please help me implement these sorts, i dont know how to #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

class Solution $\{$

$//$ Implementation details here

$\}$;

$//$ Derived class implementing search and sort algorithms

class SearchAndSortProblem : public Problem $\{$

public:

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

$\}$

$//$ 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$()\{$

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 $0$;

$\}$