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In computer science, the log-structured merge-tree (also known as LSM tree, or LSMT [1]) is a data structure with performance characteristics that make it attractive for providing indexed access to files with high insert volume, such as transactional log data. LSM trees, like other search trees, maintain key-value pairs. LSM trees maintain data ...
This unsorted tree has non-unique values (e.g., the value 2 existing in different nodes, not in a single node only) and is non-binary (only up to two children nodes per parent node in a binary tree). The root node at the top (with the value 2 here), has no parent as it is the highest in the tree hierarchy.
An arrangement of nine points (related to the Pappus configuration) forming ten 3-point lines.. In discrete geometry, the original orchard-planting problem (or the tree-planting problem) asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane.
A simple B+ tree example linking the keys 1–7 to data values d 1-d 7. The linked list (red) allows rapid in-order traversal. This particular tree's branching factor is =4. Both keys in leaf and internal nodes are colored gray here. By definition, each value contained within the B+ tree is a key contained in exactly one leaf node.
An example of a recursive binary space partitioning quadtree for a 2D index. Quadtrees may be classified according to the type of data they represent, including areas, points, lines and curves. Quadtrees may also be classified by whether the shape of the tree is independent of the order in which data is processed.
Both these operations take O(log n) time. For insertions, this is slower than Fibonacci heaps, which support insertion in O(1) (constant) amortized time, and O(log n) worst-case. Leftist trees are advantageous because of their ability to merge quickly, compared to binary heaps which take Θ(n).
A "Fenwick tree" is actually three implicit trees over the same array: the interrogation tree used for translating indexes to prefix sums, the update tree used for updating elements, and the search tree for translating prefix sums to indexes (rank queries). [4] The first two are normally walked upwards, while the third is usually walked downwards.
In the early days, felled logs were transported using simple methods such as rivers to float tree trunks downstream to sawmills or paper mills. This practice, known as log driving or timber rafting, was the cheapest and most common. Some logs, due to high resin content, would sink and were known as deadheads.