alculate the time complexity for the following function in terms of Big O notation. Explain your answer. [Note: Line numbers are only for reference purpose] int fun(int n) { 1 int count = 0; 2 for (int i = n; i >= 0; i /= 2) 3 count += i; 4 for (int j = 0; j < n; j++) 5 count +=j; 6 return count; }
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Calculate the time complexity for the following function in terms of Big O notation. Explain your answer.
[Note: Line numbers are only for reference purpose]
int fun(int n)
{
1 int count = 0;
2 for (int i = n; i >= 0; i /= 2)
3 count += i;
4 for (int j = 0; j < n; j++)
5 count +=j;
6 return count;
}
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- (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.2. Consider the following function: def func1(n): output = 1 for i in range (1, n) : output = i return output Rewrite the function as a recursive function.Problem: Recursive Power Method Design a python function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised, and the exponent. Assume the exponent is a nonnegative integer. Write the main() function to input the required parameters as shown in thesample input/output. Sample Output:Average number of words per line: 26.0Enter a number: 2Enter a positive whole number between 1 and 100: 102.0 raised to the power of 10 is 1,024.00
- Write the definition of a recursive function int simpleSqrt(int n) The function returns the integer square root of n, meaning the biggest integer whose square is less than or equal to n. You may assume that the function is always called with a nonnegative value for n. Use the following algorithm: If n is 0 then return 0. Otherwise, call the function recursively with n-1 as the argument to get a number t. Check whether or not t+1 squared is strictly greater than n. Based on that test, return the correct result. For example, a call to simpleSqrt(8) would recursively call simpleSqrt(7) and get back 2 as the answer. Then we would square (2+1) = 3 to get 9. Since 9 is bigger than 8, we know that 3 is too big, so return 2 in this case. On the other hand a call to simpleSqrt(9) would recursively call simpleSqrt(8) and get back 2 as the answer. Again we would square (2+1) = 3 to get back 9. So 3 is the correct return value in this case.Python only** Use recursive function* Define countBetween with 2 parameters Use def to define countBetween with 2 parameters thas two parameters: a starting number and an ending number, and counts up (i.e., prints consecutive integers) from the starting number to the ending number. If the numbers are the same, it just prints that number; if the ending number is lower than the starting number, it prints nothing. Do not use any kind of loop Within the definition of countBetween with 2 parameters, do not use any kind of loop. Call countBetween Within the definition of countBetween with 2 parameters, call countBetween in at least one place. Python only** Use recursive function* Define countThereAndBack with 2 parameters Use def to define countThereAndBack with 2 parameters after reaching the ending number, it also counts back down to the starting number. It accepts the same two parameters defining starting and ending numbers it should print nothing if the starting number is…3. Observe the following formulae: fin) = 1 fin) = 3 + f(n-1) fin) = 2 + f(n-1) if n=0 if n is even if n is odd a) Write a direct recursive function based on the formulae above. The function prototype is given as: int f(int n); Note: You don't have to worry about n being less than 0, but beware of 0 being an even number. b) Using mutual recursion and based on the formulae above, complete the function definition for the following function prototypes: int fodd (int n) ; int fEven (int n); c) Write a complete C program to test the direct and mutual recursions that you have written in Parts (a) and (b). Prompt the user for n values.
- Write a recursive function definition for the following function: int squares(int n); //Precondition: n >= 1 //Returns the sum of the squares of numbers 1 through n. For example, squares(3) returns 14 because 12 + 22 + 32 is 14.CodeW X bFor fun X C Solved x b Answer + x https://codeworko... CodeWorkout X265: Recursion Programmlng Exercise: GCD The greatest common divisor (GCD) for a pair of numbers is the largest positive integer that divides both numbers without remainder. For function GCD , write the missing base case condition and action. This function will compute the greatest common divisor of x and y.You can assume that x and y are both positive integers and that x > y. Greatest common divisor is computed as follows: = x and GCD(x, y) = GCD(y, x % y). Examples: GCD (6, 4) -> 2 Your An swer: 1 public int GCD(int x, int y) { if > { 2. > 3. } else { 4. return GCD(y, x % y); 9. { 7. 1:09 AM 50°F Clear 1V 1. 12/4/2021 甲language: Python Problem: Write a recursive function to add a positive integer b to another number a, add(a, b), where only the unit 1 can be added, For example add(5, 9) will return 14. When creating the function, also create a test case to prove the program works. The pseudocode is: # Base case: if b is 1, you can just return a + 1# General case: otherwise, return the sum of 1 and what is returned by adding a and b - 1
- Read Chapter 12 Recursive Lines Write a recursive function that accepts an integer argument, n. The function should display n lines of asterisks on the screen, with the first line showing 1 asterisk, the second line showing 2 asterisks, up to the middle line which shows n asterisks. You will then continue to print less stars until your last line of one asterisk. With an input of 3 your output should look like below. You will need to wind the stack to print up to your largest line. You will print the last set of lines as you unwind the stack or as you come out of your recursion. * ** *** ** *Study the two functions given below. Both use the same array declared as: static int data[256*256*8]; void function1(){ int i; int j; for (i = 0; i < 32; i++) for (j = 0; j < 256; j++) data[j] = i;}void function2(){ int i; int j; for (i = 0; i < 32; i++) for (j = 0; j < 256; j++) data[j*2048] = i;} Instructions:Assume the following behaviors in a virtual memory system. Reading or writing physical memory requires 50 nanoseconds. Reading or writing disk writing 10 milliseconds. Page size is 8 kilobytes. Presume that the program has 1 megabyte of physical memory available. You may consider everything except the array access itself to take no time. You should also assume that the first 1 megabyte of the array is in physical memory ini-tially. You may ignore any memory used by the program or stack to execute these func-tions. Using this information, answer the following questions. In each case, show the work you use to…Write a recursive function that computes the sum of the digits in an integer. Use the following function header: def sumDigits(n):For example, sumDigits(234) returns Write a test program that prompts the user to enter an integer and displays its sum.
