Temperature Tracker (Practice Interview Question)

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You decide to test if your oddly-mathematical heating company is fulfilling its All-Time Max, Min, Mean and Mode Temperature Guarantee™.

Write a class TempTracker with these methods:

insert()—records a new temperature
getMax()—returns the highest temp we've seen so far
getMin()—returns the lowest temp we've seen so far
getMean()—returns the mean ↴

The mean of a set of values is the average value of all the items in the set.
$\text{mean}=\frac{\text{sum of all values}}{\text{number of values}}$

of all temps we've seen so far
getMode()—returns a
mode ↴
The mode of a set of values is the number which appears the most times.

For example, in this set:

1, 3, 6, 3, 1, 3

The number 3 appears the most times, so it's the mode.

Careful: a set may have multiple modes.
of all temps we've seen so far

Optimize for space and time. Favor speeding up the getter methods getMax(), getMin(), getMean(), and getMode() over speeding up the insert() method.

getMean() should return a double, but the rest of the getter methods can return integers. Temperatures will all be inserted as integers. We'll record our temperatures in Fahrenheit, so we can assume they'll all be in the range $0..110$ .

If there is more than one mode, return any of the modes.

Gotchas

We can get $O(1)$ time for all methods.

We can get away with only using $O(1)$ additional space. If you're storing each temperature as it comes in, be careful! You might be taking up $O(n)$ space, where $n$ is the number of temperatures we insert!

Are you trying to be fancy about returning multiple modes if there's a tie? Good idea, but read the problem statement carefully! Check out that last sentence!

Failing to carefully read or listen to the problem statement is a very common mistake, and it always looks bad. Don't let it happen to you.

Breakdown

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Where do I enter my password?

Actually, we don't support password-based login. Never have. Just the OAuth methods above. Why?

It's easy and quick. No "reset password" flow. No password to forget.
It lets us avoid storing passwords that hackers could access and use to try to log into our users' email or bank accounts.
It makes it harder for one person to share a paid Interview Cake account with multiple people.

Solution

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Where do I enter my password?

Actually, we don't support password-based login. Never have. Just the OAuth methods above. Why?

It's easy and quick. No "reset password" flow. No password to forget.
It lets us avoid storing passwords that hackers could access and use to try to log into our users' email or bank accounts.
It makes it harder for one person to share a paid Interview Cake account with multiple people.

Complexity

$O(1)$ time for each method, and $O(1)$ space related to input! (Our occurrences vector's size is bounded by our range of possible temps, in this case 0-110)

What We Learned

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Where do I enter my password?

Actually, we don't support password-based login. Never have. Just the OAuth methods above. Why?

It's easy and quick. No "reset password" flow. No password to forget.
It lets us avoid storing passwords that hackers could access and use to try to log into our users' email or bank accounts.
It makes it harder for one person to share a paid Interview Cake account with multiple people.

Bonus

There's at least one way to use a just-in-time approach, have $O(1)$ time for each operation, and keep our space cost at $O(1)$ for $n$ inserts. How could we do that?

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Gotchas

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Complexity

What We Learned

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Bonus

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