Problem Description

The problem requires us to create a function that, given a year (year) and a month (month), returns the number of days in that given month. The challenge involves accounting for the different number of days in each month and determining whether the given year is a leap year since February has 29 days instead of 28 in leap years.

Intuition

The intuition behind the solution is to use a list to map each month to its respective number of days. We know that:

• January, March, May, July, August, October, and December all have 31 days.
• April, June, September, and November have 30 days.
• February has 28 days in a normal year and 29 days in a leap year.

To handle the special case of February in a leap year, we first need to determine whether the given year is a leap year. The determination can be made using the following rules:

• A year is a leap year if it is divisible by 4, except for end-of-century years, which must be divisible by 400.
• This means that if a year is divisible by 100 and not divisible by 400, it is NOT a leap year.

From these rules, we construct a logical condition that ensures the year is a leap year if it is either divisible by 400 or divisible by 4 but not by 100.

After this, we construct a list of days where February has 29 days if it's a leap year and 28 days otherwise. Then, the function simply returns the number of days corresponding to the given month by looking up the value in the pre-constructed list based on the month index.

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Solution Approach

The solution follows a simple and direct approach using a combination of condition checking and list indexing, which are fundamental constructs in programming - especially useful for this type of calendar-related computations.

We start by determining if the provided year is a leap year. The code does this with a single line of Boolean logic:

leap = (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0)

This line employs the modulus operator % to check for divisibility. The condition checks if the year is divisible by 4 but not by 100, unless it is also divisible by 400, in which case the year is indeed a leap year.

With the leap year status determined, we proceed to construct a list that maps each month (from index 1 to 12) to its corresponding number of days:

days = [0, 31, 29 if leap else 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

Notice that February (the second element of this list) has two possible values: 29 if leap is True, otherwise 28. The list starts with a placeholder 0 at index 0 since there is no month 0, and this alignment allows us to directly use the month value as an index to the list.

Finally, the function returns the number of days corresponding to the input month by accessing the days' list using the month as an index:

return days[month]

The use of list indexing here provides an efficient and clean solution, avoiding multiple conditional statements or explicit date handling libraries, which are unnecessary for the problem at hand.

Example Walkthrough

Let's walk through a small example to illustrate the solution approach. We'll create a function named get_days_in_month that implements the described approach. Suppose we are given the year 2020 which is a leap year and the month February, and we want to find out how many days February has in this year.

Given in 2020:

year = 2020
month = 2  # Since February is the second month

We first determine if 2020 is a leap year. The code:

leap = (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0)

evaluates to:

leap = (2020 % 4 == 0 and 2020 % 100 != 0) or (2020 % 400 == 0)

As 2020 is divisible by 4 and not divisible by 100, leap becomes True. Since 2020 is a leap year, February will have 29 days.

Next, we create a list that maps each month to its number of days, accounting for leap years:

days = [0, 31, 29 if leap else 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

Which now translates to:

days = [0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

because leap is True, index 2 (which corresponds to February) is assigned the value 29.

Finally, to find out the number of days in February 2020, the function performs a simple list indexing operation:

return days[month]

Which gives us:

return days[2]

The function returns 29, which is the correct number of days in February during a leap year.

So by following these steps, our function get_days_in_month would correctly determine that there are 29 days in February 2020. A straightforward sequence of logical checks and array indexing provides us with a concise and effective solution.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the given code is O(1) because it performs a constant number of operations no matter the value of the input year and month. Checking if a year is a leap year and accessing an element from a pre-defined list both take constant time.

Space Complexity

The space complexity of the code is also O(1) as it uses a fixed amount of additional memory. The list days is of a constant size (13 elements), and the space required does not grow with the size of the input year or month.

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