You are given the problem below. Describe a simple brute force orbacktracking algorithm that solves it. State the runtime of your algorithm.Problem: You are given a tree T. Each node in T has a weight (which can be positiveor negative). Find the path in T with the largest total weight.

struct n { int val; n* l,r;} int func(n* r, int &rr){ if(!r) return 0; int x = func(r->l,rr);…

Answered: Problem: You are given a tree T. Each…

Problem: You are given a tree T. Each node in T has a weight (which can be positive or negative). Find the path in T with the largest total weight.

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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Let T be a tree. Let a be the minimum weight and b be the maximum weight over all the edge weights in T. Then the strength of T is (a2+b2). Input: An undirected weighted graph G. Task: Give an efficient algorithm for computing a spanning tree of G that maximizes the strength of the tree. Give an efficient algorithm (to the best of your knowledge) and a formal proof of correctness for your algorithm. An answer without any formal proof will be considered incomplete. Analyze the running time of the algorithm. You must write down your algorithm as pseudocode
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You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.
Let T be a tree with n vertices. How many edges does T have?