Problem 1: Give an asymptotic estimate for the number b(n) of “B”s printed by Algorithm PRINT_BS below. Your solution must consist of the following steps: (a) First express b(n) using the summation notation. (b) Next, give a closed-form expression¹ for b(n). (c) Finally, give the asymptotic value of b(n) using the e-notation. Show your work and include justification for each step. Algorithm PRINT BS (n: integer) for j← 1 to n +3 do for k← 1 to 5j do print("B") for j← 1 to n do for k← 1 to (j+ 1)² do print("B")

Order the following functions by asymptotic growth rate (number 1 is the best algorithm, and number 3 is the worst). 4nlog n+2n 2log n n³ + 2

Give asymptotic upper and lower bounds for each of the following recurrences. Justify your answer.

A sport footwear maker produces three different types of athletic shoes, namely: “Trainer”, “Runner” and “Sneaker”. Given K pairs of athletic shoes, where K is a positive integer, develop an algorithm to count and display the numbers of “Trainer”, “Runner”, and “Sneaker” pairs of athletic shoes respectively. The pairs of athletic shoes are processed one at time. The number K is provided as input to the algorithm. Specify the Algorithm using a flowchart. Hint: Processing a pair of athletic shoes involves reading/entering the type, i.e. “Trainer”, “Runner” or “Sneaker.” Note: To draw the flowchart you may use Visio, MS Words or any free flowchart solutions such as Lucidchart ( www.lucidchart.com ) or Raptor ( raptor.martincarlisle.com)   can you please make flowchart.

Solve the following recurrences using iteration methods and Master's Theorem (if possible) a. T(n) = 2T (n/3) +3 b. T(n) = 3T (n/6) + n

for i=1 to n/2: for j-i to n-i : for k=1 to j do print("hello") Let T(n) denote the number of times "hello" is printed as a function of n. 1- Find a function f(n) -> T(n)=0(f(n)) 2- Explain T(n) as three nested summations, and simplify them by step by step

Find the maximum value of the following function F(x)=2x3 , using the genetic algorithm, performing two iterations.

Cancel Let E=(0,1), Compute the language of the regular expression. (01+10) (1(11)") RESET O ft. Done