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- n-1 Geometric (n) = i=1 i=1 1 1 * n-1 П %3D Harmonic (n) = i=1 n Let's look at examples. If we use n = 4, the geometric progression would be 1 * 2 * 3 * 4 = 24, and the harmonic 1.1.1 1 progression would be 1* -= 0.04166. 2 3 4 24 Task #1 Tracing Recursive Methods 1. Copy the file Recursion.java (see Code Listing 16.1) from the Student Files or as directed by your instructor. 2. Run the program to confirm that the generated answer is correct. Modify the factorial method in the following ways: a. Add these lines above the first if statement: int temp; System.out.println ("Method call -- " + "calculating " "Factorial of: " + n); + Copyright © 2019 Pearson Education, Inc., Hoboken NJ b. Remove this line in the recursive section at the end of the method: return (factorial (n - 1) * n); c. Add these lines in the recursive section: temp = factorial (n - 1); System.out.println ("Factorial of: " (n - 1) + " is " temp); return (temp * n); 3. Rerun the program and note how the recursive calls…Assume n is the number of inputs and that the log function is base 2. Treat this piece of code as a pseudocode. Give the big-Oh characterization, in terms of n for the following algorithm: for i in range(n*logn): for j in range(i): for k range(1000): print('I did it!')TOP DOWN PARSING
- a) You are given two different codes for finding the n-th Fibonacci number. Find the time complexity of both implementations and compare the two. Implementation 1 def fibonacci_1 (n) : if n < 0: print ("Invalid input!") elif n <= 1: return n else: return fibonacci_1 (n-1) +fibonacci_1 (n-2) n = int (input ("Enter a number: ")) nth_fib= fibonacci_1 (n) print("The {}th fibonacci number is {}.". format (n, nth_fib)) Implementation 2 def fibonacci_2 (n) : if n<0: return "Invalid Input" if n<=1: return n fib [0] (n+1) fib[0] = 0 fib[1] = 1 for i in range (2, n+1): fib[i] = fib[i-1]+ fib[i-2] return fib[n] n = int(input ("Enter a number: ")) nth_fib = fibonacci_2 (n) print("The {} th fibonacci number is {}.". format (n, nth_fib))45report nodes pruned by a-ß pruning Min Маx b Min Маx h P n 6 -9 3 2 7 13 4 9 Min 1 Мах y A B D E F G H 12 8 5 2 5 7 12 6. -5 6 11 Figure 2
- Find the time complexity of the following code, for (i=1: iInstructions Create a Program that implement recursive function to display the sum of the first n integers, where n is entered by the user. name your own function, coincidence is impossible Sample output: Enter a number: 5 The sum of the first 5 integers is 15. Explanation. Because the user entered 5, the first 5 integers are added. 1 + 2 + 3 +4 + 5 = 15.Question 8 Consider the following code where n and m can be any number of more than 20. Select the correct time complexity. int iter_count = 0; for (int i = 0; i < n; i *= 2) { for (int j = 0; j < m; j++){ iter_count += 1; } for (int i = }) 0; iSEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
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