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c# - Calculate days remaining to a birthday?

I have a DateTime object with a person's birthday. I created this object using the person's year, month and day of birth, in the following way:

DateTime date = new DateTime(year, month, day);

I would like to know how many days are remaining before this person's next birthday. What is the best way to do so in C# (I'm new to the language)?

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// birthday is a DateTime containing the birthday

DateTime today = DateTime.Today;
DateTime next = new DateTime(today.Year,birthday.Month,birthday.Day);

if (next < today)
    next = next.AddYears(1);

int numDays = (next - today).Days;

This trivial algorithm fails if the birthday is Feb 29th. This is the alternative (which is essentially the same as the answer by Seb Nilsson:

DateTime today = DateTime.Today;
DateTime next = birthday.AddYears(today.Year - birthday.Year);

if (next < today)
    next = next.AddYears(1);

int numDays = (next - today).Days;

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