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The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such ...
The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1. A k-ary tree (for nonnegative integers k) is a rooted tree in which each vertex has at most k children.
The root of the path tree is the path containing the root of the original tree. Alternatively, the path tree may be formed from the original tree by edge contraction of all the heavy edges. A "light" edge of a given tree is an edge that was not selected as part of the heavy path decomposition.
The six paths from the root to the leaves (shown as boxes) correspond to the six suffixes A$, NA$, ANA$, NANA$, ANANA$ and BANANA$. The numbers in the leaves give the start position of the corresponding suffix. Suffix links, drawn dashed, are used during construction.
Reading bitwise from left to right, starting at bit d − 1, where d is the node's distance from the root (d = ⌊log 2 (i+1)⌋) and the node in question is not the root itself (d > 0). When the breadth-index is masked at bit d − 1, the bit values 0 and 1 mean to step either left or right, respectively.
In fact in order to answer a level ancestor query, the algorithm needs to jump from a path to another until it reaches the root and there could be Θ(√ n) of such paths on a leaf-to-root path. This leads us to an algorithm that can pre-process the tree in O( n ) time and answers queries in O( √ n ).
The numbers beside the vertices indicate the distance from the root vertex. In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G.
This is where the search for a particular key would begin, traversing a path that terminates in a leaf. Most pages in this structure will be leaf pages which refer to specific table rows. Because each node (or internal page) can have more than two children, a B-tree index will usually have a shorter height (the distance from the root to the ...