Starting Out with Python (4th Edition)
4th Edition
ISBN: 9780134444321
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 12, Problem 2SA
In this chapter, the rules given for calculating the factorial of a number are as follows:
If n = 0 then factorial (n) = 1
If n . 0 then factorial (n) = n × factorial (n - 1)
If you were designing a function from these rules, what would the base case be? What would the recursive case be?
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The recursive functions are those that repeat themselves again and over again
In this chapter, the rules given for calculating the factorial of a number are as follows:If n = 0 then factorial(n) = 1If n . 0 then factorial(n) = n × factorial(n – 1)If you were designing a function from these rules, what would the base case be? What wouldthe recursive case be?
Write a recursive function that takes a positive integer and returns the factorial of that integer. Attention, the function must be recursive, and its name must be "fatorial".
Chapter 12 Solutions
Starting Out with Python (4th Edition)
Ch. 12.2 - It is said that a recursive algorithm has more...Ch. 12.2 - Prob. 2CPCh. 12.2 - What is a recursive case?Ch. 12.2 - What causes a recursive algorithm to stop calling...Ch. 12.2 - What is direct recursion? What is indirect...Ch. 12 - Prob. 1MCCh. 12 - A function is called once from a program's main...Ch. 12 - Prob. 3MCCh. 12 - Prob. 4MCCh. 12 - Prob. 5MC
Ch. 12 - Prob. 6MCCh. 12 - Any problem that can be solved recursively can...Ch. 12 - Actions taken by the computer when a function is...Ch. 12 - A recursive algorithm must _______ in the...Ch. 12 - A recursive algorithm must ______ in the base...Ch. 12 - An algorithm that uses a loop will usually run...Ch. 12 - Some problems can be solved through recursion...Ch. 12 - It is not necessary to have a base case in all...Ch. 12 - In the base case, a recursive method calls itself...Ch. 12 - In Program 12-2 , presented earlier in this...Ch. 12 - In this chapter, the rules given for calculating...Ch. 12 - Is recursion ever required to solve a problem?...Ch. 12 - When recursion is used to solve a problem, why...Ch. 12 - How is a problem usually reduced with a recursive...Ch. 12 - What will the following program display? def...Ch. 12 - Prob. 2AWCh. 12 - The following function uses a loop. Rewrite it as...Ch. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Largest List Item Design a function that accepts a...Ch. 12 - Recursive List Sum Design a function that accepts...Ch. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - Ackermann's Function Ackermann's Function is a...
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- 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.arrow_forwardRecursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…arrow_forwardWrite 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 = 1arrow_forward
- Write a recursive function to find the factorial of a number.int factorial(int n);arrow_forwardConsider the recursive procedure which computes the nth Fibonacci number is the one below. procedure Fl (n) //a function which returns the nth Fibonacci number.// if n < 2 then return(n) else return (F2(2,n,1,1)) endif end Fl procedure F2(i,n,x,y) if iarrow_forwardWrite a recursive function called that takes a string of single names separated by spaces and prints out all possible combinations (permutations), each combination on a new line. When the input is: Alice Bob Charlie then the output is: Alice Bob Charlie Alice Charlie Bob Bob Alice Charlie Bob Charlie Alice Charlie Alice Bob Charlie Bob Alicearrow_forward
- Using Java programming write a recursive function that accepts two arguments into the parameters x and y. The function should return the value of x times y. Remember, multiplication can be performed as repeated addition as follows: 7 * 4=4+4+4+4+4+4+4arrow_forwardWrite a program that performs the following functionalities:1. Fibonacci: a recursive function that computes the fibonacci series, which is defined as followsfibonacci (n) = fibonacci(n-2) + fibonacci(n-1)fibonacci(0) = 0fibonacci(1) = 1 So the fibonacci looks like: 0 1 1 2 3 5 8 13 21 34 …. Therefore, fibonacci(4) = 3, fibonacci(5) = 5, fibonacci(7)=13 2. Sum: a recursive function that computes the sum of integers 1, 2, 3, …., n for a given number n. So Sum(6) should return 1 + 2 + 3 + 4 + 5 + 6 , i.e. 21.sum(n) = n + sum(n-1) 3. Largest: a recursive function that computes the largest value for an integer array of positiveand negative values. For example, for the array below, the function largest should return 22,which is the largest value in the array. You can assume there are no more 20 integers in thearray. Think of how to formulate the recurrence relation in this problem yourself. 4. The 4th problem mimics the situation where eagles flying in the sky can be spotted and…arrow_forward
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