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|
| Line 145: |
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| | <div class="mw-collapsible-content"> | | <div class="mw-collapsible-content"> |
| | :* 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 | + | :* A simple google search will give you good examples of how to combine hash values in C++ |
| | :* 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: | | :* 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: |
| | ::<syntaxhighlight lang="cpp" line> | | ::<syntaxhighlight lang="cpp" line> |
| − | size_t operator()( const _Vec2<T>& vec ) const
| + | struct HashVec2 |
| | { | | { |
| − | std::hash<T> hasher; | + | template <typename T> |
| − | auto hashx = hasher ( vec.x );
| + | size_t operator()( const _Vec2<T>& vec ) const |
| − | auto hashy = hasher ( vec.y );
| + | { |
| − | hashx ^= hashy + 0x9e3779b9 + (hashx << 6) + (hashx >> 2);
| + | std::hash<T> hasher; |
| − | return hashx;
| + | auto hashx = hasher ( vec.x ); |
| − | } | + | auto hashy = hasher ( vec.y ); |
| | + | hashx ^= hashy + 0x9e3779b9 + (hashx << 6) + (hashx >> 2); |
| | + | return hashx; |
| | + | } |
| | + | }; |
| | </syntaxhighlight> | | </syntaxhighlight> |
| | :* You pass these functors when defining the map: <code>std::unordered_map<Vei2,std::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,std::string,HashVec2> map;</code> [https://youtu.be/LsjFAx-dG5I?t=17m15s 17:15]. |
Revision as of 23:46, 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
[Expand]
- 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
[Expand]
- Main difference between ordered/unordered: 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 operator() member function, templated on T
struct EqVec2
{
template <typename T>
bool operator()( const T& lhs,const T& rhs ) const
{
return (lhs.x == rhs.x) && (lhs.y == rhs.y);
}
};
- 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
- Combining hashes from basic types to create a hash over your custom object
- A simple google search will give you good examples of how to combine hash values in C++
- You can implement a hashing functor as a
struct that defines a member function, templated on T, the basic type of the Vec2 coordinates:
struct HashVec2
{
template <typename T>
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,std::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
- Template Specialization 18:43
- Unordered map uses
std::hash by default. You can inject Template Specialization for std::hash into the std Namespace for your own custom types only
namespace std
{
template <> struct hash<Vei2>
{
size_t operator()( cont Vei2& vec ) const
{...}
};
}
- Now you don't need to pass
HashVec2 in the map definition
- The
std::unordered_map<> Bucket interface 20:00
- Allows you to get information about the buckets in the hash table and access nodes
- The bucket iterator takes an index of the bucket and allows you to iterate over all the elements in that specific bucket
- The
std::unordered_map<> Hash policy interface 21:47
- Allows you to tune your hash table (and thus the growth behavior & performance of the map)
- Load Factor = average number of elements per bucket. For performance, you typically want to keep this below 1
- You can set the maximum load factor above which the table gets rehashed
- When the load factor becomes too high, it will automaticall rehash the table and increase the number of buckets
- You can manually rehash to a number of buckets you define
- You can reserve space for max number of elements, is then derives (and manages) the required number of buckets
- When to choose
std::map over std::unordered_map? 25:15
- For simplicity and when performance is not a critical issue, no need to define a hash function;
- If you want to iterate in order;
- When you want to be able to find keys that are close to a certain key (with
lower_bound and upper_bount
- Homework assignment 26:04
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
