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- a) Given the following non-tail recursive function for determining whether a given number is even or not: (ns core-clj.core (:gen-class)) (defn even-num? [n] (if (= n 0) true (not (even-num? (dec n))))) (defn -main [] (println) (even-num? 8))) Rewrite the above clojure function (even-num?) so it can enforce the TCO condition: (b) Use the built-in higher ordered functions like (filter, map, take or reduce) to filter out the first three even numbers in given list like (4 7 9 6 19 8 21). Note: you need to call the even-num? function given in (a).s a classic example of a recursively defined function. It was originallynamed for Leonardo Fibonacci who studied it in the context of predictingthe growth of rabbit populations.Write a classifier algorithm for p(Y |X,α)
- Finite AutomataA. L = {w| w begins with an "a" and ends with a "b", should accept "aaaaabaaaab"}B. L = {w| w contains at least three a's, should accept "abababbbb" }Correct answer will be upvoted else downvoted. Computer science. Presently Nezzar has a beatmap of n particular focuses A1,A2,… ,An. Nezzar might want to reorder these n focuses so the subsequent beatmap is great. Officially, you are needed to find a change p1,p2,… ,pn of integers from 1 to n, to such an extent that beatmap Ap1,Ap2,… ,Apn is great. In case it is unthinkable, you ought to decide it. Input The primary line contains a solitary integer n (3≤n≤5000). Then, at that point, n lines follow, I-th of them contains two integers xi, yi (−109≤xi,yi≤109) — directions of point Ai. It is ensured that all focuses are unmistakable. Output In case there is no arrangement, print −1. In any case, print n integers, addressing a legitimate change p. In case there are numerous potential replies, you can print any.1. def f(x):"""Evaluates function `f(x) = x^2 - 15 \sin(x * \pi/3)`Parameters----------x : array_likeInput(s) to the functionReturns-------out : ndarrayFunction `f`, evaluated at point(s) x"""# your code here 2. def grad_f(x):"""Evaluates gradient of a function `f(x) = x^2 - 15 \sin(x * \pi/3)`Parameters----------x : array_likePoint(s) at which gradient should be avalueatedReturns-------out : ndarrayGradient of the function `f` evaluaed at point(s) x"""# your code here # TEST 1. f(x)assert f(0.) == 0.assert np.allclose(f(np.array([2.5, 7.5])), np.array([-1.25, 41.25])) assert np.allclose(f(np.arange(-10, 10, 1)), np.arange(-10, 10, 1)**2 - 15*np.sin(np.pi/3*np.arange(-10, 10, 1)))x_min = 1.33668375assert np.allclose(f(x_min), -12.9944407) # TEST 2. grad_f(x)assert np.allclose(grad_f(0.), -15.7079)assert isinstance(grad_f(0.), float) assert np.allclose(grad_f(0), - 5*np.pi*np.cos(0)), 'Gradient at point 0 is wrong'assert np.allclose(grad_f(np.arange(-10, 10, 1)), 2*np.arange(-10,…
- Suppose that recursive function ???(?) calls itself twice within its body(assume ???(?−1) called 3 times). Also assume the recursion would end when n=0. How many function calls does foo initiates? (A) O(?) (B) O(3?) (C) O(?3) (D) O(3?) Which answer is right and please explain whyWhat does the following lambda expression compute: λ(x)x × x × xGive Description of GetNumberOfConsoleInputEvents function.
- Write a code in C++ that calculates the times for each of the algorithms (functions). The code must execute the result showing the largest size n of each algorithm (function) that can be solved in time tWrite a C++ function, bool ok(int q[]), which takes an array q and returns true if the array represents a valid configuration of the eight queens and returns false otherwise.Write a FRACTION calculator program with c++ that adds, subtracts, multiplies, and divides fractions. Your program should check for the division by 0, have and use the following functions: (a) abs - returns the absolute value of a given integer. (b) min - returns the smallest of two positive integers. (c) gcd - returns the greatest common divisor of two positive integers. (d) reduce - reduces a given fraction. (e) flip - reduces a given fraction and flips the sign if the denominator is negative. (f) add - finds the reduced sum of a pair of given fractions. (g) subtract - finds the reduced difference of a pair of given fractions, by making the second fraction negative then using the add function. (h) multiply - finds the reduced product of a pair of given fractions. (i) divide - finds the reduced quotient of a pair of given fractions by inverting the second fraction then using the multiply function.