Questions and Answers of Data Structures And Algorithms In C++

Give an algorithm for finding the penultimate (second to last) node in a singly linked list where the last element is indicated by a null next link.
Write a program that can solve instances of the Tower of Hanoi problem (from Exercise C-3.12).Data from in Exercise C-3.12In the Towers of Hanoi puzzle, we are given a platform with three pegs, a, b,
Describe a nonrecursive function for finding, by link hopping, the middle node of a doubly linked list with header and trailer sentinels. What is the running time of this function?
Draw the recursion trace for the execution of function ReverseArray(A,0,4) (Code Fragment 3.39) on array A = {4,3,6,2,5}.
Draw the recursion trace for the execution of function Puzzle Solve(3,S,U) (Code Fragment 3.44), where S is empty and U = {a,b,c,d}.Code Fragment 3.44Solving a combinatorial puzzle by enumerating and
Write a short C++ function that repeatedly selects and removes a random entry from an n-element array until the array holds no more entries. Assume that you have access to a function random(k), which
Write a short recursive C++ function that finds the minimum and maximum values in an array of int values without using any loops.
Write a short C++ function to count the number of nodes in a circularly linked list.
Write a short recursive C++ function that will rearrange an array of int values so that all the even values appear before all the odd values.
Write a short recursive C++ function that takes a character string s and outputs its reverse. So for example, the reverse of "pots&pans" would be "snap&stop".
Write a short recursive C++ function that determines if a string s is a palindrome, that is, it is equal to its reverse. For example, "racecar" and "gohangasalamiimalasagnahog" are palindromes.
Use recursion to write a C++ function for determining if a string s has more vowels than consonants.
Suppose you are given two circularly linked lists, L and M, that is, two lists of nodes such that each node has a nonnull next node. Describe a fast algorithm for telling if L and M are really the
Give a pseudo-code description of the O(n)-time algorithm for computing the power function p(x,n). Also, draw the recursion trace of this algorithm for the computation of p(2,5).
Give a C++ description of Algorithm Power for computing the power function p(x,n) (Code Fragment 4.4).Data from in Fragment 4.4Computing the power function using linear recursion.To analyze the
Perform an experimental analysis to test the hypothesis that the STL function, sort, runs in O(nlog n) time on average.
Draw the recursion trace of the Power algorithm (Code Fragment 4.4, which computes the power function p(x,n)) for computing p(2,9).Data from in Fragment 4.4Computing the power function using linear
Perform an experimental analysis to determine the largest value of n for each of the three algorithms given in the chapter for solving the element uniqueness problem such that the given algorithm
Suppose you are given an n-element array A containing distinct integers that are listed in increasing order. Given a number k, describe a recursive algorithm to find two integers in A that sum to k,
Given an n-element unsorted array A of n integers and an integer k, describe a recursive algorithm for rearranging the elements in A so that all elements less than or equal to k come before any
Graph the functions 8n, 4nlog n, 2n2, n3, and 2n using a logarithmic scale for the x- and y-axes. That is, if the function is ∫ (n) is y, plot this as a point with x-coordinate at logn and
Show that if d(n) is O( ∫ (n)) and e(n) is O(g(n)), then d(n) +e(n) is O( ∫ (n)+g(n)). Algorithm Ex1(A): Input: An array A storing n ≥ 1 integers. Output: The sum of the elements in A. S←
For each function ∫ (n) and time t in the following table, determine the largest size n of a problem P that can be solved in time t if the algorithm for solving P takes ∫ (n) microseconds (one
What is the sum of all the even numbers from 0 to 2n, for any positive integer n?
Show that the summation n ₁ [log₂ i] is O(nlogn).
Order the following functions by asymptotic growth rate.4nlog n+2n 210 2log n3n+100log n 4n 2nn2 +10n n3 nlog n
Consider the Fibonacci function, F(n) (see Proposition 4.20). Show by induction that F(n) is Ω((3/2)n).
Show that if d(n) is O( ∫ (n)) and e(n) is O(g(n)), then d(n)−e(n) is not necessarily O( ∫ (n)−g(n)).
Show that (n+1)5 is O(n5).
Show that 2n+1 is O(2n).
Algorithm A executes an O(log n)-time computation for each entry of an n-element array. What is the worst-case running time of Algorithm A?
Describe a recursive function for computing the nth Harmonic number, n H = Σ, 1/i. Hn

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