Problem Description

In this problem, you are given a non-negative floating point number celsius, which represents a temperature in Celsius. This value is rounded to two decimal places for precision. Your task is to convert this Celsius temperature to two other temperature scales: Kelvin and Fahrenheit.

To return your answers, you will need to create an array ans = [kelvin, fahrenheit], where kelvin is the temperature in Kelvin and fahrenheit is the temperature in Fahrenheit.

It is important to remember two key conversion formulas:

1. To convert Celsius to Kelvin, you add 273.15 to the Celsius temperature.
2. To convert Celsius to Fahrenheit, you multiply the Celsius temperature by 1.80 and then add 32.00 to the result.

The problem specifies that your answers will be accepted as long as they are within 10^-5 of the correct answer, allowing for a very small amount of numerical error which is common when dealing with floating-point arithmetic.

Intuition

The intuition behind the solution is straightforward since the problem simply involves applying the given conversion formulas. There are no complex algorithms or data structures involved, just basic arithmetic.

To solve the problem, follow these steps:

1. Add 273.15 to the celsius value to get the Kelvin temperature.
2. Multiply the celsius value by 1.8 and then add 32 to get the Fahrenheit temperature.

These steps are based directly on the conversion formulas given in the problem description. Once you have both converted values, you create an array containing the Kelvin and Fahrenheit temperatures in that order and return it. This is made simple in Python with list notation.

Because the problem involves real numbers and potentially floating-point precision issues, it's important to ensure that calculations are performed with enough precision to meet the requirement of being within 10^-5 of the actual value. However, Python's built-in floating-point arithmetic should be precise enough for this task without needing any specialized numerical techniques.

Learn more about Math patterns.

Solution Approach

The solution approach is remarkably direct and does not involve any complex algorithms or use of advanced data structures. It adheres to the simplicity of the problem statement, which requires basic arithmetic operations based on the formulas given for temperature conversion. Here's how the provided solution in Python implements the approach step by step:

1. Define a class Solution and a method convertTemperature within it. The method accepts one parameter celsius, which is a floating-point number representing the temperature in Celsius.

2. Inside the method, perform the arithmetic conversions as per the formulas given in the problem description:

   • Convert Celsius to Kelvin by adding 273.15 to the celsius value. This relies on the formula Kelvin = Celsius + 273.15.

   • Convert Celsius to Fahrenheit by multiplying the celsius value by 1.8 and then adding 32. This follows the formula Fahrenheit = Celsius * 1.80 + 32.00.

3. Return the results of the conversions in an array [kelvin, fahrenheit]. In Python, this is accomplished by returning the values in a list.

The solution does not use any complex data structures. It only requires a simple list to store the two resulting temperature values. No patterns or algorithms are needed; the problem is solved by directly applying the given mathematical conversion formulas.

Here's what the implementation looks like in code:

class Solution:
    def convertTemperature(self, celsius: float) -> List[float]:
        kelvin = celsius + 273.15  # Convert Celsius to Kelvin
        fahrenheit = celsius * 1.8 + 32  # Convert Celsius to Fahrenheit
        return [kelvin, fahrenheit]  # Return the results in an array

Note that in the code snippet, the conversion operations have been spelled out in separate statements for clarity, although the original solution provided performs the calculations inline within the return statement. Both approaches are functionally equivalent and produce the same result.

Example Walkthrough

Let's illustrate the provided solution approach with a small example. Suppose we have a temperature in Celsius that is 25.00 degrees. We want to convert this to Kelvin and Fahrenheit using the formulas from the problem description.

1. The formula to convert Celsius to Kelvin is: Kelvin = Celsius + 273.15. So we start with our Celsius value 25.00 and add 273.15 to it.

   Kelvin = 25.00 + 273.15
   Kelvin = 298.15

2. The formula to convert Celsius to Fahrenheit is: Fahrenheit = Celsius * 1.80 + 32.00. We take the same original Celsius value and apply the formula.

   Fahrenheit = 25.00 * 1.80 + 32
   Fahrenheit = 45.00 + 32
   Fahrenheit = 77.00

So with our input celsius being 25.00 degrees, after the conversion, we have 298.15 Kelvin and 77.00 Fahrenheit. We then create an array with these two values in the order described: [kelvin, fahrenheit].

Following the solution approach, our result array would look like this:

ans = [298.15, 77.00]

This array is what we would expect the convertTemperature method of the Solution class to return when it is passed 25.00 as the celsius parameter.

The complete code would look like this:

class Solution:
    def convertTemperature(self, celsius: float) -> List[float]:
        kelvin = celsius + 273.15  # Convert Celsius to Kelvin
        fahrenheit = celsius * 1.8 + 32  # Convert Celsius to Fahrenheit
        return [kelvin, fahrenheit]  # Return the results in an array

And calling the method would look like this:

sol = Solution()
print(sol.convertTemperature(25.00))  # Output will be [298.15, 77.00]

The output of the code accurately reflects the calculated Kelvin and Fahrenheit temperatures based on the Celsius input, and this walkthrough demonstrates how the solution approach is followed to arrive at the result.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the convertTemperature function is O(1), which is constant time complexity. This is because the function does only a fixed number of mathematical operations (two operations in this case) that do not depend on the size of the input.

Space Complexity

The space complexity of the convertTemperature function is also O(1). The function creates a list with two elements every time it is called, and the size of this list does not depend on the input size but is fixed.

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