Problem Description

You are given a string date that represents a date in the Gregorian calendar using the format yyyy-mm-dd (year-month-day).

Your task is to convert this date into its binary representation by following these steps:

1. Take the year, month, and day values from the date
2. Convert each of these decimal numbers to their binary representation (without leading zeros)
3. Combine them back together in the same year-month-day format, but now using binary numbers

For example, if the date is "2024-12-05":

• Year 2024 in binary is 11111101000
• Month 12 in binary is 1100
• Day 5 in binary is 101
• The result would be "11111101000-1100-101"

The solution works by:

1. Splitting the input date string by the - delimiter to get the year, month, and day as separate strings
2. Converting each string to an integer, then to its binary representation using f"{int(s):b}" format
3. Joining the binary representations back together with - delimiters

The time complexity is O(1) since the date string has a fixed format, and the space complexity is also O(1).

Intuition

When we look at this problem, we need to transform a date from decimal format to binary format while preserving its structure. The key observation is that the date already comes in a nicely separated format (yyyy-mm-dd), which makes our job easier.

The natural approach is to handle each component (year, month, day) independently since they're already separated by hyphens. We don't need to parse the entire date or deal with complex date logic - we simply need to:

1. Break apart the existing string at the delimiter points
2. Transform each piece individually
3. Reassemble them with the same delimiter

This leads us to think about string manipulation operations. Python's split("-") method perfectly handles breaking the date into its components. For each component, we need to convert from string → integer → binary string. Python's built-in int() function handles the first conversion, and the format specifier :b or the bin() function (without the '0b' prefix) handles the binary conversion.

The elegance of the solution comes from recognizing that we can combine these operations in a single line using a generator expression with join(). The pattern "-".join(f"{int(s):b}" for s in date.split("-")) mirrors the structure of our problem: split by delimiter, transform each part, then rejoin with the same delimiter.

This approach avoids any complex date parsing libraries or manual string building, leveraging Python's string methods to directly map the input structure to the output structure with just a transformation applied to each segment.

Learn more about Math patterns.

Solution Approach

The solution uses a straightforward simulation approach that processes the date string in three steps:

1. String Splitting: We use date.split("-") to break the input string into a list of three components. For example, "2024-12-05" becomes ["2024", "12", "05"].

2. Binary Conversion: For each component in the list, we apply the transformation f"{int(s):b}":

   • int(s) converts the string to an integer (e.g., "05" → 5)
   • The format specifier :b converts the integer to its binary representation without leading zeros (e.g., 5 → "101")
   • This is done using a generator expression that processes all three components

3. String Joining: Finally, we use "-".join() to combine the binary representations back into a single string with hyphens as separators.

The entire process is accomplished in a single line:

return "-".join(f"{int(s):b}" for s in date.split("-"))

This implementation leverages Python's string manipulation capabilities and format strings to achieve the conversion efficiently. The generator expression (f"{int(s):b}" for s in date.split("-")) creates an iterator that yields each converted binary string, which join() then concatenates with the - delimiter.

The algorithm processes each component exactly once, making it both time and space efficient for the fixed-size input format of dates.

Example Walkthrough

Let's walk through the solution with the date "2080-02-29":

Step 1: Split the string by delimiter

• Input: "2080-02-29"
• After date.split("-"): ["2080", "02", "29"]
• We now have three separate strings representing year, month, and day

Step 2: Convert each component to binary

• Process "2080":

  • int("2080") → 2080 (decimal)
  • f"{2080:b}" → "100000100000" (binary)

• Process "02":

  • int("02") → 2 (decimal, leading zero removed)
  • f"{2:b}" → "10" (binary)

• Process "29":

  • int("29") → 29 (decimal)
  • f"{29:b}" → "11101" (binary)

Step 3: Join with hyphens

• Binary components: ["100000100000", "10", "11101"]
• After "-".join(): "100000100000-10-11101"

Final Result: "100000100000-10-11101"

The entire transformation happens in one line:

return "-".join(f"{int(s):b}" for s in date.split("-"))

The generator expression processes each element in sequence:

1. s = "2080" → produces "100000100000"
2. s = "02" → produces "10"
3. s = "29" → produces "11101"

Then join() combines them with - separators to create the final output.

Solution Implementation

Time and Space Complexity

The time complexity is O(n), where n is the length of the input string date. This is because:

• date.split("-") traverses the entire string once, taking O(n) time
• The split operation creates 3 components (year, month, day)
• For each component, int(s) performs string-to-integer conversion in O(len(s)) time
• The binary conversion :b takes O(log(value)) time, which is bounded by the length of the component
• "-".join() combines the results, traversing the output once
• Since the number of components is constant (3) and each operation is proportional to the input size, the overall complexity is O(n)

The space complexity is O(n). This accounts for:

• The list created by split("-") which stores substrings totaling O(n) characters
• The generator expression creates binary strings whose total length is proportional to the input
• The final joined string output requires O(n) space
• Although the binary representation might be slightly different in length than the decimal, it remains proportional to n

Learn more about how to find time and space complexity quickly.

Common Pitfalls

1. Forgetting to Handle Leading Zeros in Input

The date string may contain leading zeros (e.g., "2024-01-05"), but these are automatically handled when converting to integers. However, beginners might try to preserve them or handle them specially, which is unnecessary and can complicate the solution.

Issue Example:

# Overcomplicated attempt to handle leading zeros
if component.startswith('0'):
    component = component.lstrip('0')
binary_value = bin(int(component))[2:]

Solution: Simply use int(component) which automatically handles leading zeros correctly.

2. Using Wrong Binary Conversion Methods

There are multiple ways to convert to binary in Python, and mixing them up can cause issues:

Common Mistakes:

# Mistake 1: Forgetting to remove '0b' prefix when using bin()
binary_value = bin(int(component))  # Returns '0b101' instead of '101'

# Mistake 2: Using incorrect format specifier
binary_value = f"{int(component):d}"  # Uses decimal format instead of binary

# Mistake 3: Trying to use binary literals
binary_value = 0b{int(component)}  # Syntax error

Solution: Use either bin(int(component))[2:] or format(int(component), 'b') or f"{int(component):b}" consistently.

3. Incorrect String Splitting or Joining

Using the wrong delimiter or forgetting to join properly:

Common Mistakes:

# Mistake 1: Using wrong delimiter
date_components = date.split("/")  # Wrong delimiter for "YYYY-MM-DD" format

# Mistake 2: Forgetting to join back with hyphens
return binary_components  # Returns a list instead of string

# Mistake 3: Using wrong join delimiter
return "/".join(binary_components)  # Uses slash instead of hyphen

Solution: Always use split("-") and "-".join() to maintain the correct format.

4. Type Confusion Between Strings and Integers

Attempting operations on wrong data types:

Common Mistake:

# Trying to apply binary conversion directly to string
binary_value = format(component, 'b')  # Error: component is still a string

Solution: Always convert to integer first: int(component) before applying binary conversion.