Difference between revisions of "Intermediate C++ Game Programming Tutorial 24"

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** Combining hashes from basic types to create a hash over your custom object  
 
** Combining hashes from basic types to create a hash over your custom object  
 
** Stack Overflow question "How do I combine hash values in C++" give the example as used in the boost library
 
** Stack Overflow question "How do I combine hash values in C++" give the example as used in the boost library
−
** You can implement a hashing functor as a <code>struct</code> that defines a <code>size_t operator()( const _Vec2<T>& vec ) const</code> member function, templated on <code>T</code>, the basic type of the <code>Vec2</code> coordinates with the body:
+
** You can implement a hashing functor as a <code>struct</code> that defines a member function, templated on <code>T</code>, the basic type of the <code>Vec2</code> coordinates:
−
*:- <code>std::hash<T> hasher;</code>
+
*: <code>size_t operator()( const _Vec2<T>& vec ) const</code>
−
*:- <code>auto hashx = hasher ( vec.x );</code>
+
*: <code>{</code>
−
*:- <code>auto hashy = hasher ( vec.y );</code>
+
*:: <code>std::hash<T> hasher;</code>
−
*:- <code>hashx ^= hashy + 0x9e3779b9 + (hashx << 6) + (hashx >> 2);</code>
+
*:: <code>auto hashx = hasher ( vec.x );</code>
−
*:- <code>return hashx;</code>
+
*:: <code>auto hashy = hasher ( vec.y );</code>
 +
*:: <code>hashx ^= hashy + 0x9e3779b9 + (hashx << 6) + (hashx >> 2);</code>
 +
*:: <code>return hashx;</code>
 +
*: <code>}</code>
 +
 
 
** You pass these functors when defining the map: <code>std::unordered_map<Vei2,stt::string,HashVec2> map;</code> [https://youtu.be/LsjFAx-dG5I?t=17m15s 17:15]
 
** You pass these functors when defining the map: <code>std::unordered_map<Vei2,stt::string,HashVec2> map;</code> [https://youtu.be/LsjFAx-dG5I?t=17m15s 17:15]
 
*:- Note that the comparison functor is not needed: we can revert back to the equality operator already defined in the <code>Vec2</code> class definition
 
*:- Note that the comparison functor is not needed: we can revert back to the equality operator already defined in the <code>Vec2</code> class definition

Revision as of 20:47, 2 February 2020

Associative containers are super useful, both as a convenient fast way to create dictionary or mapping for real-world problems like managing game resources, and as a data structure to help solve more abstract algorithmic computer science problems. And hash tables are fast as balls.

Topics Covered

Part 1: ordered associative containers

  • std::map container interface
  • Binary tree data structure
  • std::map key requirements (comparison)
  • std::map gotchas (std::remove_if and const keys)
  • std::set
  • std::multimap and std::multiset

Part 2: unordered associative containers

  • Hash table performance vs. binary tree performance
  • Hash table data structure
  • std::unordered_map key requirements
  • Hash combining
  • std::unordered_map bucket interface and hashing policy
  • When to choose std::map over std::unordered_map

Video Timestamp Index

Tutorial 24.1: The ordered associative containers


  • The std::map<KeyType,ValueType> class 0:46
    • Maps consist of keys to lookup (associated) values
    • map.insert( {key,value} ) to insert (key,value) pairs
    • map[key] returns a reference to the ValueType for a KeyType
  • A Binary Tree data structure is used to manage the order of map elements 2:46
    • std::map performs lookup in O(log(n)), it uses a Binary tree data structure
    • Key properties of a Binary Tree (BT):
    - Nodes can have at most 2 children (hence: binary)
    - Each left child is smaller and each right child is larger than its parent
    - Insertion is done by navigating the tree along a route Left for smaller, Right for larger such that the order property always holds
    • The big advantage of the BT properties is that retrieval is very fast
    • The beauty of std::map is that we don't have to implement any of this; it's all there in the STL 7:00
    • The STL implementation is further optimized, e.g. it uses a red-black tree for BT rebalancing
  • A look at the std::map cppreference.com documentation: insert, lookup & find 7:35
    • map.insert() takes a pair type std::pair<KeyType,ValueType>, the Map's elements
    • C++ can deduce the pair Type, so map.insert({keyX,valueXYZ}); with curly braces will do the job
    • An even better way to insert is through map.emplace() operation; it will construct the pair in-place.
    • For lookup, you can use square braces, map[x] will return a reference to the corresponding value
    • Note: a lookup with a new key value will create that element in the map with the default constructed ValueType value
    • insert or emplace with a key that already exists will NOT override the existing value: std::map::emplace returns a std::pair<iterator,bool> where the bool inidicates whether an insertion took place
    • map.find("xyz") returns an iterator to the element if it exitst, and an iterator to map.end() if it doesn't exist (useful to check if a key already exists)
    • std::map comes with iterators and because it is a sorted map, when you iterate over its elements with for (auto& el : map), it will be in order (of the keys)
  • Requirements on KeyType 14:30
    • The KeyType has to be comparable. The third template parameter is a functor for KeyType Comparison that defaults to std::less<KeyType>
    • So by default keys have to implement the "less than" comparison operator or provide your own comparison functor when defining the map
  • std::map cppreference.com documentation continued: erase 15:28
    • std::map::erase offers three basic ways to erase elements:
    - With an iterator; returns an iterator following the last removed element
    - With an iterator range, idem
    - By key through map.erase(const KeyType& key); this operation returns the number of elements erased (in size_type)
  • Two important things to know when working with associative containers 16:04
    • std::remove_if does not work with associative containers (will come with C++20).
    - You have to iterate over the elements with for( auto i = map.begin(); i != map.end();)
    - And apply i = map.erase(i); in the body of your if logic, and ++i in the else block.
    • Keys are const. You're not allowed to modify the keys 18:38
    - Makes sense: the keys define the structure of the binary tree.
    - If you modify the key you invalidate this structure (it would require a deletion and insertion to do it properly)
  • The std::set<KeyType> class 20:00
    • With a set, you only have keys, and a unique entry for each unique key
    • Use case: ensure that there are no duplicates in a set
  • The std::multimap and std::multiset classes 21:28
    • Map has unique keys, with multimap you can insert multiple elements with the same key
    • This enables operations like std::multimap::equal_range that returns a pair of iterators (begin and end) of the range where these elements have that same key
    • std::multimap::count will return the number of elements with specific key
  • Practical example of a multimap use case 22:30
    • Implementation example of a custom Comparison functor for the Vei2 class (2D coordinate vector).
    - Chili's choice for ordering (used in the body of the functor):
    - return (lhs.x == rhs.x) ? lhs.y < rhs.y : lhs.x < rhs.x;
    • Example of how to find and print multiple elements in a multimap using equal_range()
  • Lookup in multimaps 25:21
    • Note: the multimap class does not have an index operator []
    • When you do a lookup on a multimap, you should use equal_range()
    • The problem with find() on a multimap, is that if there are several elements with key in the ccontainer, any of them may be returned

Tutorial 24.2: The unordered associative containers

  • Main difference between ordered/unordered is performance 0:14
    • Implication: if you iterative over an unordered container, keys will appear in (seemingly) random order
    • Releasing the ordering requirement makes it possible to use a hash table with performance advantages: O(1) contant time insertion and lookup
  • Using an unordered map 1:38
    • The interface is pretty much the same as its ordered counterpart
    • Include <unordered_map>, declare using std::unordered_map<KeyType,ValueType>
    • You can initialize your map object with an initializer list if you wanted to using ({ {..,..},{..,..},... }) inside your declaration
  • The Hash Table data structure 3:20
    • A hash table allows you to get the quick access to values, comparable to array access using the index, but with efficient memory usage
    • Buckets are used to group keys; this is done by mapping keys to buckets using a hash function (a.k.a. hashing)
    • Multiple keys can map to the same bucket in a hash table ("collision"). We use a linked list to store multiple {key,value} pairs in a bucket
    • Two ways to minimize hash collisions: i) more buckets, ii) smart hash function that distributes key values uniformly across your bucket space
    • Hashing a a two step process 9:26:
    - A hash function takes in the KeyType input (typically a string or int) and outputs a size_t
    - the size_t output is reduced/ditributed to the size of the hash table (number of buckets)
    • The Standard Library provides general hashing functions for all the standard types
    • For general use of unordered maps, we don't have to worry about the technical details of how the hash table works, the STL provides this
  • Requirements for the KeyType of an unordered_map / a hash table 11:56
    • There needs to be a working hash function defined for the KeyType
    • There need to be comparison and equality functor definitions for the KeyType
  • Example: map from Vec2 class (2D coordinates) to a string 12:46
    • In order to make this work, you need to define a hash function and the comparators for Vei2
    • You can implement a comparison/equality functor as a struct that defines a bool operator()( const T& lhs,const T& rhs ) const member function, templated on T
    • Defining a custom hashing function is an art, it requires knowledge of cryptography, abstract algebra, discrete math, etc.
    • Luckily, we don't need this; you can revert to the standard hashing functions for the basic types that make up any custom type
  • Hash combining 14:25
    • Combining hashes from basic types to create a hash over your custom object
    • Stack Overflow question "How do I combine hash values in C++" give the example as used in the boost library
    • You can implement a hashing functor as a struct that defines a member function, templated on T, the basic type of the Vec2 coordinates:
    size_t operator()( const _Vec2<T>& vec ) const
    {
    std::hash<T> hasher;
    auto hashx = hasher ( vec.x );
    auto hashy = hasher ( vec.y );
    hashx ^= hashy + 0x9e3779b9 + (hashx << 6) + (hashx >> 2);
    return hashx;
    }
    • You pass these functors when defining the map: std::unordered_map<Vei2,stt::string,HashVec2> map; 17:15
    - Note that the comparison functor is not needed: we can revert back to the equality operator already defined in the Vec2 class definition
    • Unordered map uses std::hash by default. You can inject Template Specialization for std::hash into the std Namespace 18:43 for your own custom types only
    namespace std
    {
    template <> struct hash<Vei2>
    {
    size_t operator()( cont Vei2& vec ) const
    {...}
    };
    }


  • [WORK-IN-PROGRESS]

Homework Assignment

The homework for this video is to enable use of a custom datatype in unordered_map hashing over multiple (4) members of that datatype. The solution video is here.

Supplementary Link

See also

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