Please solve Q1, this is a discrete math
question. "O" represents Oh notation, f=O(g) if there are positive
constants c and n0 such that for any n≥ n0,
f(n) ≤ c·g(n). Please include all your explanations.
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Please solve Q1, this is a discrete math
question. "O" represents Oh notation, f=O(g) if there...
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...
ONLY THE LAST ONE (4) . DISCRETE MATH Problem 1: Show that f(n) = (n +...
ONLY THE LAST ONE (4) . DISCRETE MATH
Problem 1: Show that f(n) = (n + 2) log2(n+ 1) + log2 (n3 + 1) is O(n log2 n). Problem 2: Prove that x? + 7x + 2 is 12(x°). Problem 3: Prove that 5x4 + 2x} – 1 is ©(x4). Problem 4: Find all pairs of functions in the following list that are of the same order: n2 + logn, 21 + 31, 100n3 +n2, n2 + 21, n? +...
***Please answer all the following (Computer science) Discrete math question completely.*** Q2. Growth of functions. In...
***Please answer all the following (Computer science)
Discrete math question completely.***
Q2. Growth of functions. In each of the following cases, either construct a function /(/n) that satisfies the specified constraints or state that no such function exists. (2pt each) b, (n)-Ω(n2) and/(n)-O (n + n') In the following two questions, arrange the functions in a list so that each function is a big-O of the next function. (2pt each) d. nlog n, V', log n, (log2n+log n+n), 12 n,...
if possible solve part d in detail. a) fi(n) n2+ 45 n log n b) f:(n)-1o+...
if possible solve part d in detail.
a) fi(n) n2+ 45 n log n b) f:(n)-1o+ n3 +856 c) f3(n) 16 vn log n 2. Use the functions in part 1 a) Isfi(n) in O(f(n)), Ω(fg(n)), or Θ((6(n))? b) Isfi(n) in O(f(n)), Ω(f,(n)), or Θ((fs(n))? c) Ísf3(n) in O(f(n)), Ω(f(n)), or Θ(f(n))? d) Under what condition, if any, would the "less efficient" algorithm execute more quickly than the "more efficient" algorithm in question c? Explain Give explanations for your answers...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci...
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,...
Please help me with question 13(c,f,h,i,k,m) 13. Show that the following equalities are correct: (a) 5n2...
Please help me with question 13(c,f,h,i,k,m)
13. Show that the following equalities are correct: (a) 5n2 - 6n(n2) (b) n! - O(n) (c) 2n22"+ n logn-e(n22) (d) I012(n3) (h) 6n3/(log n+1)O(n3) (i) n1.001 + n logn (n1.001) (j) nkte + nk logn 6(nkte) for all fixed k and e, k 0 and e> 0 (1) 33n3 + 4n2 2(n2) (m) 33n3 + 4n23)
4. Big-Oh and Rune time Analysis: describe the worst case running time of the following pseudocode...
4. Big-Oh and Rune time Analysis: describe the worst case running time of the following pseudocode functions in Big-Oh notation in terms of the variable n. howing your work is not required (although showing work may allow some partial t in the case your answer is wrong-don't spend a lot of time showing your work.). You MUST choose your answer from the following (not given in any particular order), each of which could be re-used (could be the answer for...
1. For each of the following pairs of functions, prove that f(n)-O(g(n)), and / or that...
1. For each of the following pairs of functions, prove that f(n)-O(g(n)), and / or that g(n) O(f(n)), or explain why one or the other is not true. (a) 2"+1 vs 2 (b) 22n vs 2" VS (c) 4" vs 22n (d) 2" vs 4" (e) loga n vs log, n - where a and b are constants greater than 1. Show that you understand why this restriction on a and b was given. f) log(0(1) n) vs log n....
PYTHON: Im stuck here, big O notation and runtime. What is it and Why are they...
PYTHON: Im stuck here, big O notation and runtime. What
is it and Why are they those? Please look at the pic, need help as
Im confused. Thank You!
def method3(n): for i in range(n): for j in range(100): for k in range(n): print(i+j+k) What is the runtime (tightest/closest bound in terms of O) for the above python function (method 3)? Please briefly explain. Enter your answer here def method4(n): for i in range(n): for j in range(n, o, -2):...
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...
ONLY THE LAST ONE (4) . DISCRETE MATH
Problem 1: Show that f(n) = (n + 2) log2(n+ 1) + log2 (n3 + 1) is O(n log2 n). Problem 2: Prove that x? + 7x + 2 is 12(x°). Problem 3: Prove that 5x4 + 2x} – 1 is ©(x4). Problem 4: Find all pairs of functions in the following list that are of the same order: n2 + logn, 21 + 31, 100n3 +n2, n2 + 21, n? +...
***Please answer all the following (Computer science)
Discrete math question completely.***
Q2. Growth of functions. In each of the following cases, either construct a function /(/n) that satisfies the specified constraints or state that no such function exists. (2pt each) b, (n)-Ω(n2) and/(n)-O (n + n') In the following two questions, arrange the functions in a list so that each function is a big-O of the next function. (2pt each) d. nlog n, V', log n, (log2n+log n+n), 12 n,...
if possible solve part d in detail.
a) fi(n) n2+ 45 n log n b) f:(n)-1o+ n3 +856 c) f3(n) 16 vn log n 2. Use the functions in part 1 a) Isfi(n) in O(f(n)), Ω(fg(n)), or Θ((6(n))? b) Isfi(n) in O(f(n)), Ω(f,(n)), or Θ((fs(n))? c) Ísf3(n) in O(f(n)), Ω(f(n)), or Θ(f(n))? d) Under what condition, if any, would the "less efficient" algorithm execute more quickly than the "more efficient" algorithm in question c? Explain Give explanations for your answers...
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,...
Please help me with question 13(c,f,h,i,k,m)
13. Show that the following equalities are correct: (a) 5n2 - 6n(n2) (b) n! - O(n) (c) 2n22"+ n logn-e(n22) (d) I012(n3) (h) 6n3/(log n+1)O(n3) (i) n1.001 + n logn (n1.001) (j) nkte + nk logn 6(nkte) for all fixed k and e, k 0 and e> 0 (1) 33n3 + 4n2 2(n2) (m) 33n3 + 4n23)
4. Big-Oh and Rune time Analysis: describe the worst case running time of the following pseudocode functions in Big-Oh notation in terms of the variable n. howing your work is not required (although showing work may allow some partial t in the case your answer is wrong-don't spend a lot of time showing your work.). You MUST choose your answer from the following (not given in any particular order), each of which could be re-used (could be the answer for...
1. For each of the following pairs of functions, prove that f(n)-O(g(n)), and / or that g(n) O(f(n)), or explain why one or the other is not true. (a) 2"+1 vs 2 (b) 22n vs 2" VS (c) 4" vs 22n (d) 2" vs 4" (e) loga n vs log, n - where a and b are constants greater than 1. Show that you understand why this restriction on a and b was given. f) log(0(1) n) vs log n....
PYTHON: Im stuck here, big O notation and runtime. What
is it and Why are they those? Please look at the pic, need help as
Im confused. Thank You!
def method3(n): for i in range(n): for j in range(100): for k in range(n): print(i+j+k) What is the runtime (tightest/closest bound in terms of O) for the above python function (method 3)? Please briefly explain. Enter your answer here def method4(n): for i in range(n): for j in range(n, o, -2):...
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