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Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
function Depth-Limited-Search-Backward(u, Δ, B, F) is prepend u to B if Δ = 0 then if u in F then return u (Reached the marked node, use it as a relay node) remove the head node of B return null foreach parent of u do μ ← Depth-Limited-Search-Backward(parent, Δ − 1, B, F) if μ null then return μ remove the head node of B return null
In depth-first search (DFS), the search tree is deepened as much as possible before going to the next sibling. To traverse binary trees with depth-first search, perform the following operations at each node: [3] [4] If the current node is empty then return. Execute the following three operations in a certain order: [5] N: Visit the current node.
The function strongconnect performs a single depth-first search of the graph, finding all successors from the node v, and reporting all strongly connected components of that subgraph. When each node finishes recursing, if its lowlink is still set to its index, then it is the root node of a strongly connected component, formed by all of the ...
Input: A graph G and a starting vertex root of G. Output: Goal state.The parent links trace the shortest path back to root [9]. 1 procedure BFS(G, root) is 2 let Q be a queue 3 label root as explored 4 Q.enqueue(root) 5 while Q is not empty do 6 v := Q.dequeue() 7 if v is the goal then 8 return v 9 for all edges from v to w in G.adjacentEdges(v) do 10 if w is not labeled as explored then 11 ...
Let S be any finite set, f be any endofunction from S to itself, and x 0 be any element of S.For any i > 0, let x i = f(x i − 1).Let μ be the smallest index such that the value x μ reappears infinitely often within the sequence of values x i, and let λ (the loop length) be the smallest positive integer such that x μ = x λ + μ.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
A 1-dimensional range tree on a set of n points is a binary search tree, which can be constructed in () time. Range trees in higher dimensions are constructed recursively by constructing a balanced binary search tree on the first coordinate of the points, and then, for each vertex v in this tree, constructing a (d−1)-dimensional range tree on the points contained in the subtree of v.