question about big oh notation
Q1) Show, by applying the definition of the O-notation, that each of the following is true. – If f(n)= n(n-1)/2, then f(n) = O(n^2). – If f(n)= n+ log n, then f(n) = O(n). – 1+ n+ n^2 + n^3 = O(n^3). Q2) State without proof whether each of the following is True or False. – 7 = O(1). – n + n^4 = O(n^3). – For any polynomial T(n), T(2n) = O(T(n)). – For any function T(n), T(2n) = O(T(n)). Q3) Show, by the definition of the O-notation, that n^3 != O(n^2). (Note != means not-equal.) Q4) Let T1(n)= O(f(n)) and T2(n)= O((g(n)). Prove by the definition of the O-notation, this implies T1(n) + T2(n)= O(f(n) + g(n)). Q5) Let T1(n)= O(f(n)) and T2(n)= O((g(n)). Prove by the definition of the O-notation, this implies T1(n) * T2(n)= O(f(n) * g(n)).
Looking for solution of this Assignment?
WHY CHOOSE US?
We deliver quality original papers |
Our experts write quality original papers using academic databases. |
Free revisions |
We offer our clients multiple free revisions just to ensure you get what you want. |
Discounted prices |
All our prices are discounted which makes it affordable to you. Use code FIRST15 to get your discount |
100% originality |
We deliver papers that are written from scratch to deliver 100% originality. Our papers are free from plagiarism and NO similarity |
On-time delivery |
We will deliver your paper on time even on short notice or short deadline, overnight essay or even an urgent essay |