2-3-4 Trees and Red/Black Trees

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Red-Black Insertion‣ Insertion Algorithm:– 1. Insert node into normal BST location (at aleaf location) and color it RED– 2a. If the node's parent is black (i.e. the leafused to be a 2-node) then DONE (i.e. younow have what was a 3- or 4-node)– 2b. Else perform fixTree transformations thenrepeat step 2 on the parent or grandparent(whoever is red)‣ fixTree involves either– recoloring or– 1 or 2 rotations and recoloring‣ Which case of fixTree you performdepends on the color of the new node's"aunt/uncle"© Copyright 2013 Brent Nash & Mark Redekopp, All Rights Reservedparentxgrandparent10203040aunt/uncle26
fixTree Cases1.RecolorGGGPUPUNP G UN PUNcNcabab2.RecolorPGUPGUP N G UP NGUaNaN3.RecolorRootbcRbRcNote: For insertion/removalalgorithm we consider nonexistentleaf nodes as blacknodes© Copyright 2013 Brent Nash & Mark Redekopp, All Rights Reserved27
Page 2: Definition‣ 2-3-4 trees are very
Page 5 and 6: 2-3-4 Insertion Algorithm‣ Key: R
Page 7 and 8: 2-3-4 Insertion Algorithm‣ Key: S
Page 9 and 10: 2-3-4 Insertion Exercise 2Add 5820
Page 11 and 12: 2-3-4 Insertion Exercise 3Resulting
Page 13 and 14: TREE ROTATIONS© Copyright 2013 Bre
Page 15 and 16: BST Subtree Ranges‣ Consider a bi
Page 17 and 18: Right Rotation‣ Define a right ro
Page 19 and 20: Left Rotation‣ Define a left rota
Page 21 and 22: Rotation's Effect on Height‣ When
Page 23 and 24: Red Black Trees‣ A red-black tree
Page 25: Red-Black Tree Properties‣ Valid
Page 29 and 30: Insertion‣ Insert 10, 20, 30, 15,
Page 31 and 32: ‣ Insert 10, 20, 30, 15, 25, 12,
Page 33 and 34: Insertion Exercise 1Insert 271253 1
Page 35 and 36: Insertion Exercise 2Insert 401253 1
Page 37 and 38: Insertion Exercise 2A1253 10G1520P2
Page 39 and 40: Insertion Exercise 3Insert 50121252
Page 41 and 42: Insertion Exercise 4Insert 45121252
Page 43 and 44: Final Result125273 1020408152530504
Page 45 and 46: Insertion Exercise 5125273 92040810
Page 47 and 48: ‣ Implement private methods:- fin
Page 49 and 50: FOR PRINT© Copyright 2013 Brent Na
Page 51: fixTree Cases4.1 Rotate /RecolorNPG

2-3-4 Trees and Red/Black Trees

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