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  2. Euler tour technique - Wikipedia

    en.wikipedia.org/wiki/Euler_tour_technique

    The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree

  3. List ranking - Wikipedia

    en.wikipedia.org/wiki/List_ranking

    List ranking can equivalently be viewed as performing a prefix sum operation on the given list, in which the values to be summed are all equal to one. The list ranking problem can be used to solve many problems on trees via an Euler tour technique, in which one forms a linked list that includes two copies of each edge of the tree, one in each direction, places the nodes of this list into an ...

  4. Heavy-light decomposition - Wikipedia

    en.wikipedia.org/wiki/Heavy-Light_Decomposition

    In combinatorial mathematics and theoretical computer science, heavy-light decomposition (also called heavy path decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition, each non-leaf node selects one "heavy edge", the edge to the child that has the greatest number of descendants (breaking ...

  5. Level ancestor problem - Wikipedia

    en.wikipedia.org/wiki/Level_ancestor_problem

    [2] [4] This solution is based on the Euler tour technique for processing trees. The main observation is that LA(v,d) is the first node of depth d that appears in the Euler tour after the last appearance of v. Thus, by constructing the Euler tour and associated information on depth, the problem is reduced to a query on arrays, named find ...

  6. Lowest common ancestor - Wikipedia

    en.wikipedia.org/wiki/Lowest_common_ancestor

    In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...

  7. Tree contraction - Wikipedia

    en.wikipedia.org/wiki/Tree_contraction

    With the Euler tour technique, a tree could be represented in a flat style, and thus prefix sum could be applied to an arbitrary tree in this format. In fact, prefix sum can be used on any set of values and binary operation which form a group: the binary operation must be associative, every value must have an inverse, and there exists an ...

  8. Vanna White’s ‘heartthrob’ son, Nikko, reacts to ‘thirsty ...

    www.aol.com/news/vanna-white-heartthrob-son...

    Vanna White's son, Nikko, generated a viral moment in the kitchen with his mom after fans declared him to be "handsome," and desperately wanted to know more.

  9. Eulerian path - Wikipedia

    en.wikipedia.org/wiki/Eulerian_path

    An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once