• What input or parameter value impacts the number of times the recursive function will be called. • Give three specific examples of input/parameter values and, for each, state the number of times the recursive function will be called. • Devise a formula with respect ton that describes the number of times the recursive function will be called, where n is either the value passed or some property of the value passed (e.g. n might be the length of a string of the size of an array).
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- Recursion in programming is described as when a function/method makes a direct or indirect call to itself. Which of the features is not valid for a recursive function. Select one: a. The Recursive calls can be more then one b. The Recursive Call – the function calls itself with an input which is a step closer to the stop condition c. The Stoping Conditions can be more than one d. The Recursive call is optional. e. A Stop Condition – the function returns a value when a certain condition is satisfied, without a further recursive callPython only* Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle Do not use any kind of loop Within the definition of…Python only* Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle Do not use any kind of loop Within the definition of…
- 8. Ackerman's Function Ackermann's Function is a recursive mathematical algorithm that can be used to test how well a system optimizes its performance of recursion. Design a function ackermann(m, n), which solves Ackermann's function. Use the following logic in your function: If m = 0 then return n + 1 If n = 0 then return ackermann(m-1,1) Otherwise, return ackermann(m-1,ackermann(m,n-1)) Once you've designed yyour function, test it by calling it with small values for m and n. Use Python.Python program (recursive function) A recursive function is a function defined in terms of itself via self-referential expressions. This means that the function will continue to call itself and repeat its behavior until some condition is met to return a result. Write a python recursive functionprod that takes x as an argument, and returns the result where, result=1*1/2*1/3*….*1/n Include a screenshot that shows a python program that uses the above function and prints the rounded result to three decimal placesafter prompting the user to enter a number, x. Use x=3. N.B: The code should be included please.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…
- Midterm Practice Problems 1. Use recursion to write a function count_ones that returns how many Is there are in a number n when represented in decimal (base 10). For example, 1231 has two 1s. You can assume that n is nonnegative and at most 9 digits long. Do not use global (or static) variables. In main perform at least three tests of count_ones and use assert to check that the returned value is correct. Your function should have the following prototype: // count_ones (n) returns the number of is in the decimal representation of n // requires: 0 <= n < 10^9 int count_ones (int n);Identify the base case in this recursive function. Assume i> 0 when the function is invoked. (Line numbers are not part of the code.) 1. def add(i, j): 2. if i == 0: 3. return j 4. else: 5. return add(i - 1, j + 1) This function has no base case O line 5 line 1 line 4 O line 2 Question 6 The following recursive function is supposed to return a list that is the reverse of the list it was given. But it has a bug. What is the bug? (Line numbers are not part of the code.) MooP eok DrConsider the recursive function provided above. After the initial call to the function ham has been made with argument 26 then how many subsequent recursive calls will be made before a value a final result can be returned? This question is internally recognized as variant 235. Q11) 1 2 3 4 5 6 7 8 none of the above
- 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.QUESTION 9 There are several rules to keep in mind when writing a recursive function. Select all of them from the following list. of al Tust A. The recursive function may not call any other function or method. B. The value of all arguments passed to the recursive function must change for every recursive call. C. The recursive method must cal the main function in order to begin. D.There must be a clearly stated base case. CE. The function must contain a break statement to end the recursion. OF. The recursive function may not include a return statement. G. Recursive calls to the function must converge on the base case. is called. H.One or more arguments passed to the function must change in value each time the function iEach of the following recursive function definitions contains an error. Briefly but fully and clearly explain what is wrong with each definition. f(x) = 3*f(x-5) where x is a positive integer. f(0) = 7 2. g(x) = 2 - 4*g(x) where x is a positive integer. g(1) = 3 g(2) = 4