Data Types

There are several main data types that are used in contests: integers, floating point numbers, booleans, characters, and strings. Assuming that you are familiar with the language you are using, this should be mostly review.

The normal 32-bit integer data type (int in C++ and Java) supports values between $-2\,147\,483\,648$ and $2\,147\,483\,647$, which is roughly equal to $\pm 2 \cdot 10^9$.

Some problems require you to use 64-bit integers (long long in C++ and long in Java) instead of 32-bit integers (int). 64-bit integers are less likely to have overflow issues, since they can store any number between $-9\,223\,372\,036\,854\,775\,808$ and $9\,223\,372\,036\,854\,775\,807$ which is roughly equal to $\pm 9 \times 10^{18}$. In Python, ints have unlimited size.

Sometimes (but not always) a USACO problem statement (ex. Haircut) will contain a warning such as the following:

Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

Contest problems are usually set such that the 64-bit integer is sufficient, so for lower divisions it might be a good idea to use 64-bit integers in place of 32-bit integers everywhere. Of course, you shouldn't do this when time and/or memory limits are tight, which may be the case in higher divisions of USACO. Also note that in Java, you will need to cast long back to int when accessing array indices.

Additionally, there exist 16-bit integers (short in C++ and Java). However, these are generally not useful as the extra memory saved by using them is usually negligible. Unsigned integers (unsigned int, unsigned long long, etc.) also exist. They aren't used as frequently, though the 2-fold increase in size is sometimes the difference between overflowing and not overflowing.

Floating point numbers are used to store decimal values. It is important to know that floating point numbers are not exact, because the binary architecture of computers can only store decimals to a certain precision. Hence, we should always expect that floating point numbers are slightly off, so it's generally a bad idea to compare two floating-point numbers for exact equality (==).

Contest problems will usually accommodate the inaccuracy of floating point numbers by checking if the absolute or relative difference between your output and the answer is less than some small constant like $\epsilon=10^{-9}$.

• If your output is $x$ and the answer is $y$, the absolute difference is $|x-y|$.
• If your output is $x$ and the answer is $y$, the relative difference is $\frac{|x-y|}{|y|}$.

This is not the case for USACO, where problems generally have a unique correct output. So when floating point is necessary, the output format will be something along the lines of "Print $10^6$ times the maximum probability of receiving exactly one accepted invitation, rounded down to the nearest integer." (ex. Cow Dating).

Boolean variables have two possible states: true and false. We'll usually use booleans to mark whether a certain process is done, and arrays of booleans to mark which components of an algorithm have finished. Booleans require 1 byte (8 bits) of storage, not 1 bit, wasting the other 7 bits of storage. To use less memory, one can use bitsets (std::bitset in C++ / BitSet in Java). Unfortunately, bitsets are not available in Python.

Character variables represent a single character. They are returned when you access the character at a certain index within a string. Characters are represented using the ASCII standard, which assigns each character to a corresponding integer. This allows us to do arithmetic with them; for example, both cout << ('f' - 'a'); in C++ and System.out.print('f' - 'a'); in Java will print 5. In Java, characters are 16 bits, while in C/C++, characters are 8 bits.

Strings are effectively arrays of characters. You can easily access the character at a certain index and take substrings of the string (charAt() and substring() in Java).