I. Compute for the running time for each algorith 1. for i = 1 to n do Statement B 2. for(j=1; js n*n*n;j++) for (k=1; ksn) Statement f; for(m=1;m
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- int functionC (int n) { int i, j, sumC = 0; for (i=n; i > 0; i=i-5) for (j=1; j 0) { if (functionC(n) % 2 == 0) { for (i=m; i > 0; i=i/3) sumE++; } else (10) Asymptotic runtime of functionE { for (i=m; i > 0; i=i-3) sumE--; } n--; } return sumE;sum= 0; for (int i = 0; i 1) { sum++; i= 1/2; } = 2*log2 (n) We denote by Ta(n), Tb (n), Te(n) the running time of the three fragments. 1. Give evaluations for Ta(n), Tb (n), Te(n). 2. Is T(n) = O(Ta(n)) ? Answer YES or NO and justify your answer. 3. Is Te(n) = (Ta(n)) ? Answer YES or NO and justify your answer.Write a recursive function to compute the following series: m(i) = 1/2 + 2/ 3 + . . . + i/i + 1 Write a test program that prompts the user to enter an integer for i and displays m(i).
- I Evaluate the time complexity of following code: int a-0; for (i-0; i< N; i++){ aa+i;) for (i 0; i< N; i+){ a-a+i;) 2sum = 0; for (int i = 1; i< n; i = sum++ || 2*i)Write recursive functions for the following equations:a. Harmonic number is defined by the equationb. Fibonacci numbers are defined by the formula:FN = FN-2 + FN-1, for N ≥ 2 with F0 = 0 and F1 = 1
- 1. a) Given a recursive algorithm as below: int F(int n) { if (n <= 1) return 1; else if (n % 2 == 0) return F(n-1) + n; else return F(n/2) - 1; } Illustrate how you will find out the value of F(10) using the above algorithm. You need to show all the steps. b) Given a function as below: int recFx(int a, int b) { If (a < b) return a +b; else return recFx(a - b, b + 1); } Determine the values of: recFx(-10, 8) recFx(148, 78) (11) Must show all the steps.Write a recursive function to compute the following series: m(i) = 1 + 1/2 + 1/3 + . . . + 1/i Write a test program that displays m(i) for i 1, 2, ..., 10.Write a recursive algorithm with the following prototype: int add (int x, int y); that returns x if y is 0; and adds x to y otherwise. THE FUNCTION MUST BE RECURSIVE. (hint: the base case should involve a test for y being 0; recursive case should reduce y towards 0)
- java C++ Ackermann’s FunctionAckermann’s Function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s Function. Use the following logic in your function:If m = 0 then return n + 1If n = 0 then return A(m−1, 1) Otherwise, return A(m−1, A(m, n−1))Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2) SAMPLE RUN #0: ./AckermannRF Hide Invisibles Highlight: Show Highlighted Only The·value·of·A(0,·0)=·1↵ The·value·of·A(0,·1)=·2↵ The·value·of·A(1,·1)=·3↵ The·value·of·A(1,·2)=·4↵ The·value·of·A(1,·3)=·5↵ The·value·of·A(2,·2)=·7↵ The·value·of·A(3,·2)=·29↵a) Write a recursive method that calculates the following series: F(n)= (n1+i)ni=1*(n2+i)n/2i=1*(n4+i)n/4i=1*(n8+i)n/8i=1*....*2 b) Write the recurrence expression T(n).4. CodeW. X b For fun X Solved x b Answer x+ Ohttps://codeworko... CodeWorkout X264: Recursion Programming Exercise: Multiply For function multiply,write the missing base case condition and action. This function will multiply two numbers x and y.You can assume that both x and y are positive. Examples: multiply(2, 3) -> 6 Your Answer: 1 public int multiply(int x, int y) { 2. if > { > } else { return multiply(x 1, y) + y; 3. 5. { 7. 1:08 AM 50°F Clear 日
