5. State g(n)'s runtime complexity: int f(int n){ if(n <= 1){ return 1; } return 1 + f(n/2); } int g(int n){ for(int i f(i); } 1; i < n; i *= 2){
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- Do not use static variables to implement recursive methods. USING JAVA What is the worst case runtime complexity of the following code in terms of n for (int pass = 1; pass <= n; pass++) { for (int index = 0; index < n; index++) { for (int count = 1; count < 10; count++) { // constant time operation } // end for } // end for } // endWhat is the running time for this java code? I want the complexity and asymptotic upper bound using Big-Oh notation class lcs { static void LongestCommonArraySubsequence(int X[], int Y[], int n, int m) { // dp[][] array int[][] dp = new int[n + 1][m + 1]; // dp matrix initialization for (int i = 0; i <= n; i++) for (int j = 0; j <= m; j++) dp[i][j] = 0; for (int i = n - 1; i >= 0; i--) { for (int j = m - 1; j >= 0; j--) { if (X[i] == Y[j]) dp[i][j] = dp[i + 1][j + 1] + 1; // bottom up fill } } int max = 0; // maximum length int Xindex = 0; // starting index of array X int Yindex = 0; // starting index of array Y for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { // calculating the maximum value in dp matrix if (dp[i][j] > max) {…Write a recursive method in Java that displays a portion of a given array backward. Consider the last entry in the portion first.
- Jad has n students in his class. He wants to calculate the average grade in exaam 1. a) (Java language) Write the code using a recursive method named double average(int[] A, int startIndex, int n). where A is the array of grades. b) (Java language) Write the code using the iterative way. c) Find the time complexity of the codes in parts (a) and (b).Which is the base case of the following recursion function: def mult3(n): if n == 1: return 3 else: return mult3(n-1) + 3 else n == 1 mult3(n) return mult3(n-1) + 3Using recursion, write a Java program that takes an input ‘n’ (a number) from a user to calculate and print out the Fibonacci using the following modified definition: F(N) = 1 if n = 1 or n = 2 = F((n+1)/2)2 + F((n-1/2)2 if n is odd = F(n/2 + 1)2 – F(n/2 – 1)2 if n is even Your solution must implement recursion to receive points for this question.
- convert the recursion code to alterative code in java public int array11(int[] nums, int index) { if (index == nums.length) return 0; if (nums[index] == 11) return 1 + array11(nums, index + 1); return array11(nums, index + 1); }C programing Draw the recursion tree to find out the value of f(5)int f(int n){int ans;int i;if(n<3)return n;ans = f(n/2);for(i=0; i<n; i++)ans += f(i);return ans;}Draw the recursion tree for n = 12 (array length). sumSquares (array, first, last): if (first == last) return array [first] array[first]; int mid = (first + last)/2; return sumSquares (array, first, mid) + sumSquares (array, mid + 1, last); Recursion tree node count formula. Big-C runtime? • Formulate tree height. Big-C memory? Recursive vs iterative.
- In Java Ackermann’s Function Ackermann’s function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a method ackermann(m, n), which solves Ackermann’s function. Use the following logic in your method: If m = 0 then return n + 1 If n = 0 then return ackermann(m - 1, 1) Otherwise, return ackermann(m - 1, ackermann(m, n - 1)) Test your method in a program that displays the return values of the following method calls: ackermann(0, 0) ackermann(0, 1) ackermann(1, 1) ackermann(1, 2)ackermann(1, 3) ackermann(2, 2) ackermann(3, 2)In Java!!!. Design and implement a recursive version of a binary search. For the recursive version, instead of using a loop to repeatedly loop for the target value, allow each call to a recursive method check one value. If the value is not the target, refine the search space and call the method again. The indexes that define the range of viable candidates can be passed to the method. The base case is either finding the target value or running out of data to search. Design the program to work for on an array of sorted String objects.Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamicprogramming based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer.
