Apply the simple GCD algorithm for:
1. a = 112, y = 32
2. a = 114, y = 68
Explain or prove the correctness of your analysis.
Apply Euclid’s algorithm to find the GCD (Greatest Common Divisor) of 126 and 28. Describe or give the pseudocode of the consecutive integer checking algorithm for finding the GCD. What is the time complexity of this second algorithm? Explain.
3. Use Euclid's algorithm to compute the following. Show all your steps 1. gcd(781, 994) 2. gcd(67457, 43521)
2) In class we showed a Matrix algorithm for Fibonacci numbers: 1 112 1 0 n+1 F (Note: No credit for an induction proof that this is true. I'm not asking that.) a) What is the running time for this algorithm? (3 pts.) b) Prove it. (9 pts.)
1. (10 points) GCD Algorithm The greatest common divisor of two integers a and b where a 2 b is equal to the greatest common divisor of b and (a mod b). Write a program that implements this algorithm to find the GCD of two integers. Assume that both integers are positive. Follow this algorithm: 1. Call the two integers large and small. 2. If small is equal to 0: stop: large is the GCD. 3. Else, divide large by...
1. (15 points) Use the Euclidean Algorithm to find GCD(344,72). Note: You must show all major steps of the algorithm to derive your answer.
1) A Java program that implements an insertion sort algorithm. (InsertionSort.java): Must include the proper comments in the code. 2) A report in pdf. It contains: a) the pseudocode of the insertion sort algorithm and assertions between lines of the algorithm. b) As insertion sort has a nested-loop of two layers, you need to put one assertion in each loop. c) a proof of the partial correctness of the algorithm using mathematical induction c.1) prove the correctness of the two...
2,3,4,5,6 please
2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482, 7633) 3. Prove that if a = bq+r, then ged(a, b) = ged(b,r). such that sa tb ged(a,b) for the following pairs 4. Use Bézout's theorem to find 8 and a. 33, 44 b. 101, 203 c. 10001, 13422 5. Prove by induction that if p is prime and plaja... An, then pla, for at least one Q. (Hint: use n = 2 as...
Prove that the Merge() function of your own merge sort algorithm in the question 2 is correct using "induction on loop invariants" by following the guidelines below : (10 points) 3.1 Write down general description of loop invariant technique in your own words as proof of correctness. (2 points) 3.2 Identify the loop invariant of the loop in your merge() function (3 points) 3.3 Describe initialization step (0 points) 3.4 Describe maintenance step (4 points) 3.5 Describe Termination step (1...
1. GDP Population Inflation interest rate 78 14 111 0.09 88 15 112 0.1 45 25 113 0.12 65 32 114 0.14 98 25 112 0.06 88 45 112.5 0.05 85 47 114 0.111 68 85 107.5 0.124 92 66 107 0.123 81 63 106 0.147 79 54 105.5 0.159 77 87 105 0.25 73 25 104 0.16 76 45 110 0.12 66 30 102 0.08 80 50 100 0.09 Considering GDP as dependent variable and other variables as independent...
For the RSA encryption algorithm , do the following (a) Use p=257,q=337(n=pq=86609),b=(p-1)(q-1)=86016. Gcd(E,b)=1, choose E=17, find D, the number which has to be used for decryption, using Extended Euclidean Algorithm (b) One would like to send the simple message represented by 18537. What is the message which will be sent? (c) Decrypt this encrypted message to recover the original message.