1) a) b) Consider the following recursive function. You can assume that it will be invoked with non-negative integers. int mystery (int n, { } = m) if (n == return n; int m) else if (n == 0) return m; else if (m == 0) return n; else return mystery(m, n % m); Trace the execution of the three function calls mystery(363, 55), mystery(126, 49), and mystery(81, 37). For each of these three cases, how many calls do each of them make until they return the answer? What are the values of the parameters in each of the calls? Which base case do they reach? What does the mystery function actually do? Can you connect it to a known algorithm for solving this problem?
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- 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 14.1. Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is:********************Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern. 2. A palindrome is a string that reads the same both forward and backward. For example, the string "madam" is a palindrome. Write a program that uses a recursive function to check whether a string is a palindrome. Your program must contain a value-returning recursive function that returns true if the string is a palindrome and false otherwise. Do not use any global variables; use the appropriate parameter.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…
- 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…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8. A country has coins of denomination 3, 5 and 10 respectively. Write a recursive function canchange() which returns -1 if it is not possible to pay a value of k using these coins. Otherwise, it returns the minimum number of coins needed to make the payment. For example, canchange(7) will return -1. On the other hand, canchange(14) will return 4 because 14 can be paid as 3+3+3+5 and there is no other way to pay with fewer coins
- Digital Sum The digital sum of a number n is the sum of its digits. Write a recursive function digitalSum(n:int) -> int that takes a positive integer n and returns its digital sum. For example, digitalSum (2019) should return 12 because 2+0+1+9=12. Your Answer: 1 # Put your answer here 2 SubmitConsider the following function: void fun_with_recursion(int x) { printf("%i\n", x); fun_with_recursion(x + 1); } What will happen when this function is called by passing it the value 0?Write a recursive function PrintPattern2 that receives two arguments: (i) a character ch; (ii) number of lines and print the pattern.Example:PrintPattern2('*',5) will print the following pattern
- 4. CodeW X For func X C Solved b Answer x+ https://codeworkou... ... [+) CodeWorkout X271: Recursion Programming Exercises: Minimum of array For function recursiveMin, write the missing part of the recursive call. This function should return the minimum element in an array of integers. You should assume that recursiveMin is initially called with startIndex = 0. Examples: recursiveMin({2, 4, 8}, 0) -> 2 Your Answer: 1 public int recursiveMin(int numbers[], int startIndex) { numbers.length - 1) { if (startIndex 2. return numbers[startIndex]; } else { return Math. min(numbers[startIndex], >); 5. { 1:11 AM 50°F Clear 12/4/2021Identify 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 following recursive function. What does it calculate in terms of x, y, and z? 01: Private Function CalcRecurse(ByVal x As Integer, ByVal y As Integer, ByVal z As Integer) As Integer 02: If x <= 1 Then 'Assume that CalcRecurse always starts with x > 1 03: Return y 04: Else 05: Return z + CalcRecurse(x - 1, y, z) 06: End If 07: End Function