Efficient sorting

Hello,

In another exercise I was trying, I am trying to write an efficient
sorting algorithm.

Here's mine, with a random number generator at the end to make
testfiles. How do I improve the efficiency of the sorting process?
I've read about the various techniques but without statistical
analysis it is not immediately clear which is best or if there is
indeed a better way than the known best.

Example: Number of operations with a random seed of 0 and a 100,000
line file: 704982704 (assuming my definition of operations is the same
as people who claim nlog(n) - n^2 operations)

Thanks for any input.

// This program sorts a vector of numbers in ascending order
#include <fstream>
#include <stdlib.h>
#include <string>
#include <iostream>
#include <math.h>

using namespace std;

int main()
{
string line;
int i=0, count = 0, temp_int2;

fstream myfile("vector_in.txt");
// Read in number of lines
while (!myfile.eof())
    {
    getline(myfile,line);
    count++;
    }

count = count - 1;
myfile.clear(); // forget we hit the end of file
myfile.seekg(0, ios::beg); // move to the start of the file
 cout << "Number of file lines = "<< count << "\n";
int vector_in[count];

// Read in data
while (i < count)
    {
    getline(myfile,line);
    vector_in[i] = atoi(line.c_str());
    i++;
    }

// Swapping sort

int temp_int = 0, operations = 0;

for (int j = 0; j < count; j++)
    {
    for (i = j+1; i < count; i++)
        {
        operations++;
        if (vector_in[i] < vector_in[j])
            {
            temp_int = vector_in[i];
            vector_in[i] = vector_in[j];
            vector_in[j] = temp_int;
            }
        }
    }

for (i = 0; i < count; i++)
cout << vector_in[i] << "\n";
cout << "Number of operations = " << operations << "\n";

return 0;
}

Random number generator:
===================

// This program sorts a vector of numbers in ascending order
#include <fstream>
#include <stdlib.h>
#include <string>
#include <iostream>
#include <math.h>

using namespace std;

int main()
{
string line;
int i=0, count = 0, temp_int2, seed, length;

// Randomly generate file?
fstream myfile("vector_in.txt", ios::out);
cout << "Random seed value less than " << RAND_MAX << "\n";
cin >> seed;
cout << "Length of testfile?" <<"\n";
cin >> length;
// system ("rm vector_in.txt");
    {
    for (i = 0; i < length; i++)
        {
        temp_int2 = rand();
        myfile << temp_int2 << "\n";
        }
    myfile<<std::flush;
    myfile.close();
    }

cout << "File generated.\n";
return 0;
}

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