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- - a) Answer these Theoretical Questions: 1. Explain the rule of thumb for the Big O. Provide at least one example of applying each rule. 2. What is the Big O of each of the following functions? a) (n + 1)³/n b) (n³ + logзn) ³/n c) n + 100n³ + n d) 3n+ 100n3 + 3n * e) n 3n+ n * 33n 3. Describe an algorithm for finding the occurrence of the max element in an array. Analyze the complexity of the algorithm. 4. What is Divide-and-Conquer? What is the difference between Divide-and-Conquer and Dynamic Programming? What are the benefits of using one over another if any? 5. Is it possible to design an algorithm for finding the max element in a list using Divide-and-Conquer? What is the complexity of this algorithm? Hint: In this approach, the initial array is divided into two halves... b) Programming assignment: Implement initiative / naïve method to find a max element in an array. Implement the method that uses the Divide-and-Conquer approach to find the max element in an array. Test both…arrow_forward9. Given the following Boolean Function: F(P, Q, R) = PQ+QR+PR F(P,Q,R) (i) Derive the canonical SOP (sum of minterms) for F. (ii) Derive the canonical POS (product of maxterms) for F. (iii) Draw the truth table, clearly marking which rows are minterms of F and which rows correspond to maxterms of F. 10) For n Boolean variables, how many distinct Boolean functions exist? Give the answer as a function of n and briefly justify it.arrow_forwardPlease Show an Example in R: Find (or invent) some data (not from the “Data” directory supplied with EssentialR) and import it into R. (It is not a bad idea to include a commented line with units for each variable in your .txt or.csv file). a) What did you have to do to “clean it up” so it would read in? b) Are you satisfied with the console output of summary(yourdata)? Did all the variables import in the way (format) you thought they should? c) Include the output of summary(yourdata) and head(yourdata).arrow_forward
- 7. Convert Standard POS form to Canonical POS form. (A+B)(A+ C)(B+C) 8. Given that F(a, b, c, d) = Σm(1, 3, 4, 6, 8, 9, 12), (i) Write the product of maxterms (canonical POS) for F. (ii) Write the canonical SOP and canonical POS for F.arrow_forward1. Evaluate the following expression when A = 1, B = O, C = 1, D = 0 F = AB + CD + (A + B)C 2. Find F, the complement of function F, Write your answer using overbars. F(W, X, Y, Z) = WX + YZ +XZ 3. Determine the truth table for the function F = XY+XZ 4. Show with a truth table that the following is true: X(YZ) = XY+XZarrow_forward. 6. Find the dual of the Boolean expressions. (swap + with and O with 1; do not complement variables). a) A + BC b) (X + Y)(X + Z) c) P+Q+ RSarrow_forward
- 5. Simplify the following Boolean expression. Show each simplification step and identity used. a) ABAB + ABC b) (MN)(M + P) + MParrow_forwardBoolean Algebra HW #4 Show all intermediate steps (truth tables, algebraic steps, and justifications such as identities or theorems) for full credit. 1. Evaluate the following expression when A = 1, B = O, C = 1, D = 0 F = AB + CD + (A+B)C 2. Find F, the complement of function F, Write your answer using overbars. F(W,X,Y,Z) = WX+YZ+XZ 3. Determine the truth table for the function F=XY+XZ 4. Show with a truth table that the following is true: X(Y+Z) = XY+XZ 5. Simplify the following Boolean expression. Show each simplification step and identity used. a) AB + AB + ABC b) (M+N)(M + P) + MP 6. Find the dual of the Boolean expressions. (swap + with and O with 1; do not complement variables). a) ABC b) (X + Y)(X + Z) c) P+Q+ RS 7. Convert Standard POS form to Canonical POS form. • (A+B)(Ā + C) (B+C) 8. Given that F(a, b, c, d) = Em(1, 3, 4, 6, 8, 9, 12) (i) Write the product of maxterms (canonical POS) for F. (ii) Write the canonical SOP and canonical POS for F.arrow_forwardConsider the following statement, which is intended to assign the value of the expression, the variable result Assume that the double variables. x-ya and b have been properly declared and initialized. (xy) to double result = missing code /: 17 Mark for Review Which of the following can replace / missing code / so that the statement works as intended? Math.sqrt((x + y) 2/ Math.abs(a, b)) Math.sqrt((x + y) 2/ Math.abs(a - b)) Math.sqrt(Math.pow(x + y, 2) / Math. abs(a, b)) Math.sqrt(Math.pow(x + y, 2) / Math.abs (a - b))arrow_forward
- Consider the following code segment, which is intended to print the digits of the two-digit int number num in reverse order. For example, if num has the value 75, the code segment should print 57. Assume that num has been properly declared and initialized. /missing code */ System.out.print (onesDigit); System.out.print (tensDigit); 14 Mark for Review Which of the following can be used to replace / missing code so that the code segment works as intended? int onesDigit num 10; int tensDigit num / 10; int onesDigit- num / 10; int tensDigit num 10; int onesDigit -10/num; int tensDigit 10 num; -Undo int onesDigit num 100; Undo int tensDigit-num / 100;arrow_forwardThe following code segment is intended to round yal to the nearest integer and print the result double val--0.7 int roundedVal (int) (val +0.51 System.out.println(roundedValu 25 Mark for Review Which of the following best describes the behavior of the code segment? The code segment does not work as intended because the expression (val +0.5) should be cast to a double instead of an int The code segment does not work as intended because val should be cast to an int before 0.5 is added to it. Highlights & Notes Reference Undo Undo The code segment does not work as intended because the expression -Unda positive ר .arrow_forwardIn the following code segment, mon and tue are properly declared String variables. String strl-mon.substring(9. mon.indexOf(" "). String str2-tue.substring(tue.indexOf(" ") + 1). System.out.println(strl+and+str2): க 21 Mark for Review For which of the following values of mon and tue will the code segment print "cloudy and foggy"? mon tue "cloudy today" "foggy tomorrow" mon tue "cloudy today" "tomorrow foggy" mon tue "today cloudy" "foggy tomorrow" mon tue "today cloudy" "tomorrow foggy"arrow_forward
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