Problem 5. Code the function sieve(n), where n is an integer greater than 1, which computes and returns the list of all the prime numbers that are less than or equal to n using the sieve of Eratosthenes algorithm.
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- 7. For each of these lists of integers, provide a simple formula or rule that generatesthe terms of an integer sequence that begins with the given list. Assuming thatyour formula or rule is correct, determine the next three terms of the sequence.a. 3,6,11,18,27,38,51,66,83,102,...b. 7,11,15,19,23,27,31,35,39,43,...c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .d. 1,2,2,2,3,3,3,3,3,5,5,5,5,5,5,5,...e. 0, 2, 8, 26, 80, 242, 728, 2186, 6560, 19682, . . .f. 1,3,15,105,945,10395,135135,2027025, 34459425, . . .g. 1,0,0,1,1,1,0,0,0,0,1,1,1,1,1,...h. 2, 4, 16, 256, 65536, 4294967296, . . .(a) Write a function matrix_multiply(mat1, mat2) that takes two matrices and returns the result of the matrix multiplication between mat1 and mat2. If the two matrices are not compatible with multiplication, then None should be returned. (b) Write a function print_sums(list1, list2) that takes two equal-length lists of numbers and prints all the sums of the corresponding elements. Thus the first line is the sum of the first element of list1 and the first element of list2, the second line is the sum of the second elements, and so on.1. Implement Euclidean Algorithm for calculating greatest common divisorFirst write and test a function that calculates the greatest common divisor of two nonnegative integers, as follows: /* precondition: a>=b>=0 *//* postcondition: return d=gcd(a,b) */int EuclidAlgGCD (int a, int b); Then implement the extended Euclidean Algorithm to find not only the greatestcommon divisor of two integers, but also find the integer coefficients that expressesthe gcd in terms of the integers, as illustrated below: /* precondition: a>=b>=0 *//* postcondition: return d=gcd(a,b), s and t are set so that d=sa+tb */int ExtendedEuclidAlgGCD (int a, int b, int & s, int & t);
- 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 scalaWrite a program to sort the elements in 1D array in descending order and also implement linear search on the same array. Both sorting and searching operations should be done inside user-defined function: "Task". So,for achieving the required functionality,pass,array into the function: Task () from main () using pass by reference/or address approach.Write a C function to search for a given number using binary search in a given array ofsorted numbers, sorted in ascending order. The function should return the index wherethe number is found, or zero otherwise
- Q#2 Write a recursive function zeroCount ( int a[ ], int s, int e) that receives an array of integers a [], a start index s, and an end index e. The function should return the number of zeros in that array between s and e. int zeroCount ( int a[ ], int s, int e); Trace your function given the following array and function call. Draw your steps. int a[ ] = {1, 0, 0, 5}; int zeros = zeroCount(a, 0, 3); language c++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 xImplement the following function, without using any data structure or #include <bits/stdc++.h> /* 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) THIS IS NOT THE CORRECT SOLUTION / include headers #include <bits/stdc++.h> // deinfe the namespace using namespace std; // function fo rchecking same bool…
- Use Sage to program Exercise 5.In 1202 AD, Leonardo Pisano asked the following famous problem:A certain man had a pair of rabbits together in a certain enclosedplace, and one wishes to know how many are created from the pair inone year when it is the nature for of them in a single month to bearanother pair, and in the second month those born bear also. Becausethe abovewritten pair in the first month bore, you will double it. therewill be two pairs in one month. One of these, namely the first, bears inthe second month, and thus there are in the second month three pairs;of these in one month two are pregnant, and in the third month 2pairs of rabbits are born, and thus there are 5 pairs in the month;...Explain how the rabbits reproduce. Create a list F where F[x] is the number ofrabbits in month x. (so F[0]=1, F[1]=2) Find F[12]. Find F[100].Question #2 Consider there is a list i.e. listA = {20, 10, 5, 15, 3} Write python code that: a. Creates a function updateListA(), which takes listA as input parameter, adds 30 after 20, and adds 40 at the end of the listA. [Hint: create a parameterized function] b. Creates a function newList(), which takes listA as input parameter and creates a new list newList with same elements as listA but in reverse order. c. If there is a function defined as below: def example(par1, par2=30): print(‘valid’) From the following function calls: i. example(par1=1) ii. example(1, 2) iii. example(par2=1) iv. example(par1=5, par2=6) Which call is valid? Write the values of par1 and par2 if a call is valid? Suggest corrections if a call is invalid.Language: C Implement the binary search algorithm, to find an integer in a sorted array. a) Declare an array of N integers. Use the preprocessor #define directive for the size of the array. Let the first element be 0. Fill the array, by assigning to each element the value of the previous element plus a pseudorandom, nonnegative number. b) Given a sorted array of N integers, write a function to recursively search for a given element x in and return the index of x in the array, or -1 if the element is not found. To this end, divide the interval into two halves. If the value of the element is less than the item in the middle of the interval, search further in the lower half of the interval, otherwise, search it in the upper half. c) Test your results, searching for randomly picked element from the array.