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- Answer the given question with a proper explanation and step-by-step solution. C++ 11.12 LAB: Fibonacci sequence (recursion) The Fibonacci sequence begins with 0 and then 1 follows. All subsequent values are the sum of the previous two, for example: 0, 1, 1, 2, 3, 5, 8, 13. Complete the Fibonacci() function, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1. Ex: If the input is: 7 the output is: Fibonacci(7) is 13 Note: Use recursion and DO NOT use any loops. main.cpp #include <iostream>using namespace std; int Fibonacci(int n) {/* Type your code here. */ } int main() {int startNum;cin >> startNum;cout << "Fibonacci(" << startNum << ") is " << Fibonacci(startNum) << endl;return 0;}Exercise 2. Give a recursive definition for the factorial operation k! n! for n ≥ 1. (remember that 1! = 0! = 1) Provide an algorithm in pseudo code to evaluate k! n! as one function Provide an algorithm in pseudo code to evaluate k! n! as three functions Evaluate the complexity of the algorithm at point 2 Evaluate the complexity of the algorithm at point 3Solve it with Python language For doing the lab activity: 1) Apply Recursive function technique to solve Problem 1 and 2. (Do not use iterative method) 1.Evaluate Binomial Coefficient. nCr=n! / (r! *(n-r)!) 2. Fibonacci Numbers (Sequence): 0, 1, 1, 2, 3, 5, 8 …
- The function below has the recursive relation T(x,y) = 2T(y/2)+O(1) when x,y>0Knowing these information, find the following: 1) The worst-case time complexity of the function2) The worst-case auxiliary space complexity of the function3) Explanation as to how the time complexity of the function can be improved without using multiplication operations.Recursive form given below Find the open form of the T n () function and write down the Big-Oh complexity.Provide an example of how the Structured Programming Theorem can be used to eliminate GOTO uncertainty and simplify convoluted code. You should use only your own words in the essay of the required length that you will be writing.
- Consider the post-fix expression below as input Input: [”2”, ”1”, ”+”, ”4”, ”*”] Java program to evaluate the given post-fix expression in O( n) time and with O(n) space complexity. The space complexity is derived from a data-structure which helps you solve the expressionArrange this functions in increasing order of asymptotic complexity Select one: a. f1, f2, f3 b. f2, f1, f3 c. f2, f3, f1Analyze the following codes for Time and space complexity. Determine Big O for the following code fragments in the average case. Assume that all variables are of type int. (i) sum = 0; if (EVEN(n)) for (i=0; i<n; i++) sum++; else sum = sum + n; sum1 = 0;
- Q1. (A) Draw a solution algorithm (at the same time) to find the maximum and minimum values of n matrix elements, and input the pseudo code. (B) The number of comparisons between the algorithms is recursively related and solved by assuming n=2k . © How to compare this algorithm with a simple algorithm to solve the same problem?Recursive formula for 2, 5, 10, 17, 26 in the form of a_n = a_n-1 + Cn + DDescribe a Branch & Bound algorithm to solve the employee to project assignment reward problem. You are given n employees and n projects. You are also given an array A[i,j] which contains the revenue realized by that assignment of employee i to project j. Describe your B&B solution to maximize the reward.