Answered: (a) Use a recursion tree to determine a…

(a) Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n) = T() + n² (b) Use the substitution method to verify your answer

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

Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

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(a) Use a recursion tree to determine a good asymptotic upper
bound on the recurrence T(n) = T(2) + n² (b) Use the
substitution method to verify your answer

Branch of computer science concerned with using technology to solve problems that typically require human intelligence.

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(c) Draw the recursion tree for the recurrence T(n) = 3T (|n/V3|) + cn, where c is a constant, and determine a good asymptotic upper bound on its solution. Verify your bound by the substitution method.
(b) Solve the recurrence relation : T (n) =T O(n). 3 using the recursion tree method.
Problem 3. Consider the following recurrence. T(n) = {(n) = 37(n T(n) = 3T(n/2) + n² if n=1 otherwise. (a) Solve this recurrence exactly by the method of substitution. You may assume n is a power of 2. (b) Solve it using the recursion tree method.
Part I For each of the following two recurrences, construct a recursion tree and use it to solve the recurrence. Your solution should include a chart similar to examples in lecture and studio with columns for the depth, number of nodes, work per node, and work per level at each level of the tree; a summation giving the total work of the recurrence; and ● a closed-form asymptotic solution to the recurrence. You may assume for simplicity that the input size n is a power of b, the denominator of the size in the recursive term, and that T(1) = d for some constant d. You may hand-draw or typset the chart, but please typeset the summation and its closed-form solution. 1. T(n) = 3T(n/2) + n² 2. T(n) = 4T(n/2) + n²
for the following problem we need to use a recursion tree. so we can determine an asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. the substitution method must be used to solve.
For the algorthim write a recurrence for its runtime, use the recurrence tree method to solve the recurrence, and and find the tightest asymptotic upper bound on the runtime of the algorthim. Algorthim: Algorithm Z divides an instance of size n into 2 subproblems, one with size n/4 and one with size n/5,recursively solves each one, and then takes O(n) time to combine the solutions and output the answer.
For each of the following recurrences, verify the answer you get by applying the master method, by solving the recurrence algebraically OR applying the recursion tree method. T(N) = 2T(N-1) + 1 T(N) = 3T(N-1) + n
Please explain Solve the recurrence: T(n)=2T(2/3 n)+n^2. first by directly adding up the work done in each iteration and then using the Master theorem. Note that this question has two parts (a) Solving IN RECURSION TREE the problem by adding up all the work done (step by step) and (b) using Master Theorem
(a) For each of the following recurrences, give an expression for theruntime T (n) if the recurrence can be solved with the Master Theorem.Otherwise, indicate that the Master Theorem does not apply.(i) T (n) = T (n/2) + T(n/2) + T(n/2) + n2(ii) T (n) = 0.5T (n/2)+ 1/n(iii) T (n) = 3T (n/3) + n(iv) T (n) = 4T (n/2) + nlogn
For the algorthim write a recurrence for its runtime, use the recurrence tree method to solve the recurrence, and and find the tightest asymptotic upper bound on the runtime of the algorthim. Algorrthim Problem: Algorithm V divides an instance of size n into 6 subproblems of size n/6 each, recursively solves each one, and then takes O(n) time to combine the solutions and output the answer.
Solving recurrences Solve the following recurrence relations and give a Θbound for eachof them. Do not use the Master Theorem. You must use the recursion tree method. For each recurrence,state the branching factor, the height of the tree, the size of the subproblems at depth k, and the number of subproblems at depth k. You can draw the recursion tree to help find the solution, but do not include the tree in your submission as it will not be graded.(a) T (n) = 4T (n/3)+n(b) T (n) = 3T (n/3)+n(c) T (n) = 4T (n/4)+√n(d) T (n) = 16T (n/4)+n2(e) T (n) = 3T (n/4)+1
For the algorthim write a recurrence for its runtime, use the recurrence tree method to solve the recurrence, and and find the tightest asymptotic upper bound on the runtime of the algorthim. Algorthim Problem: Algorithm H divides an instance of size n into 4 subproblems of size n/3 each, recursively solves each one, and then takes O(n^2) time to combine the solutions and output the answer.