Big Phi Notation Demonstrate that fn 5 32log3n 23log2n is

Big Phi Notation Demonstrate that f(n) = 5 + 3^2log_3n + 2^3log_2^n is Phi(n^3). Remember that big-O is an upper bound, big-Ohm is a lower bound, and big-Phi is a tight bound, big-Ohm. upper and lower. To prove that fin) is Phi(g(n)) you must prove both that f(n) is O(g(n)) and that f(n) is Ohm g(n)). Make sure you prove this using the formal definition of big-Phi. not just an intuitive explanation. Detailed answer for Problems 1.1 through 1.4 C++ code used for Problem 1.4 (b) (and optional 1.4(d)) Sample results of Problem 1.4 (b) (and optional 1.4(d))

Solution

Big O notation is that the language we have a tendency to use for articulating however long associate algorithmic rule takes to run. It\'s however we have a tendency to compare the potency of various approaches to a drag.

With massive O notation we have a tendency to categorical the runtime in terms of—brace yourself—how quickly it grows relative to the input, because the input gets at random massive.

Let\'s break that down:

how quickly the runtime grows—Some external factors have an effect on the time it takes for a operate to run: the speed of the processor, what else the pc is running, etc. thus it\'s exhausting to form stermy statements regarding the precise runtime of associate algorithmic rule. Instead we have a tendency to use massive O notation to specific however quickly its runtime grows.
relative to the input—Since we\'re not viewing a particular variety, we want one thing to phrase our runtime growth in terms of. we have a tendency to use the dimensions of the input. thus we are able to say things just like the runtime grows \"on the order of the dimensions of the input\" (O(n)O(n)) or \"on the order of the sq. of the dimensions of the input\" (O(n^2)O(n
2
)).
as the input gets at random large—Our algorithmic rule could have steps that appear overpriced once nn is little however area unit eclipsed eventually by alternative steps as nn gets immense. for large O analysis, we have a tendency to care most regarding the things that grows quickest because the input grows, as a result of everything else is quickly eclipsed as nn gets terribly massive. If you recognize what associate straight line is, you would possibly see why \"big O analysis\" is typically known as \"asymptotic analysis.\"
Big O notation is like maths except it\'s associate awful, not-boring reasonably maths wherever you get to wave your hands through the main points and simply specialise in what is essentially happening.