Problem Description

You are given a temperature value in Celsius as a floating-point number rounded to two decimal places. Your task is to convert this temperature to both Kelvin and Fahrenheit scales.

The conversion formulas are:

• Kelvin = Celsius + 273.15
• Fahrenheit = Celsius * 1.80 + 32.00

You need to return both converted values as an array in the format [kelvin, fahrenheit].

The problem accepts answers within 10^-5 of the actual answer, allowing for small floating-point precision differences.

For example, if given celsius = 36.50, you would:

1. Calculate Kelvin: 36.50 + 273.15 = 309.65
2. Calculate Fahrenheit: 36.50 * 1.80 + 32.00 = 97.70
3. Return the array: [309.65, 97.70]

The solution is straightforward - apply both conversion formulas to the input Celsius value and return the results in the specified array format.

Intuition

This is a direct mathematical conversion problem with no hidden complexity. Since we're given explicit formulas for converting Celsius to both Kelvin and Fahrenheit, the most straightforward approach is to simply apply these formulas.

The key insight is that both conversions are independent linear transformations:

• Converting to Kelvin is just adding a constant (273.15)
• Converting to Fahrenheit involves scaling by 1.8 and then adding 32

There's no need for optimization or clever algorithms here because:

1. We're performing exactly two arithmetic operations for Kelvin conversion
2. We're performing exactly three arithmetic operations for Fahrenheit conversion
3. Both conversions can be computed in constant time O(1)

The natural approach is to compute both values directly and return them in the required array format. Since the problem guarantees the input is already a valid floating-point number and accepts answers within 10^-5 precision, we don't need to worry about edge cases or precision handling - standard floating-point arithmetic will suffice.

This leads us to the simple solution: create an array containing [celsius + 273.15, celsius * 1.8 + 32] and return it.

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Solution Approach

The implementation follows a simulation approach where we directly apply the temperature conversion formulas.

Step-by-step implementation:

1. Input: We receive a single parameter celsius of type float

2. Apply the conversion formulas:

   • Calculate Kelvin: celsius + 273.15
   • Calculate Fahrenheit: celsius * 1.8 + 32

3. Return the results: Package both calculated values into a list [kelvin, fahrenheit]

The solution can be implemented in a single line:

return [celsius + 273.15, celsius * 1.8 + 32]

Why this approach works:

• Both temperature conversions are deterministic mathematical operations
• No intermediate variables are needed since each conversion is a simple expression
• The list constructor directly creates our output format

Time Complexity: O(1) - We perform a fixed number of arithmetic operations regardless of input value

Space Complexity: O(1) - We only create one output list with exactly two elements

The beauty of this solution lies in its simplicity. Since the problem provides exact formulas and requires no validation or edge case handling, we can translate the mathematical formulas directly into code without any additional logic or data structures.

Example Walkthrough

Let's walk through the solution with a concrete example: celsius = 22.00

Step 1: Apply Kelvin conversion

• Formula: Kelvin = Celsius + 273.15
• Calculation: 22.00 + 273.15 = 295.15

Step 2: Apply Fahrenheit conversion

• Formula: Fahrenheit = Celsius * 1.80 + 32.00
• Calculation: 22.00 * 1.80 + 32.00
  • First multiply: 22.00 * 1.80 = 39.60
  • Then add: 39.60 + 32.00 = 71.60

Step 3: Package results into array

• Create array: [295.15, 71.60]
• Return this array as the final answer

Let's trace through the code execution:

def convertTemperature(celsius):
    return [celsius + 273.15, celsius * 1.80 + 32.00]

# When celsius = 22.00:
# 1. Evaluate celsius + 273.15 → 22.00 + 273.15 → 295.15
# 2. Evaluate celsius * 1.80 + 32.00 → 22.00 * 1.80 + 32.00 → 71.60
# 3. Create list [295.15, 71.60]
# 4. Return [295.15, 71.60]

The solution directly applies both conversion formulas in a single return statement, computing both temperature values simultaneously and packaging them into the required output format.

Solution Implementation

Time and Space Complexity

The time complexity is O(1) because the function performs a fixed number of arithmetic operations (one addition for Kelvin conversion and one multiplication plus one addition for Fahrenheit conversion) regardless of the input value. These operations take constant time.

The space complexity is O(1) because the function creates and returns a list containing exactly 2 float values, which occupies a constant amount of memory space that doesn't scale with the input.

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

Common Pitfalls

1. Floating-Point Precision Issues

While this problem appears straightforward, developers often encounter unexpected floating-point precision errors when working with decimal numbers.

The Pitfall:

# Problematic approach - using intermediate calculations
celsius = 36.50
kelvin = celsius + 273.15  # Results in 309.65000000000003 on some systems
fahrenheit = celsius * 9/5 + 32  # May produce slight variations

Due to how floating-point numbers are represented in binary, operations like 36.50 + 273.15 might not yield exactly 309.65 but rather something like 309.65000000000003.

Solution: The problem statement mentions accepting answers within 10^-5 of the actual answer, which handles this gracefully. However, if exact precision were required, you could:

• Round the results to a specific number of decimal places
• Use Python's decimal module for arbitrary precision arithmetic

2. Using Integer Division or Wrong Formula Coefficients

The Pitfall:

# Wrong - using integer division in Python 2 style
fahrenheit = celsius * 9//5 + 32  # This truncates the result!

# Wrong - using 1.8 vs 9/5 inconsistently
fahrenheit = celsius * (9/5) + 32.00  # Correct but mixing notation

Solution: Stick to the exact formulas provided in the problem:

• Use 1.8 or 1.80 for Fahrenheit conversion (not 9/5 which equals 1.8)
• Always use floating-point division to maintain precision

3. Incorrect Order of Operations

The Pitfall:

# Wrong - parentheses in wrong place
fahrenheit = celsius * (1.8 + 32)  # This adds before multiplying!

Solution: Follow the mathematical order of operations (PEMDAS):

fahrenheit = celsius * 1.8 + 32  # Multiplication first, then addition

4. Returning Values in Wrong Order

The Pitfall:

# Wrong order - returning [Fahrenheit, Kelvin] instead
return [celsius * 1.8 + 32, celsius + 273.15]

The problem specifically asks for [kelvin, fahrenheit] in that order.

Solution: Always verify the required output format:

return [celsius + 273.15, celsius * 1.8 + 32]  # Kelvin first, then Fahrenheit