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What are the big-O notations for the following functions? Show your proofs. (B4) n³ log(3n)+ 2nª + 3n² + 127 (B5) V2n + 30log(4n)² + 27n – 3 (В6) (п + 1)! + 27 (B7) Vn2 + 3n log²(2n) + 4n7

What are the big-O notations for the following functions? Show your proofs. (B4) n³ log(3n)+ 2nª + 3n² + 127 (B5) V2n + 30log(4n)² + 27n – 3 (В6) (п + 1)! + 27 (B7) Vn2 + 3n log²(2n) + 4n7

Database System Concepts
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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What are the big-O notations for the following functions? Show your proofs. (B4) n³ log(3n) + 2nª + 3n² + 127 (B5) V2n + 30 log(4n)² + 27n – 3 (B6) (n + 1)! + 2" (B7) Vn2 + 3n log²(2n) + 4n7
Transcribed Image Text:What are the big-O notations for the following functions? Show your proofs. (B4) n³ log(3n) + 2nª + 3n² + 127 (B5) V2n + 30 log(4n)² + 27n – 3 (B6) (n + 1)! + 2" (B7) Vn2 + 3n log²(2n) + 4n7
B4. n³ log(3n) + 2nª + 3n² + 127 What will be the leading term? What is of higher order n³log(3n) or 2n*? Or equivalently, log(3n) vs n. Recall the long-term log property in Lecture 03. Hint: Big-O (n*) 2n* < 2 x n* n³ log(3n) < 1 x n* (when n 2 ?) 3n? < 3 × n* (when n2?) 127 < 127 × n* (when n >?) B5. V2n + 30 log(4n) + 27n – 3 = v2 x n7 + 30 log(4n) + 27n – 3 Hints: Big-0 (n) B6. Hint: Big-O((n + 1)!) 2 B7. Vn? + 3n log²(2n) + 4n7 = n3 + 3n log²(2n) + 4n7 Hint: Big-0 (n log²(2n))
Transcribed Image Text:B4. n³ log(3n) + 2nª + 3n² + 127 What will be the leading term? What is of higher order n³log(3n) or 2n*? Or equivalently, log(3n) vs n. Recall the long-term log property in Lecture 03. Hint: Big-O (n*) 2n* < 2 x n* n³ log(3n) < 1 x n* (when n 2 ?) 3n? < 3 × n* (when n2?) 127 < 127 × n* (when n >?) B5. V2n + 30 log(4n) + 27n – 3 = v2 x n7 + 30 log(4n) + 27n – 3 Hints: Big-0 (n) B6. Hint: Big-O((n + 1)!) 2 B7. Vn? + 3n log²(2n) + 4n7 = n3 + 3n log²(2n) + 4n7 Hint: Big-0 (n log²(2n))
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