// CSE1502 Spring 2009 Homework #4, Matt Mahoney

// This program inputs a number n and prints e to n decimal places.

#include <iostream>
#include <string>
using namespace std;

// Divide a by b and put the result back in a, where a is a string of
// digits and b > 0.
void divide(string & a, int b)
{
  int carry = 0;
  for (int i=0; i<int(a.size()); ++i)
  {
    int d = carry * 10 + a[i] - '0';
    a[i] = d / b + '0';
    carry = d % b;
  }
}

// Add a and b as string of digits and return the sum. Assume that
// a, b, and the sum are all the same length.
string add(string a, string b)
{
  int carry = 0;
  for (int i=int(a.size()) - 1; i >= 0; --i)
  {
    a[i] += (b[i] - '0' + carry);
    if (a[i] > '9')
    {
      a[i] -= 10;
      carry = 1;
    }
    else
      carry = 0;
  }
  return a;
}

// Get n and calculate e to n decimal places
int main()
{

  // Get n = number of digits from user
  int n;
  cout << "How many decimal places of e would you like? ";
  cin >> n;

  // calcuate e = 1 + 1/1! + 1/2! + 1/3! + 1/4! +... until term is 0
  string e = "1" + string(n, '0');
  string term = e;
  string zero = string(n+1, '0');
  for (int i=1; term != zero; ++i)
  {
    divide(term, i);
    e = add(term, e);
  }

  // Insert decimal point in result
  cout << "e = " << e[0] << "." << e.substr(1) << endl;
  return 0;
}