Slightly offtopic, but very practical use of a comparable algorithm is to determine to what extent a date ranges falls between a first and last date (e.g. first

Slightly offtopic, but very practical use of a comparable algorithm is to determine to what extent a date ranges falls between a first and last date (e.g. first date of the year, last date of year). e.g. in Excel it would look like: MAX((MIN(end date range; last date) - MAX(Start date range;first date) + 1);0)/(last date - first date + 1). This results in 0 in case of no match, a fraction when only a part of the date range falls between the first and last date, and 1 in case it matches completely or even exceeds the first and last date.