Function Height of a tree tree and index index

Height of a tree tree

Format:

Height of a tree tree and index index

Input:

Output:

Properties that reference this function:

Conditional properties that reference this function:

• if the element at index i of stack tree = node (v, (-1), (-1)), then Height of a tree tree and index i = 1

  (link)

• if the element at index i of stack tree = node (v, left, (-1)), then Height of a tree tree and index i = (Height of a tree tree and index left) + 1

  (link)

• if the element at index i of stack tree = node (v, (-1), right), then Height of a tree tree and index i = (Height of a tree tree and index right) + 1

  (link)

• if the following are true:

  • the element at index i of stack tree = node (v, a, b)
  • Height of a tree tree and index a > Height of a tree tree and index b

  then Height of a tree tree and index i = (Height of a tree tree and index a) + 1

  (link)

• if the following are true:

  • the element at index i of stack tree = node (v, a, b)
  • Height of a tree tree and index a < Height of a tree tree and index b

  then Height of a tree tree and index i = (Height of a tree tree and index b) + 1

  (link)

• if the following are true:

  • the element at index i of stack tree = node (v, a, b)
  • Height of a tree tree and index a = Height of a tree tree and index b

  then Height of a tree tree and index i = (Height of a tree tree and index a) + 1

  (link)

• if the following are true:

  • find root index in tree = ri
  • the element at index ri of stack tree = node (rvalue, left, right)
  • Height of a tree tree and index left = Height of a tree tree and index right

  then result of balancing the tree tree = tree

  (link)

• if the following are true:

  • find root index in tree = ri
  • the element at index ri of stack tree = node (rvalue, left, right)
  • Height of a tree tree and index left > (Height of a tree tree and index right) + 1
  • the element at index left of stack tree = node (lvalue, lleft, lright)
  • Height of a tree tree and index lleft > Height of a tree tree and index lright

  then result of balancing the tree tree = result of rotating tree clockwise

  (link)

• if the following are true:

  • find root index in tree = ri
  • the element at index ri of stack tree = node (rvalue, left, right)
  • Height of a tree tree and index left > (Height of a tree tree and index right) + 1
  • the element at index left of stack tree = node (lvalue, lleft, lright)
  • Height of a tree tree and index lleft < Height of a tree tree and index lright

  then result of balancing the tree tree = result of rotating (result of rotating tree twice) clockwise

  (link)

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