What is the big O of the following formulae respectively: 1 ) (n+7)(n-2) 2) 100n+5 3)...
What is the big O of the following formulae respectively:
1 ) (n+7)(n-2)
2) 100n+5
3) n log n + n!
4) 2+ 4 + 6 + 8 + ...+ 2n where n is a positive integer
5) 1+ 3 + 5 + 7 + 9
a. Quadratic,Linear, Factorial, Quadratic,Constant
b. Factorial, Quadratic, Constant, Linear, Quadratic
c. Quadratic, linear, Constant, Quadratic, Linear
d. Quadratic, linear, Constant,Factorial, Quadratic
explain your answer
Homework Answers
1) (n+7)(n-2) => O(n^2) (so, it is Quadratic) 2) 100n+5 => O(n) (so, it is Linear) 3) n log n + n! => O(n!) (so, it is Factorial) 4) 2+ 4 + 6 + 8 + ...+ 2n where n is a positive integer => O(n^2) (so, it is Quadratic) 5) 1+ 3 + 5 + 7 + 9 => 25 = O(1) (so, it is Constant) So, answer is a. Quadratic,Linear, Factorial, Quadratic,Constant
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What is the big O of the following formulae respectively:
1 ) (n+7)(n-2)
2) 100n+5
3)...
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Please explain big O. I don't get it Prove the following, using either the definition of...
Please explain big O. I don't get it
Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2(n)) (b) 2^n elementof O(n!) (c) log_2(n^2) + log_2 (100n^10) elementof O(log_2 (n)) (d) n^1/2 elementof O(n^2/3) (e) log(3n) elementof O(log(2n)) (f) 2^n elementof O(3^n/n^2)
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1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove...
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) =
0.5n3 . Prove that f(n) = O(g(n)) using the definition
of Big-O notation. (You need to find constants c and n0).
b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use
the definition of big-O notation to prove that
f(n) = O(g(n)) (you need to find constants c and n0) and
g(n) = O(f(n)) (you need to find constants c and n0).
Conclude that...
Number 3 +4n + 8 is O(n). 3. Give a formal proof that f(n) 5m3 +3n2...
Number 3
+4n + 8 is O(n). 3. Give a formal proof that f(n) 5m3 +3n2 4. Give a formal proof that f(n)-7*2n+ 9m3 is O(2n). 5. Give a formal proof that log (n + 1) is O(log n).
Questions 3, 5, 7 - Mathematical Structures | 1ỏ +2° +33 ...3 - Rº(n1) for all...
Questions 3, 5, 7 - Mathematical Structures
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Prove using mathematical induction that for every positive integer n, = 1/i(i+1) = n/n+1. 2) Suppose...
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1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark...
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Please explain big O. I don't get it
Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2(n)) (b) 2^n elementof O(n!) (c) log_2(n^2) + log_2 (100n^10) elementof O(log_2 (n)) (d) n^1/2 elementof O(n^2/3) (e) log(3n) elementof O(log(2n)) (f) 2^n elementof O(3^n/n^2)
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) =
0.5n3 . Prove that f(n) = O(g(n)) using the definition
of Big-O notation. (You need to find constants c and n0).
b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use
the definition of big-O notation to prove that
f(n) = O(g(n)) (you need to find constants c and n0) and
g(n) = O(f(n)) (you need to find constants c and n0).
Conclude that...
Number 3
+4n + 8 is O(n). 3. Give a formal proof that f(n) 5m3 +3n2 4. Give a formal proof that f(n)-7*2n+ 9m3 is O(2n). 5. Give a formal proof that log (n + 1) is O(log n).
Questions 3, 5, 7 - Mathematical Structures
| 1ỏ +2° +33 ...3 - Rº(n1) for all integers n > 1. 2. Use induction to prove that the following identity holds for all integers n > 1: 1+3+5+...+(2n - 1) =n. 3. Use induction to show that for all positive integers n. 4. Use induction to establish the following identity for any integer n 1: 1-3+9 -...+(-3) - 1- (-3)"+1 5. Use induction to show that, for any integer n >...
Prove using mathematical induction that for every positive integer n, = 1/i(i+1) = n/n+1. 2) Suppose r is a real number other than 1. Prove using mathematical induction that for every nonnegative integer n, = 1-r^n+1/1-r. 3) Prove using mathematical induction that for every nonnegative integer n, 1 + i+i! = (n+1)!. 4) Prove using mathematical induction that for every integer n>4, n!>2^n. 5) Prove using mathematical induction that for every positive integer n, 7 + 5 + 3 +.......
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