#include

#include

#include

#include

$//$ Forward declaration of Solution class

class Solution;

$//$ Abstract base class

class Problem $\{$

public:

virtual Solution solveDivideAndConquer$()=0$;

virtual Solution solveGreedy$()=0$;

virtual Solution solveLasVegas$()=0$;

virtual bool solved$()=0$;

virtual bool trivial$()=0$;

virtual Solution createSolution$()=0$;

virtual std::vector makeSubproblems$()=0$;

virtual Solution combineSolutions$($std::vector partialSolutions$)=0$;

virtual Problem applyBestAction$()=0$;

virtual Problem applyRandomAction$()=0$;

$\}$;

$//$ Solution class $-$ implement as needed

class Solution $\{$

$//$ Implementation details here

$\}$;

$//$ Derived class implementing search and sort algorithms

class SearchAndSortProblem : public Problem $\{$

public:

$//$ Implement methods required by Problem class

Solution solveDivideAndConquer$()$ override $\{$

$//$ Implement divide and conquer algorithm

$\}$

Solution solveGreedy$()$ override $\{$

$//$ Implement greedy algorithm

$\}$

Solution solveLasVegas$()$ override $\{$

$//$ Implement Las Vegas algorithm

$\}$

bool solved$()$ override $\{$

$//$ Implementation

$\}$

bool trivial$()$ override $\{$

$//$ Implementation

$\}$

Solution createSolution$()$ override $\{$

$//$ Implementation

$\}$

std::vector makeSubproblems$()$ override $\{$

$//$ Implementation

$\}$

Solution combineSolutions$($std::vector partialSolutions$)$ override $\{$

$//$ Implementation

$\}$

Problem applyBestAction$()$ override $\{$

$//$ Implementation

$\}$

Problem applyRandomAction$()$ override $\{$

$//$ Implementation

$\}$

$//$ Implement sorting algorithms

void mergeSort$($std::vector& arr$)\{$

$//$ Implement merge sort

$\}$

void heapSort$($std::vector& arr$)\{$

$//$ Implement heap sort

$\}$

void quickSort$($std::vector& arr$)\{$

$//$ Implement quick sort

$\}$

$//$ Other helper methods if needed

$\}$;

int main$()\{$

$//$ Test your algorithms here

SearchAndSortProblem problemInstance;

$//$ Generate random data

std::vector data$(10)$;

std::generate$($data$.$begin$(),$ data.end$(),[]()\{$ return rand$()\%100$; $\})$;

$//$ Test sorting algorithms

problemInstance.mergeSort$($data$)$;

$//$ Output sorted data

for $($int num : data$)\{$

std::cout $$ num ;

$\}$

std::cout $$ std::endl;

return $0$;

$\}$PProperties $/$ Methods $-$ Class Diagramrogramming Assignment: Search and Sort Algorithms with C$++20$ and STL

Objective: The objective of this programming assignment is to implement various search algorithms $($divide and conquer, greedy, Las Vegas$)$ and sorting algorithms $($merge sort, heap sort, quick sort$)$ within the context of an abstract base class in C$++20$ using the Standard Template Library $($STL$).$ This assignment aims to enhance your understanding of algorithmic strategies and their application in real$-$world problem$-$solving scenarios.

Figure $1$: The Abstract Problem Class

Assignment Tasks:

Implement the required abstract methods required by the solve$\_$divide$\_$and$\_$conquer$(),$ solve$\_$greedy$(),$ and solve$\_$las$\_$vegas$()$ methods in the Problem class. Choose appropriate algorithms for each.

Implement the merge$\_$sort$(),$ heap$\_$sort$(),$ and quick$\_$sort$()$ methods in the derived SearchAndSortProblem class using C$++20$ and STL$.$

Test the implemented algorithms by creating an instance of the SearchAndSortProblem class with randomly generated data.

Assessment Criteria:

Your assignment will be assessed based on the following criteria:

Algorithmic Correctness: Ensure that your implementations of search and sort algorithms are correct and produce the expected results.

Code Readability: Write clear, well$-$documented, and organized code. Use meaningful variable and function names.

STL Usage: Demonstrate effective use of C$++20$ features and STL algorithms for sorting and other operations.

Abstraction: Utilize the abstract base class appropriately, providing concrete implementations for the specified methods.

Testing: Conduct thorough testing of the implemented algorithms to validate their correctness and efficiency.