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Types of Linked List
A sequence of data elements connected through links is called a linked list (LL). The elements of a linked list are nodes containing data and a reference to the next node in the list. In a linked list, the elements are stored in a non-contiguous manner and the linear order in maintained by means of a pointer associated with each node in the list which is used to point to the subsequent node in the list.
Linked List
When a set of items is organized sequentially, it is termed as list. Linked list is a list whose order is given by links from one item to the next. It contains a link to the structure containing the next item so we can say that it is a completely different way to represent a list. In linked list, each structure of the list is known as node and it consists of two fields (one for containing the item and other one is for containing the next item address).
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- A triple (x, y, z) of positive integers is pythagorean if x2 + y2 = z2. Using the functions studied in class, define a function pyth which returns the list of all pythagorean triples whose components are at most a given limit. For example, function call pyth(10) should return [(3, 4, 5), (4, 3, 5), (6, 8, 10), (8, 6, 10)]. [Hint: One way to do this is to construct a list of all triples (use unfold to create a list of integers, and then a for-comprehension to create a list of all triples), and then select the pythagorean ones. def unfold[A, S](z: S)(f: S => Option[(A, S)]): LazyList[A] = f(z) match { case Some((h, s)) => h #:: unfold(s)(f) case None => LazyList() } code in scalaGiven g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.Prove or disprove:(a)∃ sets A,B ∀ functions f: A→B, f is a bijection. (b) if f : A → B is a function, C ⊆ A, and D ⊆ B, then f : C → D is always a function.[Note 1: one is true, the other is false.][Note 2: feel free to draw bubble-arrow pictures here, but make sure you explain what’s going on very carefully.]
- Let A and B be sets. How to show the following?:1. If A es is countable and there exists a surjective function f: A → B, then B is countable.2. If B is countable and there exists an injective function f: A → B, then A is countableComputer Science Prove that the set M = {x ∈ R: x 2 = 2a3 b , a ∈ N, b ∈ N} is countably infinite. Your solution should either give a bijective function f : N → M or give pseudo-code of a program that prints all the values of such a function, in the following format (in this case you don’t have to define f explicitly, but need to also show the first five lines of output): 0: element of M 1: another element of M 2: yet another element of MWrite the following three functions: a) The function gets an array A of length n of ints, and a boolean predicate pred. It returns the smallest index i such that pred(A[i])==true.If no such element is not found, the function returns -1.int find(int* A, int n, bool (*pred)(int)); b) The function gets an array A of length n of ints, and a function f. It applies f to each element of A.void map(int* A, int n, int (*f)(int)); c) The function gets an array A of length n of ints, and a function f. The function f gets 2 ints and works as follows: Start with accumulator = A[0] For i=1...length-1 compute accumulator=f(accumulator, A[i]) Return accumulator For example, if f computes the sum of the two inputs, then reduce() will compute the sum of the entire array.int reduce(int* A, int n, int (*f)(int,int));
- Write a function linear_independence that takes a collection of vectors with integer entries (each written as a list), and returns True if this collection of vectors is linearly independent, and False otherwise. Examples: linear_independence([1,2]) should return True. linear_independence([1,3,7],[2,8,3],[7,8,1]) should returnTrue. linear_independence([1,3,7],[2,8,3],[7,8,1],[1,2,3]) should return False.State whether each of the following functions is injective, surjective, bijective, or none ofthese categories: (N is the set of natural numbers, and Σ∗is the set of all strings over Σ.)(a) f : N → N , f(n) = n div 3(b) g : N → N , g(n) = n2 + 2n + 1 (c) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = a|w| (d) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = wRState whether each of the following functions is injective, surjective, bijective, or none ofthese categories: (N is the set of natural numbers, and Σ∗is the set of all strings over Σ.)(a) f : N → N , f(n) = n div 3(b) g : N → N , g(n) = n2 + 2n + 1(c) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = a|w|. (d) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = wR.
- Implement the Tic-Tac-Toe game in C++ using functions and 2D array of 3X3 size. Rules of the Game a) The game is to be played between computer and user.b) One of the players chooses ‘O’ and the other ‘X’ to mark their respective cells.c) The game starts with one of the players and the game ends when one of the players has onewhole row/ column/ diagonal filled with his/her respective character (‘O’ or ‘X’).d) If no one wins, then the game is said to be draw.Write a function solver that takes a non-negative integer upper_bound as an argument, and prints all non-negative integers i line-by-line in ascending order such that i is at most upper_bound, and i+100 and i+268 are perfect squares. Note that the function solver prints the numbers instead of returning them, but you may want to define a helper function is_perfect_square to return whether a number is a perfect square.Implement the following function, without using any data structure. /* Given two vectors of chars, check if the two vectors are permutations of each other, i.e., they contains same values, in same or different order.e.g., V1=[‘a’,’b’,’a’] and V2=[‘b’,’a’,’a’] stores same multi-set of data points: i.e., both contains two ‘a’, and one ‘b’. e.g., V3=[‘a’,’c’,’t’,’a’] and V4=[‘a’,’c’,’t’] are not same multi-set. V3 contains two ‘a’s, while V4 has only one ‘a’. Note: when considering multiset, the number of occurrences matters. @param list1, list2: two vectors of chars @pre: list1, list2 have been initialized @post: return true if list1 and list2 stores same values (in same or different order); return false, if not. */ bool SameMultiSet (vector<char> list1, vector<char> list2)