data structures - Red-black trees, relation between black and red nodes -

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one of questions homework find exact lower bound of 

(#black nodes)/(#red nodes)

in rb-tree. bound must not asymptotic. suggestions?

your appreciated.

assuming homework:

let's review properties of redblack trees wikipedia:

  1. ...
  2. the root black.
  3. all leaves black.
  4. both children of every red node black.
  5. ...

to lower bound on #b/#r want construct tree has many red nodes possible. (unfortunately, due 2,3,4 cannot construct red tree)

some questions worth thinking about:

  • can fit more red nodes in balanced or not-so-balanced trees?
  • does or odd maximal height make difference?
  • given tree contains 3, 7, ..., (2^n)-1 nodes how many red ones can fit in?

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