jonasspinner / 22st-advanced-data-structures

Fortgeschrittene Datenstrukturen

• Vorlesungswebseite
• Aufgabenbeschreibung
• Wikipedia AVL tree

Bitvektoren in Blattknoten

SmallDynamicBitVector<> und SmallStaticBitVector<>

Building and Running

mkdir build && cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
make ads_program_a

build/ads_program_a bv [input] [output]

build/ads_program_a bp [input] [output]

Aufgabe 1: Dynamischer Bitvektor ads::DynamicBitVector<>

## Inner and Leaf Node ##

## Query operations on nodes ##

    bool access(node, i)
    bool access(inner, i)
    void flip(node, i)
    void flip(inner, i)
    void rank1(node, i, rank&)
    void rank1(inner, i, rank&)
    void select1(node, i, result&)
    void select1(inner, i, result&)
    void select0(node, i, result&)
    void select0(inner, i, result&)

## Tree modifying operations ##
Operations that insert or remove bits from the tree.

    Inner* split(leaf, high_bit)
    {node, changed} insert(node, i, b)
    {node, deleted_bit} remove(node, i)
    {node, deleted_bit} remove_second_level(inner, i)
        -- Special case for nodes with height two.
           Allows finding neighboring leaves for merging.
    {node, deleted_bit} remove_first_level(inner, i)
        -- Special case for nodes with height one.
           Allows finding neighboring leaves for merging.
    Leaf* merge(inner)

### Node info dispatch ###

    int height(node)

## AVL Tree balance operations ##

    int balance_factor(node)
    int balance_factor(inner)
    Inner* balance(inner)
        -- Checks whether balancing is needed and applies one of the four rotations
    Inner* rotate_left_left(inner)
    Inner* rotate_left_right(inner)
    Inner* rotate_right_left(inner)
    Inner* rotate_right_right(inner)

## Node deletion ##
Used in destructor.

    void delete_node(NodeHandle)
    void delete_node(Inner*)
    void delete_node(Leaf*)

## Debug checks ##

## Required bits upperbound ##

## Constructor/Destructor ##

## BV operations ##

### BV modifying operations ##

    void insert(i, b)
    void remove(i)
    void flip(i)

### BV query operations ##

    bool access(i)
    size_type rank(i, b)
    size_type select(i, b)
    size_type size()


## Misc ##

    void clear()    
    std::ostream << overload
    size_type required_bits_upperbound()

Aufgabe 2: Balanced Parantheses ads::BP<>

## Inner and Leaf Node ##

## Query operations on nodes ##

    bool access(node, i)
    bool access(inner, i)
    void rank1(node, i, rank&)
    void rank1(inner, i, rank&)
    void select1(node, i, result&)
    void select1(inner, i, result&)
    void select0(node, i, result&)
    void select0(inner, i, result&)

## Tree modifying operations ##
Operations that insert or remove bits from the tree.

    Inner* split(leaf, high_bit)
    {node, changed} insert(node, i, b)
    {node, deleted_bit} remove(node, i)
    {node, deleted_bit} remove_second_level(inner, i)
        -- Special case for nodes with height two.
           Allows finding neighboring leaves for merging.
    {node, deleted_bit} remove_first_level(inner, i)
        -- Special case for nodes with height one.
           Allows finding neighboring leaves for merging.
    Leaf* merge(inner)

### Node info dispatch ###

    int height(node)
    size_type total_excess(node)
    size_type min_excess(node)
    void update_excess_info_from_children_info(inner)

## AVL Tree balance operations ##

    int balance_factor(node)
    int balance_factor(inner)
    Inner* balance(inner)
        -- Checks whether balancing is needed and applies one of the four rotations
    Inner* rotate_left_left(inner)
    Inner* rotate_left_right(inner)
    Inner* rotate_right_left(inner)
    Inner* rotate_right_right(inner)

## Node deletion ##
Used in destructor.

    void delete_node(NodeHandle)
    void delete_node(Inner*)
    void delete_node(Leaf*)

## Debug checks ##

## Required bits upperbound ##

## BV operations ##

### BV modifying operations ##
These operations are allowed to disregard BP invariants,
i.e. an even and balanced number of bits.

    void insert(i, b)
    void remove(i)

### BV query operations ##

    bool access(i)
    size_type rank(i, b)
    size_type select(i, b)
    size_type size()

### BP query operations ###

    size_type find_close(i)
    size_type find_open(i)
    size_type excess(i)
    size_type enclose(i)

### BV map operation ###

    void preorder_map(f)
    void preorder_map(node, f)

## Constructor/Destructor ##

### Supported tree operations ###
        
    void insertchild(v, i, k)
    void deletenode(v)
    size_type ith_child(v, i)
    size_type parent(v)
    size_type subtree_size(v)

## Misc ##

    std::ostream << overload
    size_type required_bits_upperbound()
    size_type num_nodes()
    std::vector<size_type> preorder_out_degree_sequence()
        -- Uses preorder_map to iterate over all bits and calculate the out degree sequence
           in O(n) time.

Unterschiede von BV and BP:

diff src/DynamicBitVector.h src/BP.h