A growth-rate function is a mathematical function used to indicate an algorithm's time efficiency in terms of the size of the problem.
a. True
b. False
If a problem of size n requires time that is directly proportional to n, the problem is ______.
a. O(1)
b. O(n)
c. O(n2)
d. O(log2 n)
The recursive binary search algorithm is a logarithmic
algorithm.
a. True
b. False
Which of the following growth-rate functions indicates a problem whose time requirement is constant?
a. 1
b. n
c. n2
d. log2 n
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A growth-rate function is a mathematical function used to indicate an algorithm's time efficiency in terms...
Here are some common orders of growth, ranked from no growth to
fastest growth:
Θ(1) — constant time takes the same amount of time regardless
of input size
Θ(log n) — logarithmic time
Θ(n) — linear time
Θ(n log n) — linearithmic time
Θ(n2 ) — quadratic time
Θ(n3 ), etc. — polynomial time
Θ(2n), Θ(3n), etc. — exponential time
(considered “intractable”; these are really, really horrible)
In addition, some programs will never terminate if they get
stuck in an...
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,...
algorithm TRUE OR FALSE TRUE OR FALSE Optimal substructure applies to alloptimization problems. TRUE OR FALSE For the same problem, there might be different greedy algorithms each optimizes a different measure on its way to a solutions. TRUE OR FALSE Computing the nth Fibonacci number using dynamic programming with bottom-upiterations takes O(n) while it takes O(n2) to compute it using the top-down approach. TRUE OR FALSE Every computational problem on input size n can be...
LOGISTI We know that if the number of individuals, N, in a population at time t follows an exponential law of growth, then N-N, exr where k >0 and No is the population when t -o. es that at time, t, the rate of growth, N, of the population is proportional to dt dN the number of individuals in the population. That is, kN Under exponential growth, a population would get infinitely large as time goes on. In reality, when...
a) Prove that running time T(n)=n3+30n+1 is O(n3) [1 mark] b) Prove that running time T(n)=(n+30)(n+5) is O(n2) [1 mark] c) Count the number of primitive operation of algorithm unique1 on page 174 of textbook, give a big-Oh of this algorithm and prove it. [2 mark] d) Order the following function by asymptotic growth rate [2 mark] a. 4nlogn+2n b. 210 c. 3n+100logn d. n2+10n e. n3 f. nlogn
1 question) Arrange the following in the order of their growth rates, from least to greatest: (5 pts) n3 n2 nn lg n n! n lg n 2n n 2 question)Show that 3n3 + n2 is big-Oh of n3. You can use either the definition of big-Oh (formal) or the limit approach. Show your work! (5 pts.) 3 question)Show that 6n2 + 20n is big-Oh of n3, but not big-Omega of n3. You can use either the definition of big-Omega...
I will rate your answers so please make sure the answers are
accurate. Please answer the following questions with fully
explanations:
1) Of the following, which has the most impact on the efficiency
of searching for an item in a hash table?
a) the number of non-key fields
b) the size of the table
c) the density of the table
d) whether the size of the table is a prime number
e) the difficulty of computing the inverse of the...
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
Searching/sorting tasks and efficiency analysis - Big-oh For each problem given below, do the following: 1. Create an algorithm in pseudocode to solve the problem. 2. Identify the factors that would influence the running time of your algorithm. For example, if your algorithm is to search an array the factor that influences the running time is the array size. Assign names (such as n) to each factor. 3. Count the operations performed by the algorithm. Express the count as a...
Part A Analyze the following recurrences and show their time complexity functions using (I) iteration method and (2) Master Theorem. AI. T(n) = 2T 3 A2. T(n) = 3T 2n АЗ. Т(п) — Т(п — 2) + 3 А4. Т(п) — 2Т (п — 1) + 1 A5. T(n)= 4T +n log n A6. T(n) = 3T +n log n n2 A7. T(n) = 27 Part B Do 2.3-4 (р39) and Problem 2-1 (р39) Part C Implement MERGE-SORT() algorithm that...