In this example, which of the Big O, is true and false? **O-notation (Upper Bound – Worst Case)****Definition:**\[ O(g(n)) = \{ f(n) : \text{there exist positive constants } c \text{ and } n_0 \text{ such that } 0 \leq f(n) \leq c g(n) \text{ for all } n \geq n_0 \} \]**Diagram Explanation:**- The graph illustrates two functions: $ f(n) $ and $ c g(n) $. - The curve $ f(n) $ is shown as a blue line, which increases and intersects with the $ c g(n) $ line, depicted as a black line.- The diagram emphasizes that beyond a certain value $ n_0 $, $ f(n) $ stays below or equal to $ c g(n) $.- $ n_0 $ is the threshold from which $ f(n) = O(g(n)) $ holds true.**Explanation:**- $ g(n) $ is an asymptotic upper bound for $ f(n) $.- If $ f(n) \in O(g(n)) $, we write $ f(n) = O(g(n)) $.**Example (from the red box):**- $ 2n^2 = O(n^3) $, with $ c = 1 $ and $ n_0 = 2 $.**Examples of functions in $ O(n^2) $:**- $ n^2 $- $ n^2 + n $- $ n^2 + 1000n $- $ 1000n^2 + 1000n $**Also:**- $ n $- $ n/1000 $- $ n^{1.99999} $- $ n^2 / \lg \lg n $**Examples (True/False):**- $ 2n = O(1)? $- $ 2n = O(\log n)? $- $ 2n = O(n)? $- $ 2n = O(n^2)? $- $ 2n = O(n^3)? $

O-notation (Upper Bound - Worst Case) 14 O(g(n)) = {f(n): there exist positive constants c and no such that 0 ≤ f(n) ≤ cg(n) for all n ≥ no} . cg(n) no f(n) n f(n) = 0(g(n)) g(n) is an asymptotic upper bound for f(n). If f(n) = O(g(n)), we write f(n) = 0(g(n)) Example 2n² = 0(³), with c = 1 and no = 2. Examples of functions in 0(²): n² n² +n n²+1000m 1000m²+1000m Also, Examples (T/F): 2n=0(1)? n/1000 2n=0(lgn)? n²/lg lg lgn 1.99999 2n=0(n)? 2n=0(²)? 2n=0(³)?

O-notation (Upper Bound - Worst Case) 14 O(g(n)) = {f(n): there exist positive constants c and no such that 0 ≤ f(n) ≤ cg(n) for all n ≥ no} . cg(n) no f(n) n f(n) = 0(g(n)) g(n) is an asymptotic upper bound for f(n). If f(n) = O(g(n)), we write f(n) = 0(g(n)) Example 2n² = 0(³), with c = 1 and no = 2. Examples of functions in 0(²): n² n² +n n²+1000m 1000m²+1000m Also, Examples (T/F): 2n=0(1)? n/1000 2n=0(lgn)? n²/lg lg lgn 1.99999 2n=0(n)? 2n=0(²)? 2n=0(³)?

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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