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- What is the Big-Oh Runtime (in terms of n) for the following segment of code? int i; int used[n]; for (i = 0; i < n; i++) { used[i] = 0; } for (i = 0; i < n; i++) { if (used[i] == 0) { used[i] = 1; i = -1; } }Write a program that takes an integer N and uses the function “np.random.randint(low = 0, high = N)” to generate a random sequence of integers between 0 and N-1. Run experiments to validate the hypothesis that the number of integers generated before the first repeated value is found is “~sqrt(pi * N / 2)”. please help with last part Show that as n increases (e.g. with a doubling experiment), from n = 2 to n = 1,000, the value of “day_sim(n)” approaches “sqrt(pi * n / 2)”.What is the Big Oh runtime for the following function in terms of n? Show your work. int recurse(int n) { if (n == 0) return 1; int x = 1; while (x < n) { x = (x << 1); } return x + recurse(n - 1) }
- Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined re-cursively by f(0) = 3 and for n = 0, 1, 2, ... a) f(n + 1) = −2f(n).b) f(n + 1) = 3f(n) + 7.Trace this C code: What is the output of the following program segment? (Trace code and show your work) int i = 1, j = 1, k = 5; while (i+j < k) { printf("i = %d j = %d k = %d \n", i, j, k); i = j + k; j = i + k; k = i + j; } printf("i = %d j = %d k = %d \n", i, j, k);python this is connected to the last problem - the second part of the question is added. my attempt on this problem shows that the part b) (approaches N*NH) is not really wokring.. a) (answered) with a function “harmonic(n)” that computes the n-th harmonic number, write a function “harmonic_all(n)” that returns the number of values generated until all values are obtained as a function of the range of possible values n, then write a function “harmonic_sim(n)” that repeats “harmonic_all(n)” a total of n_sim = 100 times. (Attaching the code from the answer for a) d) Show that as n increases (e.g., with a doubling experiment), from n = 2 to n_max = 1,000, the value of “coupon_sim(n)” approaches “n * Hn”.
- 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.by using c++ .We are given an array of n points in the plane, and the problem is to find out the closest pair of points in the array. This problem arises in a number of applications. For example, in air-traffic control, you may want to monitor planes that come too close together, since this may indicate a possible collision. Recall the following formula for distance between two points p and q. Euclidean distance d( p , q ) = sqrt[(qx − px)^2 + (qy − py)^2]The Brute force solution is O(n^2), compute the distance between each pair and return the smallest. Find the smallest distance in O(nLogn) time using Divide and Conquer strategy.Code in Python Write a function, print_integers_less_than(n), which takes an integer parameter n and prints each integer k which is at least 0 and is less than n, in ascending order. Hint: use a simple for loop. For example: Test Result print_integers_less_than(2) 0 1 print_integers_less_than(5) 0 1 2 3 4 print_integers_less_than(-3)
- 3. Write a program to evaluate a polynomial \[ p(x)=c_{n} x^{n}+c_{n-1} x^{n-1}+\cdots+c_{2} x^{2}+c_{1} x+c_{0} \] and its derivative at a given pointt. The input is the row vectorcof coefficients of the polynomial arranged from highest to lowest power, and the numbert, and the two outputs arep(t)andp′(t). Computep(t)by first computing the row véctor \[ \left[t^{n}, t^{n-1}, \ldots, t^{2}, t, 1\right] \] and combine that with the vectorcto get the result. Computep′(t)by computing the coefficients of the derivative polynomial from the vectorc, and then evaluating that polynomial in the same way. Include some tests that provide evidence that your code produces the correct results. Please give proper explanation and typed answer only.Let A = {m ∈ Z | m ≡ 9 (mod 12)}. Let B = {n ∈ Z | n ≡ 1 (mod 4)}.Given an integer N and a base X, the task is to find the minimum number of operations required to represent N as a sum of the distinct powers of X. In each operation, you can either increment or decrement N. You are allowed to make the given operation any number of times Examples: Input: N = 7, X = 3 Output: 3.