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The operations we are interested in are FindRoot(Node v), Cut(Node v), Link(Node v, Node w), and Path(Node v). Every operation is implemented using the Access(Node v) subroutine. When we access a vertex v, the preferred path of the represented tree is changed to a path from the root R of the represented tree to the node v.
Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes. The height of a node is the length of the longest downward path to a leaf from that node. 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 ...
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.
procedure iterativePostorder(node) if node = null return stack ← empty stack lastNodeVisited ← null while not stack.isEmpty() or node ≠ null if node ≠ null stack.push(node) node ← node.left else peekNode ← stack.peek() // if right child exists and traversing node // from left child, then move right if peekNode.right ≠ null and ...
Child Node - Any node connected to a parent node by a directed edge. Depth - Length of the path from the root to the node. The set of all nodes at a given depth is sometimes called a level of the tree. The root node is at depth zero. Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node ...
A single vertex (a single node as the root node). A tree whose root node has two subtrees, both of which are full binary trees. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a ...
Tries are edge-labeled, and in this representation the edge labels become node labels on the binary nodes. The process of converting from a k-ary tree to an LC-RS binary tree is sometimes called the Knuth transform. [4] To form a binary tree from an arbitrary k-ary tree by this method, the root of the original tree is made the root of the ...
Initially, the current node is the root, the rank sought is the original query, and the fallback index is a special "overflow" value indicating that the rank is not in the tree. (Depending on the application, 0 {\displaystyle 0} or n + 1 {\displaystyle n+1} might be used for this purpose.)