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However, in the application of graph traversal methods in artificial intelligence the input may be an implicit representation of an infinite graph. In this context, a search method is described as being complete if it is guaranteed to find a goal state if one exists. Breadth-first search is complete, but depth-first search is not.
Level The level of a node is the number of edges along the unique path between it and the root node. [4] This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Forest A set of one or more disjoint trees. Ordered tree A rooted tree in which an ordering is specified for the children of each vertex. Size of ...
Also called a level-order traversal. In a complete binary tree, a node's breadth-index ( i − (2 d − 1)) can be used as traversal instructions from the root. 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 ...
Visit the current node for pre-order traversal. For each i from 1 to the current node's number of subtrees − 1, or from the latter to the former for reverse traversal, do: 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.
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value.
It is also possible to use depth-first search to linearly order the vertices of a graph or tree. There are four possible ways of doing this: A preordering is a list of the vertices in the order that they were first visited by the depth-first search algorithm. This is a compact and natural way of describing the progress of the search, as was ...
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 binary tree is threaded by making all right child pointers that would normally be null point to the in-order successor of the node (if it exists), and all left child pointers that would normally be null point to the in-order predecessor of the node." [1] This assumes the traversal order is the same as in-order traversal of the tree. However ...