Algorithm to add or subtract days from a date?

Question

I'm trying to write a Date class in an attempt to learn C++.

I'm trying to find an algorithm to add or subtract days to a date, where Day starts from 1 and Month starts from 1. It's proving to be very complex, and google doesn't turn up much,

Does anyone know of an algorithm which does this?

Savil

See also Efficient algorithm for converting number of days to years (including leap years) – Longsighted

Answer 1

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

Szabadka

unfortunately these functions arent very precise... or at least when i compared my results to wolfram alpha, i was off by a day or so. – Apparatus

Here: home.roadrunner.com/~hinnant/date_algorithms.html are algorithms that are precise. Their validity has been tested to be accurate on a proleptic Gregorian calendar in the range +/- 5.8 million years using 32 bit arithmetic. They count days before or after 1970-01-01. – Nye

@HowardHinnant, that looks like a great resource, thanks. One simplification you might make is to remove the -1 from doy to let it range from [1, 366] and then subtract 719469 instead of 719468 at the end to compensate. – Szabadka

Since I wrote the comment above, I have had to move my personal website. My date algorithms are now here: howardhinnant.github.io/date_algorithms.html I also noticed that the d(g) function from alcor.concordia.ca/~gpkatch/gdate-algorithm.html doesn't seem to return the inverse of g(y,m,d). Perhaps I just programmed it up wrong, but I have not yet found my error. – Nye

Answer 2

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 ;
}

Grantinaid

Will leap seconds mess up this calculation? – Oday

@vargonian: A good question; UNIX time epoch is from 1 Jan 1970, and does not count leap seconds. However setting the nominal time of day to midday will avoid any potential problem for several tens of thousands of years. – Grantinaid

Answer 3

I'm assuming this is for some kind of an exercise, otherwise you would use a time class that's already provided to you.

You could store your time as the number of milliseconds since a certain date. And then you can add the appropriate value and convert from that to the date upon calling the accessors of your class.

Alexandros

Why milliseconds? He only seems to want dates, not times, and certainly not millisecond accuracy. That even hints at accounting for leap seconds. – Landslide

Answer 4

Here's a sketch of a very simple approach. For simplicity of ideas I will assume that d, the number of days to add, is positive. It is easy to extend the below to cases where d is negative.

Either d is less than 365 or d is greater than or equal to 365.

If d is less than 365:

m = 1;
while(d > numberOfDaysInMonth(m, y)) {
    d -= numberOfDaysInMonth(m, y);
    m++;
}
return date with year = y, month = m, day = d;

If d is greater than 365:

while(d >= 365) {
    d -= 365;
    if(isLeapYear(y)) {
        d -= 1;
    }
    y++;
}
// now use the case where d is less than 365

Alternatively, you could express the date in, say, Julian form and then merely add to the Julian form and conver to ymd format.

Ardent

Answer 5

One approach is to map the date to the Julian number of the date, do your integer operations and then transform back.

You will find plenty of resources for the julian functions.

Dole

Answer 6

I would suggest writing first a routine which converts year-month-day into a number of days since fixed date, say, since 1.01.01. And a symmetric routine which would convert it back.

Don't forget to process leap years correctly!

Having those two, your task would be trivial.

Craving

Answer 7

Try this function. It correctly calculates additions or subtractions. dateTime argument must be in UTC format.

tm* dateTimeAdd(const tm* const dateTime, const int& days, const int& hours, const int& mins, const int& secs) {
    tm* newTime = new tm;
    memcpy(newTime, dateTime, sizeof(tm));

    newTime->tm_mday += days;
    newTime->tm_hour += hours;
    newTime->tm_min += mins;
    newTime->tm_sec += secs;        

    time_t nt_seconds = mktime(newTime) - timezone;
    delete newTime;

    return gmtime(&nt_seconds);
}

And there are example of using:

time_t t = time(NULL);
tm* utc = gmtime(&t);
tm* newUtc = dateTimeAdd(utc, -5, 0, 0, 0); //subtract 5 days

Brownout

Answer 8

I know this is a very old question but it's an interesting and some common one when it comes to working with dates and times. So I thought of sharing some code which calculates the new date without using any inbuilt time functionality in C++.

#include <iostream>
#include <string>

using namespace std;

class Date {
public:
    Date(size_t year, size_t month, size_t day):m_year(year), m_month(month), m_day(day) {}
    ~Date() {}

    // Add specified number of days to date
    Date operator + (size_t days) const;

    // Subtract specified number of days from date
    Date operator - (size_t days) const;

    size_t Year()  { return m_year; }
    size_t Month() { return m_month; }
    size_t Day()   { return m_day; }

    string DateStr();
private:
    // Leap year check 
    inline bool LeapYear(int year) const
        { return year % 4 == 0 && (year % 100 != 0 || year % 400 == 0); }

    // Holds all max days in a general year
    static const int MaxDayInMonth[13];

    // Private members
    size_t m_year;
    size_t m_month;
    size_t m_day;   
};

// Define MaxDayInMonth
const int Date::MaxDayInMonth[13] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};

//===========================================================================================
/// Add specified number of days to date
Date Date::operator + (size_t days) const {
    // Maximum days in the month
    int nMaxDays(MaxDayInMonth[m_month] + (m_month == 2 && LeapYear(m_year) ? 1 : 0));

    // Initialize the Year, Month, Days
    int nYear(m_year);
    int nMonth(m_month);
    int nDays(m_day + days);

    // Iterate till it becomes a valid day of a month
    while (nDays > nMaxDays) {
        // Subtract the max number of days of current month
        nDays -= nMaxDays;

        // Advance to next month
        ++nMonth;

        // Falls on to next year?
        if (nMonth > 12) {
            nMonth = 1; // January
            ++nYear;    // Next year
        }

        // Update the max days of the new month
        nMaxDays = MaxDayInMonth[nMonth] + (nMonth == 2 && LeapYear(nYear) ? 1 : 0);
    }

    // Construct date
    return Date(nYear, nMonth, nDays);
}

//===========================================================================================
/// Subtract specified number of days from date
Date Date::operator - (size_t days) const {
    // Falls within the same month?
    if (0 < (m_day - days)) {
        return Date(m_year, m_month, m_day - days);
    }

    // Start from this year
    int nYear(m_year);

    // Start from specified days and go back to first day of this month
    int nDays(days);
    nDays -= m_day;

    // Start from previous month and check if it falls on to previous year
    int nMonth(m_month - 1);
    if (nMonth < 1) {
        nMonth = 12; // December
        --nYear;     // Previous year
    }

    // Maximum days in the current month
    int nDaysInMonth = MaxDayInMonth[nMonth] + (nMonth == 2 && LeapYear(nYear) ? 1 : 0);

    // Iterate till it becomes a valid day of a month
    while (nDays >= 0) {
        // Subtract the max number of days of current month
        nDays -= nDaysInMonth;

        // Falls on to previous month?
        if (nDays > 0) {
            // Go to previous month
            --nMonth;

            // Falls on to previous year?
            if (nMonth < 1) {
                nMonth = 12; // December
                --nYear;     // Previous year
            }
        }

        // Update the max days of the new month
        nDaysInMonth = MaxDayInMonth[nMonth] + (nMonth == 2 && LeapYear(nYear) ? 1 : 0);
    }

    // Construct date
    return Date(nYear, nMonth, (0 < nDays ? nDays : -nDays));
}

//===========================================================================================
/// Get the date string in yyyy/mm/dd format
string Date::DateStr() {
    return to_string(m_year) 
        + string("/")
        + string(m_month < 10 ? string("0") + to_string(m_month) : to_string(m_month))
        + string("/")
        + string(m_day < 10 ? string("0") + to_string(m_day) : to_string(m_day)); 
}


int main() {
    // Add n days to a date
    cout << Date(2017, 6, 25).DateStr() << " + 10 days = "
         << (Date(2017, 6, 25) /* Given Date */ + 10 /* Days to add */).DateStr() << endl;

    // Subtract n days from a date
    cout << Date(2017, 6, 25).DateStr() << " - 10 days = "
         << (Date(2017, 6, 25) /* Given Date */ - 10 /* Days to subract */).DateStr() << endl;

    return 0;
}

Output
2017/06/25 + 10 days = 2017/07/05
2017/06/25 - 10 days = 2017/06/15

Eoin

Your + and - operators are very slow for bigger dates. – Nottingham

Answer 9

I know it is an old question asked almost a decade before. But a few days before I came across the same for an assignment, and here is the answer as in here

// C++ program to find date after adding 
// given number of days. 
#include<bits/stdc++.h> 
using namespace std; 

// Return if year is leap year or not. 
bool isLeap(int y) 
{ 
    if (y%100 != 0 && y%4 == 0 || y %400 == 0) 
        return true; 

    return false; 
} 

// Given a date, returns number of days elapsed 
// from the beginning of the current year (1st 
// jan). 
int offsetDays(int d, int m, int y) 
{ 
    int offset = d; 

    switch (m - 1) 
    { 
    case 11: 
        offset += 30; 
    case 10: 
        offset += 31; 
    case 9: 
        offset += 30; 
    case 8: 
        offset += 31; 
    case 7: 
        offset += 31; 
    case 6: 
        offset += 30; 
    case 5: 
        offset += 31; 
    case 4: 
        offset += 30; 
    case 3: 
        offset += 31; 
    case 2: 
        offset += 28; 
    case 1: 
        offset += 31; 
    } 

    if (isLeap(y) && m > 2) 
        offset += 1; 

    return offset; 
} 

// Given a year and days elapsed in it, finds 
// date by storing results in d and m. 
void revoffsetDays(int offset, int y, int *d, int *m) 
{ 
    int month[13] = { 0, 31, 28, 31, 30, 31, 30, 
                    31, 31, 30, 31, 30, 31 }; 

    if (isLeap(y)) 
        month[2] = 29; 

    int i; 
    for (i = 1; i <= 12; i++) 
    { 
        if (offset <= month[i]) 
            break; 
        offset = offset - month[i]; 
    } 

    *d = offset; 
    *m = i; 
} 

// Add x days to the given date. 
void addDays(int d1, int m1, int y1, int x) 
{ 
    int offset1 = offsetDays(d1, m1, y1); 
    int remDays = isLeap(y1)?(366-offset1):(365-offset1); 

    // y2 is going to store result year and 
    // offset2 is going to store offset days 
    // in result year. 
    int y2, offset2; 
    if (x <= remDays) 
    { 
        y2 = y1; 
        offset2 = offset1 + x; 
    } 

    else
    { 
        // x may store thousands of days. 
        // We find correct year and offset 
        // in the year. 
        x -= remDays; 
        y2 = y1 + 1; 
        int y2days = isLeap(y2)?366:365; 
        while (x >= y2days) 
        { 
            x -= y2days; 
            y2++; 
            y2days = isLeap(y2)?366:365; 
        } 
        offset2 = x; 
    } 

    // Find values of day and month from 
    // offset of result year. 
    int m2, d2; 
    revoffsetDays(offset2, y2, &d2, &m2); 

    cout << "d2 = " << d2 << ", m2 = " << m2 
        << ", y2 = " << y2; 
} 

// Driven Program 
int main() 
{ 
    int d = 14, m = 3, y = 2015; 
    int x = 366; 

    addDays(d, m, y, x); 

    return 0; 
} 

Maigre

Answer 10

Don't know if this helps or not. I was working on a scheduling system which (in the first simple draft) calculated start date as due date - days lead time. I worked with seconds elapsed (since epoch) to allow greater precision in future drafts of the code.

#include <iostream>
#include <ctime>

int main() {
  // lead time in days
  int lead_time = 20;
  // assign a due_date of (midnight on) 3rd November 2020
  tm tm_due_date = { 0, 0, 0, 3, 11, 2020-1900};
  // convert due_date to seconds elapsed (since epoch)
  time_t tt_due_date = mktime(&tm_due_date);
  // subtract lead time seconds
  tt_due_date -= 60 * 60 * 24 * lead_time;
  // convert back (to local time)
  tm *start_date = localtime(&tt_due_date);
  // otput the result as something we can readily read
  std::cout << asctime(start_date) << "\n";
}

Bullis