sort a file based on user input

I am trying to sort a file based on the users choice of 2 files. I'm using a string variable and passing it into the instream() but it keeps going into the if statement that says the file is corrupt or does not exist. I know it exists because when I hardcode the file name in then it works perfectly fine! I'm sure its something simple but I just can't figure it out. I'm very new to c++ so please be thorough with your answers so that I can understand and learn. Thanks in advance!

#include <iterator>
#include <algorithm>
#include <vector>
#include <fstream>
#include <iostream>
#include <string>
using namespace std;

std::string file = "";
std::ofstream out("outputfile.txt");
std::vector<int> numbers;
std::string sortType = "";

void sort(std::vector<int>);
void MergeSort(vector<int> &numbers);


int main()
{
  std::cout << "Which type of sort would you like to perform(sort or mergesort)?\n";
  std::cin >> sortType;

  std::cout << "Which file would you like to sort?\n";
  std::cin >> file;

  std::ifstream in(file);
  //Check if file exists
  if(!in)
  {
    std::cout << std::endl << "The File is corrupt or does not exist! ";
    return 1;
  }

  // Read all the ints from in:
  std::copy(std::istream_iterator<int>(in), std::istream_iterator<int>(),
            std::back_inserter(numbers));

  //check if the file has values
  if(numbers.empty())
  {
      std::cout << std::endl << "The file provided is empty!";
      return 1;
  } else
  {
      if(sortType == "sort")
      {
          sort(numbers);
      }else
      {
          MergeSort(numbers);
      }

      // Print the vector with tab separators:
      std::copy(numbers.begin(), numbers.end(),
                std::ostream_iterator<int>(std::cout, "\t"));
      std::cout << std::endl;

        // Write the vector to a text file
      std::copy(numbers.begin(), numbers.end(),
                std::ostream_iterator<int>(out, "\t"));
        std::cout << std::endl;
  }
  return 0;
}

void sort(std::vector<int>)
{
  // Sort the vector:
  std::sort(numbers.begin(), numbers.end());
  std::unique(numbers.begin(), numbers.end());

  return;
}

vector<int> Merge(vector<int> &left, vector<int> &right)
{
    std::vector<int> result;

    while (left.size() > 0 && right.size() > 0)
    {
        if (left[0] <= right[0])
        {
            result.push_back(left[0]);
            left.erase(left.begin());
        } else
        {
            result.push_back(right[0]);
            right.erase(right.begin());
        }
    }

    if (left.size() > 0)
    {
        result.insert(result.end(), left.begin(), left.end());
    } else
    {
        result.insert(result.end(), right.begin(), right.end());
    }
    return result;
}

void MergeSort(vector<int> &numbers)
{
    if (numbers.size() <= 1)
    {
        return;
    }

    // split vector into two peices
    vector<int> left, right;
    unsigned int Middle = numbers.size() / 2;

    for (unsigned int i = 0; i < Middle; i++)
    {
        left.push_back(numbers[i]);
    }

    for (unsigned int i = Middle; i < numbers.size(); i++) {
        right.push_back(numbers[i]);
    }

    MergeSort(left);
    MergeSort(right);
    numbers = Merge(left, right);
    return;
}