Sequence Alignment problem using Pthreads

Question

I am trying to implement Sequence alignment problem (Needleman-Wunsch algorithm) using p-Threads. I am confused how to map the concept of multi threading in this particular serial problem. The code of serial computation of sequence alignment is enclosed below.(Just Matrix calculation part)

#include<iostream>
#include<string.h>
#include<string>
#include<algorithm>

using namespace std;


class Matrix
{
private:
int x;
int y;
int** mat;
string gene1;
string gene2;
int match_penalty;
int mismatch_penalty;
int gap_penalty;
int minimum_penalty;

public:
Matrix(int gene1Len, int gene2Len)
{
    x = gene2Len + 1;           //gene2 length
    y = gene1Len + 1;   //gene 1 length;
    mat = new int* [x];
    for (int i = 0; i < x; i++)
        mat[i] = new int[y];

    for (int i = 0; i < x; ++i) {
        for (int j = 0; j < y; ++j) {
            mat[i][j] = 0;
        }
    }

    //Default Penalties
    match_penalty = 1;
    mismatch_penalty = 3;
    gap_penalty = 2;
    minimum_penalty=0;
}

void Print_Matrix()
{
      cout<<"\n";
    for (int i = 0; i < x; i++)
    {
        for (int j = 0; j < y; j++)
        {
            cout << mat[i][j] << "\t";
        }
        cout << "\n";
    }
}

void setGenes(string gene1, string gene2)
{
    this->gene1 = gene1;
    this->gene2 = gene2;
}

void setPenalty(int mismatch, int gp,int match)
{
    mismatch_penalty = mismatch;
    gap_penalty = gp;
    match_penalty=match;
}

void setMatrix()
{
    //1st row and 1st Column values
    for (int i = 0; i < x; i++)
    {
        mat[i][0] = i * gap_penalty;
    }

    for (int i = 0; i < y; i++)
    {
        mat[0][i] = i * gap_penalty;
    }

    // Other matrix values

    for (int i = 1; i < x; i++)
    {
        for (int j = 1; j < y; j++)
        {
            if (gene1[j - 1] == gene2[i - 1])    //Similar gene values (A==A ||T==T)
            {
                mat[i][j] = mat[i - 1][j - 1]+match_penalty;
            }
            else
            {
                mat[i][j] = max({ mat[i - 1][j - 1] + mismatch_penalty , mat[i - 1][j] + gap_penalty, mat[i][j - 1] + gap_penalty });
            }
        }
    }


}


};


int main()
{
 string gene1 = "ACCA";
 string gene2 =  "CCA";      
 int matchPenalty;
 int misMatchPenalty ;
 int gapPenalty ;
 cout<<"Enter the value of Match Penalty" << endl;
cin >>  matchPenalty;
cout<<"Enter the value of misMatchPenalty Penalty" << endl;
cin >>  misMatchPenalty;

cout<<"Enter the value of gapPenalty Penalty" << endl;
cin >>  gapPenalty;


    
Matrix dp(gene1.length(), gene2.length());
dp.setGenes(gene1, gene2);
dp.setPenalty(misMatchPenalty, gapPenalty,matchPenalty);
dp.setMatrix();
dp.Print_Matrix();

}

How can I implement the above problem in P-threads? So far, I have used two threads to calculate matrix values of 1st column and 1st row simultaneously.But I have no idea how to compute all values of matrix in parallel. Kindly see my source code:

#include<string>
#include<algorithm>
#include<iostream>
#include<string.h>
#include<pthread.h>
using namespace std;

//Global variables --shared by all threads
int matchPenalty;
int misMatchPenalty;   
int gapPenalty;

struct gene_struct {
string gene1;
string gene2;
int rowSize;
int colSize;
int **mat;
};


 void* set_matrix_row(void *args)
{
 struct gene_struct *shared_block = (struct gene_struct *) args;
 for (int i = 0; i < shared_block->rowSize; i++)
 {
 shared_block->mat[i][0] = i * gapPenalty;
 }

 return NULL;
 }


 void *set_matrix_column(void *args)
 {
 struct gene_struct *shared_block = (struct gene_struct *) args;
 for (int i = 0; i < shared_block->colSize; i++)
 {
   shared_block->mat[0][i] = i * gapPenalty;
 }


 return NULL;
}

 void set_Matrix_Diagnol(struct gene_struct shared_block)
 {
  //How Should I calculate rest of the matrix values using Pthreads?
 }

 void Print_Matrix(struct gene_struct shared_block)
 {
      cout<<"\n";
    for (int i = 0; i < shared_block.rowSize; i++)
    {
        for (int j = 0; j < shared_block.colSize; j++)
        {
            cout << shared_block.mat[i][j] << "\t";
        }
        cout << "\n";
    }
 }

int main()
{
    pthread_t ptid1, ptid2;
    string gene1, gene2;
    struct gene_struct shared_block;   
    cout << "Enter First Gene : ";
    cin >> gene1;
    cout << "Enter Second Gene : ";
    cin >> gene2;
    cout<<"Enter the value of Match Penalty" << endl;
    cin >>  matchPenalty;   
    cout<<"Enter the value of misMatchPenalty Penalty" << endl;
    cin >>  misMatchPenalty;    
    cout<<"Enter the value of gapPenalty Penalty" << endl;
    cin >>  gapPenalty;

    shared_block.gene1 = gene1;
    shared_block.gene2 = gene2;
    shared_block.rowSize = gene2.length()+1;
    shared_block.colSize = gene1.length()+1; 
    shared_block.mat = new int* [shared_block.rowSize];  //col = gene2+1
    for (int i = 0; i < shared_block.rowSize; i++)
    {
    shared_block.mat[i] = new int[shared_block.colSize];
         
 }
    
    pthread_create(&ptid1, NULL, &set_matrix_row, (void *)&shared_block);
    pthread_create(&ptid2, NULL ,&set_matrix_column, (void *)&shared_block);
    pthread_join(ptid1,NULL); 
    pthread_join(ptid2,NULL);
    
    Print_Matrix(shared_block);
 }