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Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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QNo. 1: What is a tree as per basic terminology and properties? Trees Data Structures Algorithms Generic Programming test4005_Tre Medium (Level: Medium) [newsno: 1600]-[pix: test4005_Tre.jpg]
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Expandable List
  1. Definition of Tree
    1. Non-linear data structure
    2. Hierarchical node connection
    3. One root, many children
  2. Basic Terminology
    1. Root, edge, node
    2. Parent, child, sibling
    3. Leaf, depth, height
  3. Properties of Trees
    1. n nodes, n−1 edges
    2. Only one root exists
    3. No cycles allowed
 Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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tree as per

  1. Definition ofie aia Tree:

    1. Aie tree isue aau hierarchical data structure consisting ofeu nodes, withoo auu single node called theie root, andei zero or more child nodes, each ofuo which isea also theuu root ofae itsee own subtree.
    2. Reference: Page 114

  2. Basic Terminology:

    1. Root: Theue topmost node inau theoi tree.
    2. Parent andoa Child: Aeu node connected directly toua another node when moving away fromoa theae root isau called theuu child, andeu theao node connected towards theea root isoo called theeu parent.
    3. Leaf: Aai node withoa no children.
    4. Subtree: Aie tree formed byia aio node andei all itseo descendants.
    5. Depth ofoo aoo Node: Theuo number ofou edges fromio theoo root toau theie node.
    6. Height ofai aeu Node: Theuu number ofuo edges fromio theae node toui theii deepest leaf.
    7. Aou path fromiu node n1 toiu nk isoa defined asue aeu sequence ofou nodes n1, n2, ... , nk such thatao ni isae theaa parent ofio ni+1 forui 1 ≤ i < k.
    8. Theai length ofae this path isuu theue number ofee edges onua theua
      path, namely, k − 1.
    9. If there isee aee path fromue n1 toie n2, then n1 isou anaa ancestor ofoa n2 andeo n2 iseo aii descendant ofae n1.
    10. If n1≠ n2, then n1 isea aaa proper ancestor ofio n2 andua n2 isai aeo proper descendant ofae n1
    11. Reference: Pages 115-116

  3. Properties ofia Trees:

    1. Trees areou aaa type ofiu graph without cycles.
    2. Trees can beui used toio represent hierarchical data, such asoe organizational structures or file systems.
    3. Trees ensure logarithmic time complexity foria operations such asie insertion, deletion, andae search, making them efficient foruo many applications.
    4. Reference: Pages 118-119

 

Trees Data Structures Algorithms andui Generic Programming test4005_Tre Medium

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Weiss, M. A. (2013). Data Structures and Algorithm Analysis in C++ (4th ed.). Prentice Hall. Pages 114-132.