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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.
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 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.
A labeled binary tree of size 9 (the number of nodes in the tree) and height 3 (the height of a tree defined as the number of edges or links from the top-most or root node to the farthest leaf node), with a root node whose value is 1. The above tree is unbalanced and not sorted.
A leaf is a vertex with no children. [24] An internal vertex is a vertex that is not a leaf. [24] The height of a vertex in a rooted tree is the length of the longest downward path to a leaf from that vertex. The height of the tree is the height of the root. The depth of a vertex is the length of the path to its root (root path). The depth of a ...
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 ).
This method leads to a balanced k-d tree, in which each leaf node is approximately the same distance from the root. However, balanced trees are not necessarily optimal for all applications. Note that it is not required to select the median point. In the case where median points are not selected, there is no guarantee that the tree will be balanced.
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 ...