EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Chapter 5, Problem 16E
Program Plan Intro
Recursive method:
- A recursive method is any method that calls itself.
- In recursive function base case will stop recursion and return value instead of calling function.
Program to implement recursive functions to:
- a. Check a word is palindrome or not.
- b. Check a sentence is palindrome or not.
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A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is '1\.ble was I, ereI saw Elba." Write a recursive function that detects whether a string is apalindrome. The basic idea is to check that the first and last letters of thestring are the same letter; if they are, then the entire string is a palindromeif everything between those letters is a palindrome.There are a couple of special cases to check for. If either the first orlast character of the string is not a letter, you can check to see if the restof the string is a palindrome with that character removed. Also, when youcompare letters, make sure that you do it in a case-insensitive way.Use your function in a program that prompts a user for a phrase andthen tells whether or not it is a palindrome. Here's another classic fortesting: '1\. man, a plan, a canal, Panama!"
def height(words, word):
The length of a word is easy enough to define by tallying up its characters. Taking the road less traveled, we define the height of the given word with a recursive rule for the height of the given word to follow from the heights of two words whose concatenation it is.
First, any character string that is not one of the actual words automatically has zero height. Second, an actual word that cannot be broken into a concatenation of two nonempty actual words has the height of one. Otherwise, the height of an actual word equals one plus the larger of the heights of the two actual words whose combined concatenation it can be expressed as. To make these heights unambiguous for words that can be split into two non-empty subwords in multiple ways, this splitting is done the best way that produces the tallest final height.
Since the list of words is known to be sorted, you can use binary search (available as the function bisect_left in the bisect module) to quickly…
Indirect recursion is when function A calls
function B, which in turn calls function A.
is it true or false.
Chapter 5 Solutions
EBK DATA STRUCTURES AND ALGORITHMS IN C
Ch. 5 - Prob. 1ECh. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 7ECh. 5 - Prob. 8ECh. 5 - Prob. 9ECh. 5 - Prob. 10E
Ch. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - Prob. 13ECh. 5 - Prob. 14ECh. 5 - Prob. 15ECh. 5 - Prob. 16ECh. 5 - Prob. 17ECh. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 1PACh. 5 - Prob. 3PACh. 5 - Prob. 4PACh. 5 - Prob. 5PA
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- Pascal'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_forwardQuestion#1: Let P and Q be integers and suppose F (P, Q) is recursively defined by: F(int P, int Q) if (P == 0) return Q else return F(P- 1, P + Q) Find and Trace F(8,1)arrow_forwardRemove the left recursion from the productions: S ->A a |b A ->A c |S d | €arrow_forward
- Determine whether a string is a palindrome A palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces. Some famous English palindromes include the following “Madam, I’m Adam”, and “Never odd or even”. Of course, a simpler example would be the world “radar”.The specifications for this assignment are: Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution:Make sure to Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes…arrow_forwardWrite 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".arrow_forwardWrite recursive methods for the following operations: • removeDup(String s): takes string s and returns another string r constructed from s after removing all duplicates. For example, when s = "pineapples", r will be "pineals". • intersection(String s1, String s2): takes two duplicate-free strings and returns the string consisting of all letters that appear in both s1 and s2. • union(String s1, String s2): takes two duplicate-free strings and returns the string consisting of all letters that appear in either s1 or s2. • difference(String s1, String s2): takes two duplicate-free strings and returns the string consisting of all letters that appear only in s1. For example, when s1 = "aples" and s2 = "pears", intersection(s1, s2) will return "apes", union(s1, s2) will "aplesr", and difference(s1, s2) "l". Calling method removeDup() is not allowed in intersection(s1, s2) , union(s1, s2) or difference(s1, s2) method. Your program should check strings are duplicate free before they are…arrow_forward
- 14 T OR F Recursive methods are always shorter and clearer than the equivalent nonrecursive methods.arrow_forwardProlog The sequence of Pell numbers 0,1,2,5,12,29,70,169,408,.. can be defined recursively as the sequence of numbers in which the first two numbers are 0 and 1, and each subsequent number is given by adding 2 times the preceding number to the number which precedes this. This can be defined in Haskell as: pell :: Int -> Int pell 0 = 0 pell 1 = 1 pell n = 2 * pell (n-1) + pell (n-2) Formulate the appropriate Prolog predicate "pell(N,Pn)" which is true if (and only if) "Pn" is the "N"-th term of the sequence of Pell numbers (note that we start numbering the sequence of Pell numbers with 0). That is, "pell(8,408)." would evaluate to "true", or "pell(5,Pn)." would give "Pn = 29"arrow_forwardFor function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101". Examples: decToBinary(13) -> "1101" public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}arrow_forward
- For function sumtok, write the missing recursive call. This function returns the sum of the values from 1 to k. Examples: sumtok(5) -> 15 public int sumtok(int k) { if (k <= 0) { return 0; } else { return <<Missing Recursive case action>> }}arrow_forwardT/F 1. Infinite recursion occurs where a recursive form lacks a base case.arrow_forwardUse the recursive descent parser in Section 4.4.1 below for the string a + b + c <expr> → <term> {(+ | -) <term>} <term> → <factor> {(* | /) <factor>} <factor> → id | int_constant | ( <expr> )arrow_forward
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