47 lines
3.5 KiB
Text
47 lines
3.5 KiB
Text
---
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id: data-types
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title: Data Types
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author: Darren Yao
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description: Learn about the basic data types needed for competitive programming.
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prerequisites:
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- running-code
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---
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<Resources>
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<Resource source="IUSACO" title="2.2 - Data Types">module is based off this</Resource>
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<Resource source="CPH" title="1.1 to 1.3 - Introduction"></Resource>
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<Resource source="PAPS" title="2.3 - Variables & Types"></Resource>
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</Resources>
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<br />
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(insert some table?)
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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.
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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 $\pm 9 \times 10^{18}$.
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<IncompleteSection>
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- missing 32-bit integer explanation
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</IncompleteSection>
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Sometimes (but not always) a USACO problem statement (ex. [Haircut](http://www.usaco.org/index.php?page=viewproblem2&cpid=1041)) will contain a warning such as the following:
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> 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++).
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Contest problems are usually set such that the 64-bit integer is sufficient, so 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 may need to cast `long` back to `int` when accessing array indices.
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**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. It's generally a bad idea to compare two floating-point numbers for exact equality (`==`); instead, check if their absolute difference is less than some small constant like $10^{-9}$. Contest problems will accommodate this by either asking for the greatest integer less than $10^k$ times the value, or will mark as correct any output that is within a certain $\epsilon$ of the judge's answer.
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(define absolute / relative error? USACO problems will generally have a unique answer.)
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<IncompleteSection />
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**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.
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**Character** variables represent a single Unicode 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`.
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**Strings** are stored as an array of characters. You can easily access the character at a certain index and take substrings of the string. String problems on USACO Bronze or Silver generally don't involve any special data structures, and can be solved using relatively elementary methods.
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