For "cubic time" programs the runtime is T(n) = k3^n where n is the input size and k is a constant. Complete this rule of thumb for such programs: "If the runtime is increased by 1 the runtime is ________________________________________."
For "cubic time" programs the runtime is T(n) = k3^n where n is the input size and k is a constant.
--> If the runtime is increased by 1 the runtime is, Suppose n became n+1
T(n+1) = k 3^(n+1)
= k 3^n * 3
= T(n) * 3
--> "If the input is increased by 1 the runtime is increased by 3 times".
For "cubic time" programs the runtime is T(n) = k3^n where n is the input size...
which explanation matches the following runtime complexity? T(N)=k+T(N-1) a. Every time the function is called, k operations are done, and each of the 2 recursive calls reduces N by half. b. Every time the function is called, k operations are done, and the recursive call lowers N by 1. C. Every time the function is called, k operations are done, and each recursive call lowers N by one fourth. d. Every time the function is called, k operations are done,...
Suppose that an algorithm has run-time proportional to 2n , where n is the input size. The algorithm takes 1 millisecond to process an array of size 10. How many milliseconds would you expect the algorithm take to process an array of size 20 ?
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the input. Explain the difference between the two statements below, and give an explicit example of an algorithm for which one statement is true but the other is false. 1. The worst case time complexity of A is n2. 2. A is O(n). (e) Give an example of an algorithm (with a clear input type) which has a Big-Oh (0) and Big-Omega (12) bound on...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n into 3 subproblems of sizes n/2 , n/4 , n/8 , respectively with O(n) time; Recursively call on these subproblems; and then combine the results in O(n) time. The recursive call returns when the problems become of size 1 and the time in this case is constant." (a) Let T(n) denote the worst-case running time of this approach on the problem of size n....
1- Find the time complexity of the following program, where n is given as input: i = n; while (i > 1) { j = i; while (j < n) { k = 0; while (k < n) { k += 2; } j *= 2; } i /= 2; } Express your answer using theta notation, and explain the amount of time it takes for each loop to finish.
Let T(n) denote the worst case running time of an algorithm when its input has size n. In divide and conquer algorithms, T(n) is often expressed using a recursion. Hence, expressing T(n) in terms of the big-Oh notation requires a bit of work. There are many ways of determining the growth rate of T(n). In class, I’ve shown you how to do it by drawing the recursion tree. Here are the steps: (1) draw the recursion tree out, (2) determine...
can selection be done in O(n) expected time. if the size of the input is n . If so how does it to be done? Analyse your algorithm
Let T(n) be the runtime of the following RaiseToPower() function that computes baseVal raised to the n-th power. int RaiseToPower (int baseval, int n){ int resultval; if (n == 0) { resultval = 1; } else { resultval = baseval - RaiseToPower (baseval, n-1 ); return resultval; } Which of the following is correct about T(n)? There are more than one correct answers. Select one or more: a. T(n) = CO, if n=0. (CO is a small constant variable.) b....
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full solution for c and d
In a simplified model of tumour growth, the size y(t) of the tumour at time t is given by the equation dy y dt (1-2) is the proliferation rate of the tumour where r and k are positive constants and dy versus y, clearly labelling any equilibrium solutions dt (a) Draw the phase plot (b) Sketch y(t) for sufficiently many initial conditions to display all different basic shapes for the tumour size vs....
You are given an input of k arrays each of size n. Each one of the k arrays is sorted. Give an algorithm that turns the k sorted arrays into one sorted array of k * n elements. Please explain the algorithm in words and analyze the run time.