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- A function k whose domain is the set of positive integers is defined as k(1)=4 and k(n)=k(n-1)-2. Function k was evaluated for several numbers. Select each statement below that is true. A - k(0)=−2 B - k(2)=2 C - k(3)=0 D - k(6)=3 E - k(−1)=−4a) Implement a function start( ) that takes as input a positive number a, rounds its logarithm base 4 to the nearest integer n, and returns the value of 1.0 x 2^n.In 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){
- Write the C equivalent “train” function #void train(int*A, int*B, int*C, int k) train: add $t4, $0, $0bus: add $t5, $t4, $a1 lw $t6, 0($t5) add $t5, $t4, $a2 lw $t7, 0($t5) add $t6, $t6, $t7 add $t5, $t4, $a0 sw $t6, 0($t5) addi $t4, $t4, 4 slt $t5, $t4, a3 bne $t5, $0, bus jr raUsing foldl, define a function num2int :: [Int] -> Int -> Int that converts a list of numbers and the number n into an integer of base n. >num2int [3,4,5,6] 10 3456 >num2int [1,1,0,1,0,0,0,1,0,1,0,1,1,0] 2 3456 num2int :: [Int] -> Int -> Int num2int x y = foldl (\acc (a,b) -> ___a___ + b*y^a) 0 (___b___ (\x y ->(x,y)) [0..] (___c___ x)) fill in blank spaces of a , b , and cWrite a function in C programming language that gets two ints x and y, and returns the sum of all ints between x and y, including them. int sum_interval(int x, int y); For example: - sum_interval(1, 4)returns 1+2+3+4=10. - sum_interval(10, 3)returns 3+4+5+6+7+8+9+10=52. - sum_interval(2, -1)returns (-1)+0+1+2=2. - sum_interval(-1, -1)returns -1. Note that we may have x>=y or x<=y. You may assume that the sum will be within the range of int.
- A = 3 B = 6 C = 9 D= 7 mod10(X) is a function that returns the modulus of X after dividing it to 10. abs(X) is a function that returns the absolute value of X. Examples: mod10(6) = 6, mod10(16)=6, mod10(0) = 0, mod10(15)=5, mod10(41)+12 = 13 abs(4-8) = 4, abs(8-4)=4, abs(2-9) = 7, abs(8-1) = 7, abs(4-4)=0, abs(2-9)+8 = 15 Calculate the following: K1 = mod10(A+B) + 1= ……. K2 = abs(C-D) + 3 = ……. K3 = abs(D-2) + 1 = ……. K4 = mod10(A+B+C+D) + 1 = ……. K1 = mod((A+B), 10) + 1; K2 = abs(C-D) + 3; K3 = abs((D-2)) + 1; K4 = mod((A+B+C+D),10)+1;for C++ write a progam for the greatest common divisor of integers x and y is the largest integer that evenly divides both x and y. Write a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows. If y is 0 the answer is x; otherwise gcd(x, y) is gcd(y, x%y).Write a function triple_riffle_repeat(mylist,n) which takes as input a list (again with length a multiple of 3) and outputs the result of doing a 3-way riffle shufffle n times Write a function period(m) which takes as input a number m (which we will always take as a multiple of 3) and outputs the smallest positive integer n so that triple_riffle_repeat(list(range(m)),n) == list(range(m)) Discuss, with evidence, the outputs of your function period for different values of m, writing your answer as a comment.
- Define a function which takes one parameter N, and use loop(s) to control and output a pyramid pattern as follows: print a total of N rows, the number of asterisks in each row equals the row number (e.g. the 1st row has 1 asteroid, the Nth row has N asteroids). Note the pattern should be center aligned. E.g. when N is 5, you will print the following pattern * * * * * * * * * * * * * * *I need help with this question of Data Structures and Algorithmns 1 True of False a) For two functions f(n) and g(n) if f(n) =O(g(n)) then g(n) = Ω(f(n)) (True or False) b) For two positive functions g and h if f(n) =O(g(n)) then g(n) = O(h(n)) , then f(n)= O(h(n)) (True or False) c) If g1(n) = O(f(n)) and g2(n) = O(f(n)), then g1 + g2 = O(f(n)) (True or False)The question describes a function S(k) which is defined as the sum of the positive divisors of a positive integer k, minus k itself. The function S(1) is defined as 1, and for any positive integer k greater than 1, S(k) is calculated as S(k) = σ(k) - k, where σ(k) is the sum of all positive divisors of k. Some examples of S(k) are given: S(1) = 1 S(2) = 1 S(3) = 1 S(4) = 3 S(5) = 1 S(6) = 6 S(7) = 1 S(8) = 7 S(9) = 4 The question then introduces a recursive sequence a_n with the following rules: a_1 = 12 For n ≥ 2, a_n = S(a_(n-1)) Part (a) of the question asks to calculate the values of a_2, a_3, a_4, a_5, a_6, a_7, and a_8 for the sequence. Part (b) modifies the sequence to start with a_1 = k, where k is any positive integer, and the same recursion formula applies: for n ≥ 2, a_n = S(a_(n-1)). The question notes that for many choices of k, the sequence a_n will eventually reach and remain at 1, but this is not always the case. It asks to find, with an explanation, two specific…