CS253: Balanced Binary Search Trees (2019)

https://github.com/emory-courses/cs253

Transcript

1. Binary Search Trees: Balanced Data Structures and Algorithms Emory University Jinho D. Choi https://github.com/emory-courses/cs253
3. O(n) O(n) O(n) + β O(log n) O(log n) + α O(log n) + β
4. AbstractBalancedBinarySearchTree.java public abstract class AbstractBalancedBinarySearchTree <T extends Comparable<T>, N extends AbstractBinaryNode<T, N>> extends AbstractBinarySearchTree<T, N> { @Override public N add(T key) { N node = super.add(key); balance(node); return node; } @Override public N remove(T key) { N node = findNode(root, key); if (node != null) { N lowest = node.hasBothChildren() ? removeHibbard(node) : removeSelf(node); if (lowest != null && lowest != node) balance(lowest); } return node; } /** Preserves the balance of the specific node and its ancestors. */ protected abstract void balance(N node); balance()
6. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10
7. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild();
8. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild();
9. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild(); node.setRightChild(child.getLeftChild());
10. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild(); node.setRightChild(child.getLeftChild());
11. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild(); node.setRightChild(child.getLeftChild()); node.getParent().replaceChild(node, child);
12. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild(); node.setRightChild(child.getLeftChild()); node.getParent().replaceChild(node, child);
13. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild(); node.setRightChild(child.getLeftChild()); node.getParent().replaceChild(node, child); child.setLeftChild(node);
14. Balanced BST - Rotate Left 2 5 3 7 1 4 6 8 10 N child = node.getRightChild(); node.setRightChild(child.getLeftChild()); node.getParent().replaceChild(node, child); child.setLeftChild(node);
15. protected void rotateLeft(N node) { N child = node.getRightChild(); node.setRightChild(child.getLeftChild()); if (node.hasParent()) node.getParent().replaceChild(node, child); else setRoot(child); child.setLeftChild(node); } protected void rotateRight(N node) { N child = node.getLeftChild(); node.setLeftChild(child.getRightChild()); if (node.hasParent()) node.getParent().replaceChild(node, child); else setRoot(child); child.setRightChild(node); }
16. AVLNode.java public class AVLNode<T extends Comparable<T>> extends AbstractBinaryNode<T, AVLNode<T>> { private int height; public AVLNode(T key) { super(key); height = 1; } @Override public void setLeftChild(AVLNode<T> node) { super.setLeftChild(node); resetHeights(); } @Override public void setRightChild(AVLNode<T> node) { super.setRightChild(node); resetHeights(); }
17. public void resetHeights() { resetHeightsAux(this); } private void resetHeightsAux(AVLNode<T> node) { if (node != null) { int lh = node.hasLeftChild() ? node.getLeftChild().getHeight() : 0; int rh = node.hasRightChild() ? node.getRightChild().getHeight() : 0; int height = Math.max(lh, rh) + 1; if (height != node.getHeight()) { node.setHeight(height); resetHeightsAux(node.getParent()); } } }
18. public int getBalanceFactor() { if (hasBothChildren()) return left_child.getHeight() - right_child.getHeight(); else if (hasLeftChild()) return left_child.getHeight(); else if (hasRightChild()) return -right_child.getHeight(); else return 0; }
19. AVLTree.java public class AVLTree<T extends Comparable<T>> extends AbstractBalancedBinarySearchTree<T, AVLNode<T>> { @Override public AVLNode<T> createNode(T key) { return new AVLNode<T>(key); } @Override protected void rotateLeft(AVLNode<T> node) { super.rotateLeft(node); node.resetHeights(); } @Override protected void rotateRight(AVLNode<T> node) { super.rotateRight(node); node.resetHeights(); }
20. @Override protected void balance(AVLNode<T> node) { if (node == null) return; int bf = node.getBalanceFactor(); if (bf == 2) { AVLNode<T> child = node.getLeftChild(); if (child.getBalanceFactor() == -1) // case 1 rotateLeft(child); rotateRight(node); // case 2 } else if (bf == -2) { AVLNode<T> child = node.getRightChild(); if (child.getBalanceFactor() == 1) // case 3 rotateRight(child); rotateLeft(node); // case 4 } else balance(node.getParent()); }
21. AVL Tree - Add 3 5
22. AVL Tree - Add 3 5 5
23. AVL Tree - Add 3 5 3 5
24. AVL Tree - Add 3 5 3 3 5
25. AVL Tree - Add 3 5 3 1 3 5
26. AVL Tree - Add 3 1 5 3 1 3 5
27. AVL Tree - Add 3 1 5 3 1 |Balance factor| > 1? 3 5
28. AVL Tree - Add 3 1 5 3 1 |Balance factor| > 1? Rotate right 3 5
29. AVL Tree - Add 3 1 5 3 1 |Balance factor| > 1? Rotate right 3 5
30. AVL Tree - Add 3 1 5 3 1 4 |Balance factor| > 1? Rotate right 3 5
31. AVL Tree - Add 3 1 4 5 3 1 4 |Balance factor| > 1? Rotate right 3 5
32. AVL Tree - Add 3 1 4 5 3 1 4 2 |Balance factor| > 1? Rotate right 3 5
33. AVL Tree - Add 3 1 4 2 5 3 1 4 2 |Balance factor| > 1? Rotate right 3 5
34. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 |Balance factor| > 1? Rotate right 3 5
35. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 |Balance factor| > 1? Rotate right 3 5 8
36. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 |Balance factor| > 1? Rotate right 3 5 8
37. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 |Balance factor| > 1? Rotate right 3 5 8 6
38. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 7 |Balance factor| > 1? Rotate right 3 5 8 6
39. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 7 |Balance factor| > 1? Rotate right 3 5 7 8 6
40. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 7 |Balance factor| > 1? Rotate right 3 5 Rotate left 7 8 6
41. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 7 |Balance factor| > 1? Rotate right 3 5 Rotate left 7 8 6
42. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 7 |Balance factor| > 1? Rotate right 3 5 Rotate left 7 8 Rotate right 6
43. AVL Tree - Add 3 1 4 2 5 3 1 4 2 8 6 7 |Balance factor| > 1? Rotate right 3 5 Rotate left 7 8 Rotate right 6
48. RedBlackTree.java public class RedBlackTree<T extends Comparable<T>> extends AbstractBalancedBinarySearchTree<T, RedBlackNode<T>> { public RedBlackNode<T> createNode(T key) { return new RedBlackNode<T>(key); } protected void balance(RedBlackNode<T> node) { if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } } private void balanceWithRedUncle(RedBlackNode<T> node, RedBlackNode<T> uncle) { node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); }
49. private void balanceWithBlackUncle(RedBlackNode<T> node) { RedBlackNode<T> grandParent = node.getGrandParent(); if (grandParent != null) { RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { // case 1 rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { // case 2 rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) // case 3 rotateRight(grandParent); else rotateLeft(grandParent); // case 4 } }
50. Red-Black - Add 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
51. 5 Red-Black - Add 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
52. 5 Red-Black - Add 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
53. Red-Black - Add 4 5 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
54. Red-Black - Add 4 3 5 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
55. Red-Black - Add 4 1 3 5 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
56. Red-Black - Add 4 1 3 5 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
57. Red-Black - Add 4 1 3 5 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent);
58. Red-Black - Add 4 1 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 5
59. Red-Black - Add 4 1 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 5
60. Red-Black - Add 4 1 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 5
61. Red-Black - Add 4 1 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 5
62. Red-Black - Add 4 1 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 5
63. Red-Black - Add 4 1 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 5
64. 5 Red-Black - Add 4 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 1
65. 5 Red-Black - Add 4 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 3 1
66. 5 Red-Black - Add 4 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 1 3
67. 5 Red-Black - Add 4 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 1 3
68. 5 Red-Black - Add 4 4 if (isRoot(node)) node.setToBlack(); else if (node.getParent().isRed()) { RedBlackNode<T> uncle = node.getUncle(); if (uncle != null && uncle.isRed()) balanceWithRedUncle(node, uncle); else balanceWithBlackUncle(node); } node.getParent().setToBlack(); uncle.setToBlack(); RedBlackNode<T> grandParent = node.getGrandParent(); grandParent.setToRed(); balance(grandParent); RedBlackNode<T> parent = node.getParent(); if (grandParent.isLeftChild(parent) && parent.isRightChild(node)) { rotateLeft(parent); node = parent; } else if (grandParent.isRightChild(parent) && parent.isLeftChild(node)) { rotateRight(parent); node = parent; } node.getParent().setToBlack(); grandParent.setToRed(); if (node.getParent().isLeftChild(node)) rotateRight(grandParent); else rotateLeft(grandParent); 1 3