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- Develop Pseudo-code (English-like) for: In the Find Largest pseudo-code algorithm of Figure 2.14, listed below, if the numbers in our list were not unique and therefore the largest number could occur more than once. Modify the algorithm below to find all the occurrences of the largest number and their position in the list.Implement a priority queue sorting algorithm according the textbook (Data structures and algorithms by micheal goodrich) JavaEvaluations of algorithmsCalculate the algorithmic complexity of binary search in terms of time. Please offer detailed instructions.
- Algorithm Binary Search Input: L = a1, a2, ... , an list of distinct integers; x integer Output: p integer i = 1; j = n; found = F; p = 0; while i ≤ j and found = F m = ⌊i+j2⌋; if am = x then found = T and p = m else if am < x then i = m + 1 else j = m - 1; return p; When performing Algorithm Binary Search with input L = 1,3,5,7,9,11,13 and x = 9, how many times is x compared to an element ai of the list L?Define and justify why stopping conditions are required for all recursive algorithms, such as the recursive binary search, in your own words.Describe how following algorithms work and give an example where it could be implemented: a. Greedy Algorithm b. Divide and Conquer Algorithm c. Dynamic Programming
- For the following algorithms, find their i) worst-case complexity, ii)best-case complexity, and iii) loop invariant. I. An algorithm that finds the largest number in a list of n numbers.II. An algorithm that finds the greatest common divisor of two integersIII. An algorithm that converts a decimal number to its binary equivalentWrite algorithm for Recursive Backtracking Algorithms pre-cond: I is an instance of the problem. post-cond: optSol is one of the optimal solutions for the instance I, and optCost is its cost.Write pseudocode for Fibonacci Heap-Specific Algorithms?
- A halting condition is required for all recursive algorithms; describe the halting condition for the recursive binary search and explain why this is the case.You are advised to refer to the recommended textbook “Introduction to Algorithms (3rdedition) by Thomas H. Corman, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein”. Have areading through Chapter 04 and answer the following questions as a follow up exercise 1) Compute big-oh of the given T(n) using Recursion Tree MethodThe algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b)Require: a, b > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn a We want to prove the correctness of this algorithm using the loop invariant technique. a. In a first attempt to prove the correctness of this algorithm, we propose the following loop invariant property: “GCD(a, b) is a factor of a and b”. Explain why this property willnot help you as is. b. Use your previous observation to propose another loop invariant property that willhelp you to prove the correctness of the version of Euclid’s algorithm presented above. c. Show that your loop invariant property is true before executing the While loop forthe first time (i.e., initialization property)