Question

Data Structures and Algorithms

1. What is the:
   a. maximum number of levels that a binary search tree with 100 nodes can have?
   b. minimum number of levels that a binary search tree with 100 nodes can have?
   c. maximum total number of nodes in a binary tree that has N levels? (Remember that the root is level 0.)
   d. maximum number of nodes in the Nth level of a binary tree?
   e. number of ancestors of a node in the Nth level of a binary search tree?
   f. number of different binary trees that can be made from three nodes that contain the key values 1, 2, and 3?
   g. number of different binary search trees that can be made from three nodes that contain the key values 1, 2, and 3?

Answer 1

a) Berch tho manimum mumbr d lavels that a bena ty wilh 100 madis ean have is 99. in drder to monimize th mumbur laels, wr med to minimiz uumbr al modes af each lvrl. Jhe minimum Mumber Aay afoch level can be 1. pareut euo child uodo X-e. eachucc how one aud liks BST would laok omei and the level o level Lovel 99 (e) thiminimum numbur lwels thol a u wilh 10o ods cau hauwe i Searuh in dn to minimiz mbr luels, we have to amoximiz mumbr d medes of each Bwel Nades aj lw cau b aN ho mauimum Mumbur th tu has M lvel, whuh sthe minimum can kawe

The minimiin poorens e. eachuce hos one aud e BST would look omethg eno child liko and th lvel o Level 98 lerl 2 lovel 98 lovel 99. search luels thol a b) Thminimum mbur tu wlh 100 nods can have i lurls, we have to in order to minimiz br nedes of each lwel monimizs mumbr Nos al Lud N cau be 2 he mauimum Mumber W tw hos m lved, whuh sthe minimum can howe hon 2 100 a"- 2 1017"

Hoor (loy to1))6. manimun total mumba of mods that hos N lovrls ina March manimum tool numbr af Acl ina ods of Lwel i should lal mouimum a N lwels s BST henee tolol no. Modes in th 24214242N pring G.P Aum (G.P.: Gyeometi a Phopeni) -) 2-20 (d) man mumum mumbur d wodus n th Nh lavd of tivany,s

a) Berch tho manimum mumbr d lavels that a bena ty wilh 100 madis ean have is 99. in drder to monimize th mumbur laels, wr med to minimiz uumbr al modes af each lvrl. Jhe minimum Mumber Aay afoch level can be 1. pareut euo child uodo X-e. eachucc how one aud liks BST would laok omei and the level o level Lovel 99 (e) thiminimum numbur lwels thol a u wilh 10o ods cau hauwe i Searuh in dn to minimiz mbr luels, we have to amoximiz mumbr d medes of each Bwel Nades aj lw cau b aN ho mauimum Mumbur th tu has M lvel, whuh sthe minimum can kawe

The minimiin poorens e. eachuce hos one aud e BST would look omethg eno child liko and th lvel o Level 98 lerl 2 lovel 98 lovel 99. search luels thol a b) Thminimum mbur tu wlh 100 nods can have i lurls, we have to in order to minimiz br nedes of each lwel monimizs mumbr Nos al Lud N cau be 2 he mauimum Mumber W tw hos m lved, whuh sthe minimum can howe hon 2 100 a"- 2 1017"

Hoor (loy to1))6. manimun total mumba of mods that hos N lovrls ina March manimum tool numbr af Acl ina ods of Lwel i should lal mouimum a N lwels s BST henee tolol no. Modes in th 24214242N pring G.P Aum (G.P.: Gyeometi a Phopeni) -) 2-20 (d) man mumum mumbur d wodus n th Nh lavd of tivany,s