Data Structures and Algorithms in Java
6th Edition
ISBN: 9781118771334
Author: Michael T. Goodrich
Publisher: WILEY
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Chapter 5, Problem 8R
Describe a recursive
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Describe a recursive algorithm for converting a string of digits into the integer it represents. For example, '13531'
represents the integer 13, 531.
please code in python
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. 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.
One of the most common examples of recursion is an algorithm to calculate the factorial of an integer. The notation n! is used for the factorial ofthe integer n and is defined as follows:0! is equal to 11! is equal to 12! is equal to 2 × 1 = 23! is equal to 3 × 2 × 1 = 6
Chapter 5 Solutions
Data Structures and Algorithms in Java
Ch. 5 - Prob. 1RCh. 5 - Prob. 2RCh. 5 - Prob. 3RCh. 5 - Prob. 4RCh. 5 - Prob. 5RCh. 5 - Draw the recursion trace for the execution of...Ch. 5 - Prob. 7RCh. 5 - Describe a recursive algorithm for converting a...Ch. 5 - Prob. 9RCh. 5 - Prob. 10R
Ch. 5 - Prob. 11CCh. 5 - Prob. 12CCh. 5 - Give a recursive algorithm to compute the product...Ch. 5 - In Section 5.2 we prove by induction that the...Ch. 5 - Write a recursive method that will output all the...Ch. 5 - In the Towers of Hanoi puzzle, we are given a...Ch. 5 - Write a short recursive Java method that takes a...Ch. 5 - Write a short recursive Java method that...Ch. 5 - Use recursion to write a Java method for...Ch. 5 - Write a short recursive Java method that...Ch. 5 - Prob. 21CCh. 5 - Prob. 22CCh. 5 - Prob. 23CCh. 5 - Isabel has an interesting way of summing up the...Ch. 5 - Prob. 25CCh. 5 - Prob. 26CCh. 5 - Prob. 27PCh. 5 - Write a program for solving summation puzzles by...Ch. 5 - Prob. 29PCh. 5 - Write a program that can solve instances of the...
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- write program that uses recursion to calculate triangular numbers. Enter a value for the term number, n, and the program will display the value of the corresponding triangular number.shows the triangle.cpp program.arrow_forwardPascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2, pascal(1, 2) -> 0 public int pascal(int row, int column) { }arrow_forwardImplement the The triangle.cpp Program.This program uses recursion to calculate triangular numbers. Enter a value for the term number, n, and the program will display the value of the corresponding triangular number.arrow_forward
- The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence:1, 1, 2, 3, 5, 8, 13, 21…Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence.Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.arrow_forwardWrite a program in elixir programming language and in which you have to find the factorial of 10 using recursionarrow_forwardjava C++ Ackermann’s FunctionAckermann’s Function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s Function. Use the following logic in your function:If m = 0 then return n + 1If n = 0 then return A(m−1, 1) Otherwise, return A(m−1, A(m, n−1))Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2) SAMPLE RUN #0: ./AckermannRF Hide Invisibles Highlight: Show Highlighted Only The·value·of·A(0,·0)=·1↵ The·value·of·A(0,·1)=·2↵ The·value·of·A(1,·1)=·3↵ The·value·of·A(1,·2)=·4↵ The·value·of·A(1,·3)=·5↵ The·value·of·A(2,·2)=·7↵ The·value·of·A(3,·2)=·29↵arrow_forward
- Consider 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_forwardDesign and implement a recursive program to determine and print the Nth line of Pascal's triangle, as shown below. Each interior value is the sum of the two values above it. Hint: Use an array to store the values on each line.arrow_forwardUsing 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_forward
- Using recursion, write a Java program that creates an array of 10 numbers entered by the user. The recursive function receives the array and the position of the starting point of the array. The function returns the index of the smallest element of the array. The main method outputs the smallest of these numbers using the returned index.arrow_forwardJava source code writing - a recursive algorithm. Please use non-recursive and recursive ways to compute the nth Harmonic number, defined as H. Turn in your java source code file with three methods, including one main() method.arrow_forwardComplete the following recursive method for computing the factorial of an integer. Assume that n is greater than or equal to 0. a. result = n * factorial(n - 1)b. result = n * factorial(n)c. result = factorial(n - 1)d. result = (n - 1) * factorial(n)e. result = (n - 1) * factorial(n - 1)arrow_forward
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