He applies the k-ary tree edge relationship kI = n - 1, substitutes values to get k * 30 = 120, and solves for k = 4.

The video provides a concise walkthrough of calculating the branching factor k for a full k-ary tree. The pedagogical approach relies on identifying given parameters (n and I) and applying the edge-counting principle. The key takeaway is the formula kI = n - 1, which links internal nodes to total edges. This relationship is derived from the fact that every edge connects a parent to a child, and in a full k-ary tree, each internal node has exactly k children. The calculation confirms that with 30 internal nodes and 121 total nodes, the tree must be a 4-ary tree. This method is standard for determining tree arity when node counts are known.

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