Use ONLY PyCharm, please.Thank you. Consider the following recursive function:def lie (n):if n == 0:return '0'elif n = 1:return '1′else:return lie (n-1) + lie (n-2)The function expects an integer argument, n ≥ 0, and returns an integer.Apply the technique of memoization to this function.

Memoization is a technique used for the optimization of recursive functions by saving results of…

Answered: Consider the following recursive…

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 12PE

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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.
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.
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.
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, the pattern generated is as follows: **** *** ** * * ** *** **** 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 preceding pattern.
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
Exercise 1: The number of combinations CR represents the number of subsets of cardi- nal p of a set of cardinal n. It is defined by C = 1 if p = 0 or if p = n, and by C = C+ C in the general case. An interesting property to nxC calculate the combinations is: C : Write the recursive function to solve this problem.
CodeW For fun X C Solved https://codeworkou... 臺亂 CodeWorkout X272: Recursion Programming Exercise: Is Reverse For function isReverse, write the two missing base case conditions. Given two strings, this function returns true if the two strings are identical, but are in reverse order. Otherwise it returns false. For example, if the inputs are "tac" and "cat", then the function should return true. Examples: isReverse("tac", "cat") -> true Your Answer: 1 public boolean isReverse(String s1, String s2) { 2. if > 3. 4. else if > return true; return false; 5. 6. else { String s1first = String s2last return s1first.equals (s2last) && 51. substring(0, 1); s2, substring(s2.length() 1); 7. 8. 6. isReverse(s1.substring(1), s2.substring(0, s2.length() 1)); { 12} 1:11AM 50°F Clear 12/4/2021
CodeW X b For func x C Solved X b Answer X https://codeworkou... CodeWorkout X270: Recursion Programming Exercise: Count Characters For function countChr() write the missing part of the recursive call. This function should return the number of times that the letter "A" appears in string "str". Recall that str.substring(a) will return the substring of str from position a to the end of str, while str.substring (a, b) will return the substring of str starting at position a and continuing to (but not including) the character at position b. Examples: countChr ("ctcoWCAt") -> 1 Your AnsSwer: 1 public int countChr(String str) { 2. if (str.length() return 0; } (0 4. { int count = 0; www. 5. 9. if (str.substring(0, 1).equals("A")) { count = 1 7. { 9. return count + > 1:10 AM 50°F Clear 12/4/2021 呼
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. * ** *** ** *
The following recursive function takes three positive integer arguments: def compute(n,x,y) : if n==0 : return x return compute(n-1,x+y,y) What is the value returned by the compute function? n*x+y x+y x+n*y x What if: will the returned value be for the compute function defined in the question above if the argument n is negative? x x-n*y x+n*y The function will never return a value.
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.

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Consider the following recursive function: def lie (n): if n == 0: return '0' elif n = 1: return '1′ else: return lie (n-1) + lie (n - 2) The function expects an integer argument, n ≥ 0, and returns an integer. Apply the technique of memoization to this function.