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Binary trees

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Assume:

  • let T = nonempty binary tree
  • let n = number of nodes
  • let n_e = number of external nodes
  • let n_i = number of internal nodes
  • let h = height of T

Then, T has following properties:

  1. height of the nonempty binary tree + 1 is less than or equal to the number of nodes in the binary tree is less than or equal to 2^(height of the nonempty binary tree + 1) — 1
  2. 1 is less than or equal to number of external nodes in the nonempty binary tree is less than or equal to 2^(height of the nonempty binary tree)
  3. height of the nonempty binary tree is less than or equal to number of internal nodes of the nonempty binary tree is less than or equal to 2^(height of nonempty binary tree) — 1
  4. log of (number of nodes in nonempty binary tree) — 1 is less than or equal to height of the nonempty binary tree is less than or equal to number of nodes in nonempty binary tree — 1

… sorry this was one was also not finished :’-(

for context plan was to illustrate this using 3djs

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