Number of Days in a Month - Video Solutions

Problem Overview: You are given a year and a month. Return how many days exist in that month for the given year. The only tricky case is February because its length depends on whether the year is a leap year.

The problem sits in the math category and mainly tests whether you remember the leap year rules and can map months to their correct number of days.

Approach 1: Month Table + Leap Year Check (O(1) time, O(1) space)

Store the number of days for each month in a fixed array such as [31,28,31,30,31,30,31,31,30,31,30,31]. For most months, simply return the value from the table using month - 1 as the index. February requires special handling. If the month is 2, determine whether the given year is a leap year and return 29 instead of 28.

The leap year rule follows the Gregorian calendar: a year is a leap year if it is divisible by 4, except years divisible by 100 are not leap years unless they are also divisible by 400. In code, this usually becomes:

(year % 4 == 0 && year % 100 != 0) || (year % 400 == 0)

After computing this condition, adjust February’s value accordingly. All other months return the precomputed value directly from the array. The algorithm performs only a few arithmetic checks and one array lookup, giving constant time and space complexity.

This approach is essentially a small implementation task backed by a simple math rule. No iteration, recursion, or extra data structures are required.

Approach 2: Conditional Month Groups (O(1) time, O(1) space)

Another way is to group months by the number of days instead of using an array. Months with 31 days are {1,3,5,7,8,10,12}. Months with 30 days are {4,6,9,11}. February is handled separately using the same leap year rule.

The logic becomes a sequence of conditional checks: if the month belongs to the 31-day set, return 31; if it belongs to the 30-day set, return 30; otherwise handle February with the leap year formula. This version avoids arrays but expresses the same idea through conditionals.

Recommended for interviews: The month-table approach is usually the cleanest and most readable. Interviewers expect you to know the leap year rule and apply it correctly. Writing the simple array plus the leap-year check demonstrates solid attention to edge cases while keeping the solution O(1) in both time and space.