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- Write a function double lagrange(double x_int[], double y_int[], int n, double x) which calculates the value of the n-th order Lagrange’s polynomial Pn(x) defined for the set of nodes {x(0), y(0)}, ..., {x(n), y(n)}, for a given value of xComputer 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 MIn C programming Mathematically, given a function f, we recursively define fk(n) as follows: if k = 1, f1(n) = f(n). Otherwise, for k > 1, fk(n) = f(fk-1(n)). Assume that there is an existing function f, which takes in a single integer and returns an integer. Write a recursive function fcomp, which takes in both n and k (k > 0), and returns fk(n). int f(int n);int fcomp(int n, int k){
- Complete the below function which takes the coefficients of a polynomial P(x) as a tuple, and a list of values, and returns a list of computed values of P(x). Note that P() can be of any order. For example, P((2,-1,1), [1,2,3]) shall compute P(x) for x=1,2,3P(x)=2x^2 -x +1where x^2 denotes the square of x. Hence, the function must return [2,7,16], because P(1) is 2, P(2) is 7, and P(3) is 16.The sequence of values: n, c(n), c(c(n)), c(c(c(n))), c(c(c(c(n)))),... is known as the hailstone sequence starting at n. Implement c(n) as a function. Use predicates to test the parity of each input n.Write a program in Python with a function squareRoot(x, epsilon) that uses bisection search to return a number y that is close enough to the square root of x, so that abs(y**2 - x) < epsilon.
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- I need a Clark and Wright Savings Algorithm in Python. Are there any templates already? I have the following distance matrix given: [0, 10, 5, 9999, 9999, 9999, 9999], [10, 0, 5, 15, 20, 9999, 9999], [5, 5, 0, 10, 9999, 9999, 9999], [9999, 15, 10, 0, 15, 20, 15], [9999, 20, 9999, 15, 0, 5, 9999], [9999, 9999, 9999, 20, 5, 0, 20], [9999, 9999, 9999, 15, 9999, 20, 0]Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses. For example, given n = 3, a solution set is: [ "((()))", "(()())", "(())()", "()(())", "()()()" ] """ def generate_parenthesis_v1(n): defadd_pair(res, s, left, right): ifleft==0andright==0: res.append(s) return ifright>0: add_pair(res, s+")", left, right-1) ifleft>0: add_pair(res, s+"(", left-1, right+1) res= [] add_pair(res, "", n, 0) returnres def generate_parenthesis_v2(n): defadd_pair(res, s, left, right): ifleft==0andright==0: res.append(s) ifleft>0: add_pair(res, s+"(", left-1, right) ifright>0andleft<right: add_pair(res, s+")", left, right-1).Consider the function, f(n), defined by the following code int f(int n) { int r = 0; if ( n % 2 == 0 ) return 1; // when n is even while ( n > 1 ) { n = n – 3; r++; } return r; } From the definitions of big-Theta and little-oh: Prove or disprove that f(n) is Θ ( n ) 2. Prove or disprove that f(n) is o ( n^2 ) ( note: function f(n) as defined by the code, that is, the return value, and is not asking about the runtime of the code.)