. Largest: a recursive function that computes the largest value for an integer array of positive and negative values. For example, for the array below, the function largest should return 22, which is the largest value in the array. You can assume there are no more 20 integers in the array. Think of how to formulate the recurrence relation in this problem yourself.
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3. Largest: a recursive function that computes the largest value for an integer array of positive
and negative values. For example, for the array below, the function largest should return 22,
which is the largest value in the array. You can assume there are no more 20 integers in the
array. Think of how to formulate the recurrence relation in this problem yourself.
Step by step
Solved in 3 steps with 1 images
- For any part that requires recursion, if you do not create a recursive function, that will result in a on that part.Exercise 1: The number of combinations CR represents the number of subsets of cardi- nal p of a set of cardinal n. It is defined by C = 1 if p = 0 or if p = n, and by C = C+ C in the general case. An interesting property to nxC calculate the combinations is: C : Write the recursive function to solve this problem.Iterative FactorialWrite an iterative version (using a loop instead of recursion) of the factorial functionshown in this chapter. Test it with a driver program.
- 2: - Write a recursive function that takes an array and a callback function and returns True if any value of that array returns True from that callback function otherwise returns False. As a callback funtion for this problem, assume that the callback function is used to check if a given input is an even number. Anals, the running time of the algorithm 3: Recursive Linear SearchThe 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 optionsConsider 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 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.Write a RECURSIVE function, without using any loops, that prints the contents of a matrix with 3 columns. The function should take the matrix and the number of rows as arguments. void print_matrix(int arr[][3], int num_rows);Write an iterative function that determines the number of even elements in an array a of integers of size n. The function should return the number of elements that are even in array a of size n. Propose an appropriate prototype for your function and then write its code. Write a recursive function to solve the above problem. Propose an appropriate prototype for your function and then write its code.
- Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…Fun with Sorting :Given the following array of numbers:8 2 3 9 10 1 4 6 7 5Show what the array looks like after each iteration of the following sorting algorithms:1) Bubble2) Selection3) Insertion4) MergesortOnly show the array contents with each algorithm. You do not need to show function callinstances if recursion is used or write any code. Just show the array at key iterations of thealgorithm. You can use your own words to describe them as well for more detail (but do notwrite any code).1. Given, nCr= n! (n-r)!r!" Write a function to compute nCr without recursion.