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Recursively traverse the current node's i-th subtree. Visit the current node for in-order traversal. Recursively traverse the current node's last subtree. Visit the current node for post-order traversal. Depending on the problem at hand, pre-order, post-order, and especially one of the number of subtrees − 1 in-order operations may be optional.
For example, leaf nodes by definition have no descendants, so given only a pointer to a leaf node no other node can be reached. A threaded tree adds extra information in some or all nodes, so that for any given single node the "next" node can be found quickly, allowing tree traversal without recursion and the extra storage (proportional to the ...
A universal traversal sequence is a sequence of instructions comprising a graph traversal for any regular graph with a set number of vertices and for any starting vertex. A probabilistic proof was used by Aleliunas et al. to show that there exists a universal traversal sequence with number of instructions proportional to O ( n 5 ) for any ...
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 node). [18] A perfect binary tree is a full binary tree.
Filled nodes are the visited ones, with color representing the distance: the redder, the closer (to the start node). Nodes in all the different directions are explored uniformly, appearing more-or-less as a circular wavefront as Dijkstra's algorithm uses a heuristic of picking the shortest known path so far.
A node that has a child is called the child's parent node (or superior). All nodes have exactly one parent, except the topmost root node, which has none. A node might have many ancestor nodes, such as the parent's parent. Child nodes with the same parent are sibling nodes. Typically siblings have an order, with the first one conventionally ...
When working with graphs that are too large to store explicitly (or infinite), it is more practical to describe the complexity of breadth-first search in different terms: to find the nodes that are at distance d from the start node (measured in number of edge traversals), BFS takes O(b d + 1) time and memory, where b is the "branching factor ...
Instead, each node's position within the trie determines its associated key, with the connections between nodes defined by individual characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization ...