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diff --git a/doc/flat_segment_tree.rst b/doc/flat_segment_tree.rst new file mode 100644 index 0000000..d5e7b8a --- /dev/null +++ b/doc/flat_segment_tree.rst @@ -0,0 +1,268 @@ +.. highlight:: cpp + +Flat Segment Tree +================= + +Overview +-------- + +Flat segment tree is a derivative of `segment tree +<https://en.wikipedia.org/wiki/Segment_tree>`_, and is designed to store +non-overlapping 1-dimensional range values such that *the values of the +neighboring ranges are guaranteed to be different.* An insertion of a range +value into this structure will always overwrite one or more existing ranges +that overlap with the new range. If an insertion of a new range would cause +any adjacent ranges to have the equal value, those ranges will be merged into +one range. + +An instance of this structure is initialized with fixed lower and upper +bounaries, which will not change throughout the life time of the instance. + +The flat segment tree structure consists of two parts: the leaf-node part +which also forms a doubly-linked list, and the non-leaf-node part which forms +a balanced-binary tree and is used only when performing tree-based queries. +The range values are stored in the leaf-nodes, while the non-leaf nodes are +used only for queries. + + +Quick start +----------- + +This section demonstrates a simple use case of storing non-overlapping ranged +values and performing queries using :cpp:class:`~mdds::flat_segment_tree`. + +First, we need to instantiate a concrete type from the template: + +.. literalinclude:: ../example/flat_segment_tree.cpp + :language: C++ + :start-after: //!code-start: type + :end-before: //!code-end: type + :dedent: 4 + +then create an instance of this type: + +.. literalinclude:: ../example/flat_segment_tree.cpp + :language: C++ + :start-after: //!code-start: instance + :end-before: //!code-end: instance + :dedent: 4 + +Here, the first and second arguments specify the lower and upper boundaries of +the whole segment. The third argument specifies the value for the empty +segments. What this line does is to create a new instance and initializes it +with one initial segment ranging from 0 to 500 with a value of 0: + +.. figure:: _static/images/fst-example1-initial.svg + :align: center + + The new instance is initialized with an initial segment. + +Internally, this initial range is represented by two leaf nodes, with the +first one storing the start key and the value for the segment both of which +happen to be 0 in this example, and the second one storing the end key of 500. +Note that the end key of a segment is not inclusive. + +The following lines insert two new segments into this structure: + +.. literalinclude:: ../example/flat_segment_tree.cpp + :language: C++ + :start-after: //!code-start: insert-1 + :end-before: //!code-end: insert-1 + :dedent: 4 + +The first line inserts a segment ranging from 10 to 20 with a value of 10, and +the second line from 50 to 70 with a value of 15: + +.. figure:: _static/images/fst-example1-insert1.svg + :align: center + + Two new segments have been inserted. + +You can insert a new segment either via :cpp:func:`~mdds::flat_segment_tree::insert_front` +or :cpp:func:`~mdds::flat_segment_tree::insert_back`. The end result will be +the same regardless of which method you use; the difference is that +:cpp:func:`~mdds::flat_segment_tree::insert_front` begins its search for +the insertion point from the first node associated with the minimum key value, +whereas :cpp:func:`~mdds::flat_segment_tree::insert_back` starts its search +from the last node associated with the maximum key value. + +After the insertions, the tree now contains a total of six leaf nodes to +represent all stored segments. Note that one leaf node typically represents +both the end of a segment and the start of the adjacent segment that comes +after it, unless it's either the first or the last node. + +The next line inserts another segment ranging from 60 to 65 having a value of +5: + +.. literalinclude:: ../example/flat_segment_tree.cpp + :language: C++ + :start-after: //!code-start: insert-2 + :end-before: //!code-end: insert-2 + :dedent: 4 + +As this new segment overlaps with the existing segment of 50 to 70, it will +cut into a middle part of that segment to make room for the new segment. At +this point, the tree contains a total of eight leaf nodes representing seven +segments: + +.. figure:: _static/images/fst-example1-insert2.svg + :align: center + + A new segment has been inserted that overlaps an existing non-empty segment. + +Next, we are going to query the value associated with a key of 15 via +:cpp:func:`~mdds::flat_segment_tree::search`: + +.. literalinclude:: ../example/flat_segment_tree.cpp + :language: C++ + :start-after: //!code-start: linear-search + :end-before: //!code-end: linear-search + :dedent: 4 + +Executing this code will yield the following output: + +.. code-block:: none + + The value at 15 is 10, and this segment spans from 10 to 20 + +One thing to note is that the :cpp:func:`~mdds::flat_segment_tree::search` +method performs a linear search which involves traversing only through the +leaf nodes in this data structure in order to find the target segment. As +such, the worst-case lookup performance is directly proportional to the number +of leaf nodes. + +There is another way to perform the query with better worse-case performance, +that is through :cpp:func:`~mdds::flat_segment_tree::search_tree` as seen in +the following code: + +.. literalinclude:: ../example/flat_segment_tree.cpp + :language: C++ + :start-after: //!code-start: tree-search + :end-before: //!code-end: tree-search + :dedent: 4 + +The signature of the :cpp:func:`~mdds::flat_segment_tree::search_tree` method +is identical to that of the :cpp:func:`~mdds::flat_segment_tree::search` method +except for the name. This code generates the following output: + +.. code-block:: none + + The value at 62 is 5, and this segment spans from 60 to 65 + +Query via :cpp:func:`~mdds::flat_segment_tree::search_tree` generally performs +better since it traverses through the search tree to find the target segment. +But it does require the search tree to be built ahead of time by calling +:cpp:func:`~mdds::flat_segment_tree::build_tree`. Please be aware that if the +segments have been modified after the tree was last built, you will have to rebuild +the tree by calling :cpp:func:`~mdds::flat_segment_tree::build_tree`. + +.. warning:: + + You need to build the tree by calling :cpp:func:`~mdds::flat_segment_tree::build_tree` + before performing a tree-based search via :cpp:func:`~mdds::flat_segment_tree::search_tree`. + If the segments have been modified after the tree was last built, you will have to + rebuild the tree by calling :cpp:func:`~mdds::flat_segment_tree::build_tree` again. + + +Iterate through stored segments +------------------------------- + +:cpp:class:`~mdds::flat_segment_tree` supports two types of iterators to allow +you to iterate through the segments stored in your tree. The first way is to +iterate through the individual leaf nodes one at a time by using +:cpp:func:`~mdds::flat_segment_tree::begin` and :cpp:func:`~mdds::flat_segment_tree::end`: + +.. literalinclude:: ../example/flat_segment_tree_itrs.cpp + :language: C++ + :start-after: //!code-start: iterate-nodes + :end-before: //!code-end: iterate-nodes + :dedent: 4 + +Each iterator value contains a pair of two values named ``first`` and ``second``, +with the first one being the key of the segment that the node initiates, and the +second one being the value associated with that segment. When executing this +code with the tree from the example code above, you'll get the following output: + +.. code-block:: none + + key: 0; value: 0 + key: 10; value: 10 + key: 20; value: 0 + key: 50; value: 15 + key: 60; value: 5 + key: 65; value: 15 + key: 70; value: 0 + key: 500; value: 0 + +Each node stores the start key and the value of the segment it initiates, and +the key stored in each node is also the end key of the segment that the +previous node initiates except for the first node. Note that the value stored +in the last node is currently not used. It is set to be the zero value of the +value type, but this may change in the future. + +One thing to keep in mind is that :cpp:class:`~mdds::flat_segment_tree` does +not support mutable iterators that let you modify the stored keys or values. + +.. note:: + + :cpp:class:`~mdds::flat_segment_tree` does not support mutable iterators; + you can only traverse the values in a read-only fashion. + +You can also use range-based for loop to iterate through the leaf nodes in a +similar fashion: + +.. literalinclude:: ../example/flat_segment_tree_itrs.cpp + :language: C++ + :start-after: //!code-start: loop-nodes + :end-before: //!code-end: loop-nodes + :dedent: 4 + +The output from this code is identical to that from the previous one. + +Now, one major inconvenience of navigating through the individual leaf nodes +is that you need to manually keep track of the start and end points of each +segment if you need to operate on the segments rather than the nodes that +comprise the segments. The good news is that +:cpp:class:`~mdds::flat_segment_tree` does provide a way to iterate through +the segments directly as the following code demonstrates: + +.. literalinclude:: ../example/flat_segment_tree_itrs.cpp + :language: C++ + :start-after: //!code-start: iterate-segments + :end-before: //!code-end: iterate-segments + :dedent: 4 + +This code uses :cpp:func:`~mdds::flat_segment_tree::begin_segment` and +:cpp:func:`~mdds::flat_segment_tree::end_segment` to iterate through one +segment at a time with the value of each iterator containing ``start``, +``end`` and ``value`` members that correspond with the start key, end key and +the value of the segment, respectively. Running this code produces the +following output: + +.. code-block:: none + + start: 0; end: 10; value: 0 + start: 10; end: 20; value: 10 + start: 20; end: 50; value: 0 + start: 50; end: 60; value: 15 + start: 60; end: 65; value: 5 + start: 65; end: 70; value: 15 + start: 70; end: 500; value: 0 + +It's also possible to iterate through the segments in a range-based for loop, by +calling :cpp:func:`~mdds::flat_segment_tree::segment_range()`: + +.. literalinclude:: ../example/flat_segment_tree_itrs.cpp + :language: C++ + :start-after: //!code-start: loop-segments + :end-before: //!code-end: loop-segments + :dedent: 4 + +This code should generate output identical to that of the previous code. + + +API Reference +------------- + +.. doxygenclass:: mdds::flat_segment_tree + :members: |