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Number of Days in a Month

Easy

Asked by:

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Given an integer month, return the number of days in that month.

Return 28 for February.

Example 1:

Input: month = 1
Output: 31
Explanation: The month of January has 31 days.

Example 2:

Input: month = 2
Output: 28
Explanation: The month of February has 28 days.

Example 3:

Input: month = 4
Output: 30
Explanation: The month of April has 30 days.

Constraints:

1 <= month <= 12

Try coding it in LeetCode

Number of Days in a Month

Easy

Asked by:

4 views

Given an integer month, return the number of days in that month.

Return 28 for February.

Example 1:

Input: month = 1
Output: 31
Explanation: The month of January has 31 days.

Example 2:

Input: month = 2
Output: 28
Explanation: The month of February has 28 days.

Example 3:

Input: month = 4
Output: 30
Explanation: The month of April has 30 days.

Constraints:

1 <= month <= 12

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What data type will the input month be (integer, string, or enum), and what range of values should I expect for the month?
What range of values should I expect for the input year, and does the year need to be validated (e.g., is a negative year possible or expected)?
Should I assume the Gregorian calendar or handle other calendar systems?
What should I return if the input month is invalid (e.g., less than 1 or greater than 12)? Should I throw an exception, return a specific error code like -1, or return a default value like 0?
Is leap year calculation required (i.e. do I need to consider the year when returning number of days)?

Brute Force Solution

Approach

The problem asks us to find the number of days in a given month. A brute-force approach is to simply check each month one-by-one and return the corresponding number of days. This means we will check January, then February, then March, and so on, until we find the month we are looking for.

Here's how the algorithm would work step-by-step:

First, check if the month is January. If it is, return 31.
If it's not January, check if the month is February.
If it is February, determine if it's a leap year. If it is a leap year, return 29. If not, return 28.
If it's not February, check if the month is March. If it is, return 31.
Continue checking each month one by one: April, May, June, July, August, September, October, November, and December.
For each of these months, return the corresponding number of days: 30 for April, 31 for May, 30 for June, 31 for July, 31 for August, 30 for September, 31 for October, 30 for November, and 31 for December.
If the month is not any of the above, this approach would not return a result, or possibly return a failure result.

Code Implementation

def number_of_days_in_a_month_brute_force(month, is_leap_year):    if month == "January":        return 31
    if month == "February":        # Need to check if it's a leap year to determine February's days
        if is_leap_year:            return 29        else:            return 28
    if month == "March":        return 31
    if month == "April":        return 30
    if month == "May":        return 31
    if month == "June":        return 30
    if month == "July":        return 31
    if month == "August":        return 31
    if month == "September":        return 30
    if month == "October":        return 31
    if month == "November":        return 30
    if month == "December":        # December is the last month, so return 31 if it matches
        return 31

Big(O) Analysis

Time Complexity

O(1) – The provided solution uses a series of if-else if statements to check the input month. The number of comparisons is limited by the total number of months, which is always 12. Regardless of the input month, the algorithm performs a maximum of 12 constant-time checks. Therefore, the time complexity is constant.

Space Complexity

O(1) – The algorithm described uses a series of if/else statements to check the month. It doesn't create any data structures like arrays, hash maps, or lists to store intermediate results. The space used is limited to a few variables to store the input month and potentially a boolean to determine if it's a leap year, which are independent of the input month number. Therefore, the auxiliary space remains constant regardless of the input, resulting in a space complexity of O(1).

Optimal Solution

Approach

To find the number of days in a given month efficiently, we'll use a direct lookup method. We'll take advantage of the fact that the number of days in each month is fixed, except for February in leap years.

Here's how the algorithm would work step-by-step:

First, recognize that most months have either 30 or 31 days, with February being the exception (28 or 29).
Create a quick way to get the number of days from a regular (non-leap year). This can be a simple list or association where each month is linked to its number of days.
Separately, determine if the provided year is a leap year or not. Leap years affect the number of days in February.
If the year is a leap year and the month is February, return 29. Otherwise if the month is February return 28
For any other month, use the previously created direct lookup structure to quickly find and return the number of days for that month.

Code Implementation

def number_of_days_in_a_month(month, year):
    # Month values are 1-12
    days_in_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

    def is_leap_year(year_number):
        if (year_number % 4 == 0 and year_number % 100 != 0) or (year_number % 400 == 0):
            return True
        else:
            return False

    # Leap year needs to be checked first.
    if is_leap_year(year):

        if month == 2:
            return 29

    # Handle February in Non-Leap Year.
    if month == 2:
        return 28

    # Use lookup for other months.
    return days_in_month[month - 1]

Big(O) Analysis

Time Complexity

O(1) – The provided solution uses a direct lookup table (or a similar constant-time mechanism) to retrieve the number of days in a month, and a single if/else check for leap years. Determining if a year is a leap year involves a fixed number of arithmetic operations. The lookup table access is constant time. Therefore, the overall time complexity does not depend on the input month or year's magnitude, resulting in O(1) time complexity. All the operations take constant time.

Space Complexity

O(1) – The algorithm utilizes a fixed-size lookup structure (e.g., a list or map) to store the number of days in each month, excluding leap year February. This lookup structure has a constant size, independent of the input year or month. A boolean variable is used to determine if the provided year is a leap year. Therefore, the auxiliary space used remains constant, regardless of the input.

Edge Cases

Case	How to Handle
Invalid month value (e.g., month = 0, month = 13)	Return an error code or throw an exception indicating an invalid month.
Non-integer input for month or year	Type check the inputs and return an error or throw an exception if they are not integers.
Year is not a valid year (e.g., year = 0 or year is a very small negative number)	Define a reasonable lower bound for the year (e.g., 1) and return an error if it's less than this bound.
Leap year (year divisible by 4, but not divisible by 100 unless also divisible by 400)	Specifically handle February correctly, adding a day if it's a leap year.
Very large year value that could cause calculations problems	Ensure the year is within a reasonable range and handle potential integer overflow during leap year calculations.
The year is before the Gregorian calendar adoption	If the year is prior to 1583, indicate invalid input, or choose a proleptic Gregorian calendar.
Negative month	Return an error indicating that the month must be a positive integer.
Input is a string or float and is not an integer	Validate the input type and if it is not an integer, return an error.

Invalid month value (e.g., month = 0, month = 13)

How to Handle:

Return an error code or throw an exception indicating an invalid month.

Non-integer input for month or year

How to Handle:

Type check the inputs and return an error or throw an exception if they are not integers.

Year is not a valid year (e.g., year = 0 or year is a very small negative number)

How to Handle:

Define a reasonable lower bound for the year (e.g., 1) and return an error if it's less than this bound.

Leap year (year divisible by 4, but not divisible by 100 unless also divisible by 400)

How to Handle:

Specifically handle February correctly, adding a day if it's a leap year.

Very large year value that could cause calculations problems

How to Handle:

Ensure the year is within a reasonable range and handle potential integer overflow during leap year calculations.

The year is before the Gregorian calendar adoption

How to Handle:

If the year is prior to 1583, indicate invalid input, or choose a proleptic Gregorian calendar.

Negative month

How to Handle:

Return an error indicating that the month must be a positive integer.

Input is a string or float and is not an integer

How to Handle:

Validate the input type and if it is not an integer, return an error.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What data type will the input month be (integer, string, or enum), and what range of values should I expect for the month?
What range of values should I expect for the input year, and does the year need to be validated (e.g., is a negative year possible or expected)?
Should I assume the Gregorian calendar or handle other calendar systems?
What should I return if the input month is invalid (e.g., less than 1 or greater than 12)? Should I throw an exception, return a specific error code like -1, or return a default value like 0?
Is leap year calculation required (i.e. do I need to consider the year when returning number of days)?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

First, check if the month is January. If it is, return 31.
If it's not January, check if the month is February.
If it is February, determine if it's a leap year. If it is a leap year, return 29. If not, return 28.
If it's not February, check if the month is March. If it is, return 31.
Continue checking each month one by one: April, May, June, July, August, September, October, November, and December.
For each of these months, return the corresponding number of days: 30 for April, 31 for May, 30 for June, 31 for July, 31 for August, 30 for September, 31 for October, 30 for November, and 31 for December.
If the month is not any of the above, this approach would not return a result, or possibly return a failure result.

Code Implementation

def number_of_days_in_a_month_brute_force(month, is_leap_year):    if month == "January":        return 31
    if month == "February":        # Need to check if it's a leap year to determine February's days
        if is_leap_year:            return 29        else:            return 28
    if month == "March":        return 31
    if month == "April":        return 30
    if month == "May":        return 31
    if month == "June":        return 30
    if month == "July":        return 31
    if month == "August":        return 31
    if month == "September":        return 30
    if month == "October":        return 31
    if month == "November":        return 30
    if month == "December":        # December is the last month, so return 31 if it matches
        return 31

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

First, recognize that most months have either 30 or 31 days, with February being the exception (28 or 29).
Create a quick way to get the number of days from a regular (non-leap year). This can be a simple list or association where each month is linked to its number of days.
Separately, determine if the provided year is a leap year or not. Leap years affect the number of days in February.
If the year is a leap year and the month is February, return 29. Otherwise if the month is February return 28
For any other month, use the previously created direct lookup structure to quickly find and return the number of days for that month.

Code Implementation

def number_of_days_in_a_month(month, year):
    # Month values are 1-12
    days_in_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

    def is_leap_year(year_number):
        if (year_number % 4 == 0 and year_number % 100 != 0) or (year_number % 400 == 0):
            return True
        else:
            return False

    # Leap year needs to be checked first.
    if is_leap_year(year):

        if month == 2:
            return 29

    # Handle February in Non-Leap Year.
    if month == 2:
        return 28

    # Use lookup for other months.
    return days_in_month[month - 1]

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Invalid month value (e.g., month = 0, month = 13)	Return an error code or throw an exception indicating an invalid month.
Non-integer input for month or year	Type check the inputs and return an error or throw an exception if they are not integers.
Year is not a valid year (e.g., year = 0 or year is a very small negative number)	Define a reasonable lower bound for the year (e.g., 1) and return an error if it's less than this bound.
Leap year (year divisible by 4, but not divisible by 100 unless also divisible by 400)	Specifically handle February correctly, adding a day if it's a leap year.
Very large year value that could cause calculations problems	Ensure the year is within a reasonable range and handle potential integer overflow during leap year calculations.
The year is before the Gregorian calendar adoption	If the year is prior to 1583, indicate invalid input, or choose a proleptic Gregorian calendar.
Negative month	Return an error indicating that the month must be a positive integer.
Input is a string or float and is not an integer	Validate the input type and if it is not an integer, return an error.

Invalid month value (e.g., month = 0, month = 13)

How to Handle:

Return an error code or throw an exception indicating an invalid month.

Non-integer input for month or year

How to Handle:

Type check the inputs and return an error or throw an exception if they are not integers.

Year is not a valid year (e.g., year = 0 or year is a very small negative number)

How to Handle:

Define a reasonable lower bound for the year (e.g., 1) and return an error if it's less than this bound.

Leap year (year divisible by 4, but not divisible by 100 unless also divisible by 400)

How to Handle:

Specifically handle February correctly, adding a day if it's a leap year.

Very large year value that could cause calculations problems

How to Handle:

Ensure the year is within a reasonable range and handle potential integer overflow during leap year calculations.

The year is before the Gregorian calendar adoption

How to Handle:

If the year is prior to 1583, indicate invalid input, or choose a proleptic Gregorian calendar.

Negative month

How to Handle:

Return an error indicating that the month must be a positive integer.

Input is a string or float and is not an integer

How to Handle:

Validate the input type and if it is not an integer, return an error.