A sequence (bn)neNo is called strictly increasing if b₁ < bn+1 for all n € No. Such a strictly increasing sequence is divergent if, for any threshold MER, we can find an index k such that bk > M. We can represent a sequence (bn) by a Python function that takes n as its argument (of type int) and returns bn (of type float). Write a function threshold_index that takes two arguments: The first one is a Python function representing a strictly increasing, divergent sequence. The second one is a threshold value M. The function threshold_index should return the smallest index n for which the sequence passes the threshold (i.e., bn ≥ M).
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- Abraham Series to Compute Write a well-documented Python program, hmwk4Q2.py, that calculates. Construct a function abr_pi.py(N) accepts an integer N and returns an estimate of computing the Abraham Series using N terms. The series is: [2(1) 3ần 2n + 1 12=0 Have the main() call upon your function for various values of N to ensure it is correctly working. π =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 a function lis_rec(arr) that outputs the length of the longest increasing sequence and the actual longest increasing sequence. This function should use divide and conquer strategy to the solve the problem, by using an auxiliary function that is recursive. For example, one possibility is to define a recursive function, lis_rec(arr, i, prev), that takes the array arr, an index i, and the previous element index prev of LIS (which is part of the array arr before index i), and returns the length of the LIS that can be obtained by considering the subarray arr[i:]. Write a dynamic programming version ofthe function, lis_dp(arr), that outputs the length of the longest increasing sequence and the actual longest increasing sequence by using a table to store the results of subproblems in a bottom-up manner. Test the performance of the two functions on arrays of length n = 100, 500, 1000, 5000, 10000. Compare the running times and memory usage of the two functions.
- code required for python: For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. my code below , however as…Write a function using Java Function Name: winInRowParameters: board: 2D integer array, row: integer, piece: integerReturn: booleanAssume board is valid 2D int array, row is valid index in the board, piece is X==1/O==2Look at indicated row at given index in board. If that row has at least 3 consecutive entries withgiven type of piece (X/O) (3 in a row XXX, OOO), then return true, otherwise false.Consider the following recursive function: if b = 0, if 6 > a > 0, a f(b, a) f (b, 2.(a mod b)) otherwise. f(a, b) = Estimate the number of recursive applications required to compute f(a, b).
- Write a C++ program that fills a 5 x 5 matrix of integers. The matrix must be a static matrix; its size must be fixed at compile-time. Display the contents of the matrix. Query the user for an integer. Pass the matrix and the integer to a bool function that searches for the first occurrence, and only the first occurrence, of the integer in thematrix. If the integer is found, the function returns true (and passes back the row and column coordinates of the first occurrence of the integer); if not, the function returns false.Write a C++ program that fills a 5 x 5 matrix of integers. The matrix must be a static matrix; its size must be fixed at compile-time. Display the contents of the matrix. Query the user for an integer. Pass the matrix and the integer to a bool function that searches for the first occurrence, and only the first occurrence, of the integer in thematrix. If the integer is found, the function returns true (and passes back the row and column coordinates of the first occurrence of the integer); if not, the function returns false. Main then displays whether the integer was found in the matrix and if so, the coordinates of the first occurrence. The use of a break to exit a loop or a function should be avoided. My code does not find the location of the first occurrence and does not use a bool function. Can you please help me to find the error. This is my code: #include <iostream> #include <random> using namespace std; int main() { int guess, array[5][5]; bool found = false; for(int…The Lucas numbers are a series of numbers where the first two Lucas numbers (i.e., at indices 0 and 1) are 2 and 1 (respectively) and the kth Lucas number L_k (where k>1) is L_(k-1) + L_(k-2). Consider the following recursive definition for a function that is supposed to find the nth element of the Lucas numbers. Select the best option that identifies the line of code that prevents this function from running recursively and provides the correct code. Question options: line 5 should be return recursive_function(n-1) + recursive_function(n-2) line 3 should be return [2,1][n-1][n-2] line 3 should be return [2,1][n-1] line 2 should be if n <= 2: line 5 should be return recursive_function(n-1 + n-2) None of these options
- Part (a) Write a python function that computes the binomial coefficient ("). The function should return the correct answer for any positive integer n and k where k=m pass Part (c) Suppose that the number of people in the trial is 100. Then: • Plot a curve that shows how the probability of type 1 error changes with the choice of m, for m = 1,...n assuming that the null hypothesis holds (in red), • On the same picture, plot the probability of type 2 error vs the value of m in the case in which the new drug is effective with proability 0.68 (in blue). You can plot the two curves using matplotlib.pyplot. You can select the color by passing color='r' or color='b' to the plt.plot() function. [4]: n - 100 # your code here def plot_curve (): pass [5]: plot_curve() Part (d) Based on the picture above, what value of m do you think would be suitable to keep both type 1 and type 2 error small at the same time? (You may assume that the company claims the new drug has 68% accuracy) [6]: # your…In programming, a recursive function calls itself. The classical example is factorial(n), which can be defined recursively as n*factorial(n-1). Nonethessless, it is important to take note that a recursive function should have a terminating condition (or base case), in the case of factorial, factorial(0)=1. Hence, the full definition is: factorial(n) = 1, for n = 0 factorial(n) = n * factorial(n-1), for all n > 1 For example, suppose n = 5: // Recursive call factorial(5) = 5 * factorial(4) factorial(4) = 4 * factorial(3) factorial(3) = 3 * factorial(2) factorial(2) = 2 * factorial(1) factorial(1) = 1 * factorial(0) factorial(0) = 1 // Base case // Unwinding factorial(1) = 1 * 1 = 1 factorial(2) = 2 * 1 = 2 factorial(3) = 3 * 2 = 6 factorial(4) = 4 * 6 = 24 factorial(5) = 5 * 24 = 120 (DONE) Exercise (Factorial) (Recursive): Write a recursive method called factorial() to compute the factorial of the given integer. public static int factorial(int n) The recursive algorithm is:…Below is a Python function definition for a linear search of a list Ist for element. It returns the first index at which element can be found in the list (or None) if element is not in the list. def linearSearch(1st, element): i = 0 for item in 1st: if element == item: return i else: i += 1 return None Write a similar MATLAB function linearSearch.m. Your MATLAB function should take as parameters an unsorted list of non-negative integers, and an integer value, and returns the index where that value is first located in the list. (No argument testing is required.) Unlike the Python code which returns None if the value is not in the array, your MATLAB function should return the value -1 if the value is not found.