The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: H₁ = Σ = = 1+ k=1 1 1 + + + 234 1 +- n (i) Write a recursive algorithm of this function returning, Hn, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n ε N. iii) Solve the recurrence relation and give the O(n) of the algorithm.

The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: H₁ = Σ = = 1+ k=1 1 1 + + + 234 1 +- n (i) Write a recursive algorithm of this function returning, Hn, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n ε N. iii) Solve the recurrence relation and give the O(n) of the algorithm.

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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