Algorithm to add or subtract days from a date?

The easiest way is to actually write two functions, one which converts the day to a number of days from a given start date, then another which converts back to a date. Once the date is expressed as a number of days, it's trivial to add or subtract to it.

You can find the algorithms here: http://alcor.concordia.ca/~gpkatch/gdate-algorithm.html

You don't really need an algorithm as such (at least not something worthy of the name), the standard library can do most of the heavy lifting; calender calculations are notoriously tricky. So long as you don't need dates earlier than 1900, then:

#include <ctime>

// Adjust date by a number of days +/-
void DatePlusDays( struct tm* date, int days )
{
    const time_t ONE_DAY = 24 * 60 * 60 ;

    // Seconds since start of epoch
    time_t date_seconds = mktime( date ) + (days * ONE_DAY) ;

    // Update caller's date
    // Use localtime because mktime converts to UTC so may change date
    *date = *localtime( &date_seconds ) ; ;
}

Example usage:

#include <iostream>

int main()
{
    struct tm date = { 0, 0, 12 } ;  // nominal time midday (arbitrary).
    int year = 2010 ;
    int month = 2 ;  // February
    int day = 26 ;   // 26th

    // Set up the date structure
    date.tm_year = year - 1900 ;
    date.tm_mon = month - 1 ;  // note: zero indexed
    date.tm_mday = day ;       // note: not zero indexed

    // Date, less 100 days
    DatePlusDays( &date, -100 ) ; 

    // Show time/date using default formatting
    std::cout << asctime( &date ) << std::endl ;
}