[Problem 4] Consider a tree Y in which each node has at most 3 descendants, called A node, B node, and C node. There are n nodes in such a tree. Each node in tree X holds an integer value k≥ 1, which we can access with node.value method. Let T(n) denote the time complexity of the following algorithm, which takes tree Y as its input. H(X.root) if (X.root == NIL) then return else H(X.root.A) c = c + X.root.value // assume c is some global variable, initially set to 0. H(X.root.B) H(X.root.C) Determine the asymptotic bound of the time complexity T(n) for the algorithm H and formally prove its correctness to receive points.

[Problem 4] Consider a tree Y in which each node has at most 3 descendants, called A node, B node, and C node. There are n nodes in such a tree. Each node in tree X holds an integer value k≥ 1, which we can access with node.value method. Let T(n) denote the time complexity of the following algorithm, which takes tree Y as its input. H(X.root) if (X.root == NIL) then return else H(X.root.A) c = c + X.root.value // assume c is some global variable, initially set to 0. H(X.root.B) H(X.root.C) Determine the asymptotic bound of the time complexity T(n) for the algorithm H and formally prove its correctness to receive points.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.

Question

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[Problem 4] Consider a tree Y in which each node has at most 3 descendants, called A node, B node,
and C node. There are n nodes in such a tree. Each node in tree X holds an integer value k ≥ 1, which
we can access with node.value method. Let T(n) denote the time complexity of the following algorithm,
which takes tree Y as its input.
H(X.root)
if (X.root == NIL) then
return
else
H(X.root.A)
c = c + X.root.value // assume c is some global variable, initially set to 0.
H(X.root.B)
H(X.root.C)
Determine the asymptotic bound of the time complexity T(n) for the algorithm H and formally prove its
correctness to receive points.

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