Consider two programs, A and B. Program A requires 1000 x n² operations and Program B requires 2" operations. For which values of n will Program A execute faster than Program B?
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- A porous membrane having a width of 1cm, contains A at a concentration of 0.5 kmol/m³. One side of the membrane is suddenly exposed to gas and concentration of A at this side is increased to 2 kmol/m³. Calculate the concentration values by finite differences method using computer programing and below data. Calculate the time it takes for the concentration of A to be 2 kmol/m3 everywhere in the membrane. Ox=0.0025m (5 space) Ot=0.01s DAB=2.5*10-4 m²/sAlgorithm X has a growth rate that is proportional to n ∗ n ∗ n . What is the function that represents the growth rate of algorithm X? What is the order of algorithm X?Suppose that you want to calculate 1434661 · 3785648743 − 100020304 · 54300201. You are told thatthe answer is a positive integer less than 90. Compute the answer mod 10 and mod 9, then combineto get the answer. Show all the necessary work to obtain your answers. Note: This technique hasoften been employed to do calculations with large integers because most of the computations use smallintegers, with only the Chinese Remainder Theorem step requiring large integers. For example, if theanswer is known to be less than 1036, the calculations can be done mod p for each prime less than100. Since the product of the primes less than 100 is approximately 2.3 × 1036, the Chinese RemainderTheorem gives the answer exactly
- You are given N sticks, where the length of each rod is a positive number. The cutting work is done on the sticks so that they are all reduced to the length of the smallest rod. Suppose we have six sticks of the following length: 544228 Then, in a single cutting operation we cut 2 lengths from each of the six sticks. In the following cut-off operation, there are four sticks (not the length of an egg), the length of which is as follows: 3 2 26 The above step is repeated until there are no sticks left. If you are given the length of the N sticks, print the number of sticks left before each subsequent cutting operation using C++ code only. Input 6 544228 Output 6 4 2 1There are two algorithms called alg1 and alg2 for a problem of size n. alg1 runs in n2 microseconds and alg2 runs in 100n log n microseconds. alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of cpu time. on the other hand, alg2 requires 15 hours of programmer time and 6 minutes of cpu time. if programmers are paid 20 dollars per hour and cpu time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using alg2 in order to justify its development cost?The size of a colony of blue bacteria growing in a petri dish is modeled by the equation where t is time in days. The size of a colony of green bacteria is modeled by the equation where t is again time in days. Both colony sizes are measured in square centimeters. Part A: Graph the growth of both colonies on the same plot over the course of 6 days in one hour increments. One way to get one hour increments is to use a step size of 1/24. Another way is to use linspace and specify that it should create 6days x 24hours evenly spaced values. In either case, make sure you start at 0 days, not 1 day. Make the color of the curve match the color of the bacteria it represents. Give your graph a title and axis labels. Part B: How large is the green bacteria colony when the blue colony reaches its maximum size. You must answer this question using Matlab calculations, not manually entering the answer. To check your work, the blue colony’s maximum size is 270.56 and when it reaches that…
- The search algorithm developed will be used for users to search the catalog for all items matching the search keyword(s), and there are a total of 15000 items in the catalog. During development, three different algorithms were created. • Algorithm A runs in constant time, with a maximum runtime of 1.10 seconds and returns all matching results. ● Algorithm B runs in logarithmic time, with a maximum runtime of 0.3 seconds, and returns only the first result. ● Algorithm C runs in linear time, with a maximum runtime of 1.50 seconds and returns all matching results. Which algorithm would be the least suitable for the requirements stated? In your answer, justify your choice by explaining why you picked that algorithm, and why you did not pick the other two algorithms.OND OND OND DADThere are two algorithms called Alg1 and Alg2 for a problem of size n. Alg1 runs in n^2 microseconds and Alg2 runs in 100nlogn microseconds. Alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of CPU time. On the other hand, Alg2 requires 15 hours of programmer time and 6 minutes of CPU time. If programmers are paid 20 dollars per hour and CPU time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using Alg2 in order to justify its development cost?There are two algorithms called Alg1 and Alg2 for a problem of size n. Alg1 runs in n? microseconds and Alg2 runs in 100n log n microseconds. Alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of CPU time. On the other hand, Alg2 requires 15 hours of programmer time and 6 minutes of CPU time. If programmers are paid 20 dollars per hour and CPU time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using Alg2 in order to justify its development cost?
- You are a computer research scientist at Tesla, and your task is to create a computer vision application for self-driving cars to detect object and avoid collision. You know that Graham's scan is a method of computing the convex hull of a finite set of points in the plane. You decide to apply this algorithm to achieve the goal of your task. a) Suppose Graham's scan executes n points, where n >= 3. Prove that, at the end of the program, the stack S consists of, from bottom to top, exactly the vertices of convex hull in counter-clockwise order.Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BWrite programs with these input and output. Given matrices A1,A2,…,An, with dimensions m1 ×m2, m2 × m3,…, mn × mn+1, respectively, each with integerentries, use dynamic programming, to find the minimumnumber of multiplications of integers needed tocompute A1A2⋯An.