Come Divide Conquer Algorithm Following Scenario Studying Different Types Rocks Island Man Q34313588

Come up with a divide and conquer algorithm for the followingscenario:

You are studying different types of rocks on an island. Thereare MANY different types of rocks, but we are guaranteed that ofthe “N” rocks on the island, there exists a majority type. Morespecifically, we are guaranteed that there exists a quantitystrictly greater than N/2 rocks of a single type.

We have access to a method called isTheSame(rock1, rock2)returning true if the rocks are of the same type, false otherwise.We must use this method in the following problem as our sole meansfor comparison between two rocks. As an example of desiredfunctionality: If rock type A is in fact the majority and in somearray we have rocks 1,4,5,6, qualifying as typeA we can return anyone of those rocks’ numbers at the end of the algorithm to indicatethat this rock’s type is indeed the majority.

The task is as follows:

a) Design a deterministic divide and conquer algorithm that usesO(nlog(n) calls to isTheSame that returns a rock the belongs to themajority type. Explain in english and provide pseudocode for thisalgorithm.

b) Explain why we make O(nlog(n)) calls to isTheSame.

c) Prove using induction why this algorithm is correct includinga hypothesis, base case, inductive step and conclusion.

Come Formula Maximum Number Nodes Vertices Full Binary Tree Built Applying Recursive Step Q34929043

Come up with a formula for the maximum number of nodes(vertices) in a full binary tree that is built up by applying therecursive step n times. Prove your formula using mathematicalinduction

Come up with a formula for the maximum number of nodes (vertices) in a full binary tree that is built up by applying the recu

Come up with a formula for the maximum number of nodes (vertices) in a full binary tree that is built up by applying the recursive step n times. Prove your formula using mathematical induction. Show transcribed image text

Combine Scheme Functions M Trying Make Function Leafpile Takes List Returns Result Pushing Q11761429

How can I combine these scheme functions?

I’m trying to make this function:

;leafpile takes a list and returns the result of pushing all ;occurrences of ‘leaf to the end of the list> (leafpile ‘(rock grass leaf leaf acorn leaf))(list ‘rock ‘grass ‘acorn ‘leaf ‘leaf ‘leaf)

and so far, I have a function with a few helper functions:

(define (helper lsh) (cond [(empty? lsh) ‘()] [(not(equal? (first lsh) ‘leaf)) (cons (first lsh) (helper (rest lsh)))] [else (helper (rest lsh))]))(define (count-leaf ls) (cond [(empty? ls) 0] [(not (equal? ‘leaf (first ls))) (count-leaf (rest ls))] [else (add1 (count-leaf (rest ls)))]))(define (leafpile ls) (append (helper ls) (make-list (count-leaf ls) ‘leaf)))

How can I combine those three into one simple function? I’musing ISL Lambda in DrRacket. Also, I need it to use the fewestamount of recursive passes possible. Also, if in that final one, wecan use something quicker than “append” (quicker = fewer recursivepasses), the better.