Decimal to Roman numeral conversion algorithm

Question

I have written a program to convert a decimal to a Roman numeral. I am wondering if my algorithm is okay or not. If it's not okay, I want suggestions on improving my code. This code only works for inputs up to 5000. I found this question in a code cracker competition at my college.

#include <iostream>
using namespace std;
int main()
{
    int num=0;
    int user;
    int temp=0;
    string ans[4];
    int mod=10;
    int n[5];
    string r1[]={"0","I","II","III","VI","V","VI","VII","VIII","IX" };
    string r2[]={"x","XX","XXX","XL","L","LX","LXX","LXXX","XC"};
    string r3[]={"C","CC","CCC","CD","D","DC","DCC","DCCC","CM"};
    string r4[]={"M","MM","MMM","MMMM"};

    cout<<"Enter Number"<<endl;
    cin>>user;

    for(int i=0;i<4;i++)
{
    num=user%mod;
    user=user-num;
    n[3-i]=num;
    mod=mod*10;
}

for(int i=0;i<4;i++)
{
    if(n[i]>999)
    {
        temp=n[i]/1000;
        ans[i]=r4[temp-1];
    }
    if(n[i]>99 && n[i]<1000)
    {
        temp=n[i]/100;
    ans[i]=r3[temp-1];
    }
    if(n[i]>9&& n[i]<100)
    {
    temp=n[i]/10;
    ans[i]=r2[temp-1];
    }
        if(n[i]>0 && n[i]<10)
    {
    temp=n[i];
    ans[i]=r1[temp];
    }
    }
    for(int i=0;i<4;i++)
    {
    cout<<ans[i];
    }
    return 0;
    }

Answer 1

This code has a bug as 14 and 16 give the same output, while the Roman representation for them should surely be different:

• 14 -> XVI
• 16 -> XVI

Answer 2

The algorithm does not seem to implement putting a Roman number together using power of ten letters "I, X, C, M" and half power of ten letters "V, L, D", and relies on pre-coded conversions in the string array. I'm not saying do it this way but I'll share a javascript function to show how this might done (consider it pseudo code for C++):

function toRoman( num)
{   var str = "";
    var xstr;
    var xdigs = String("IVXLCDMvxlcdm_______");
    var xdig;   // roman digit
    var dig;    // digit

    if( num <= 0 || num >= 4000000) // out of range error
    { return "Out of range";
    }
    for( var i = 0; num > 0; i+=2)
    {   xstr = "";
        xdig = xdigs.charAt(i);  // a power of ten Roman letter
        dig = num % 10;
        num -= dig;
        num /= 10;

        if( (dig+1) % 5 == 0)
        {   xstr = xdig; // prepend subtrahend
            ++dig;
        }
        if( dig == 10)
        {   xstr += xdigs.charAt(i+2); // use next power of 10
        }
        else
        {   if( dig >= 5) // use fives
            {   xstr += xdigs.charAt(i+1); // half of next higher power of ten
                dig -=5;
            }
            while( dig-- > 0)
            {   xstr += xdig;         // postpend addend
            }
        }
        str = xstr + str;          // build leftwards
    }
    return str;
}

Note that Roman numbers use a bar over a letter to multiply it by 1000, while this code uses lowercase to indicate multiplied by 1000. Enjoy!