CS253: Binary Search Trees (2019)

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

Transcript

1. Binary Search Trees Data Structures and Algorithms Emory University Jinho D. Choi
3. AbstractBinaryNode.java public abstract class AbstractBinaryNode<T extends Comparable<T>, N extends AbstractBinaryNode<T, N>> { protected T key; protected N parent; protected N left_child; protected N right_child; public AbstractBinaryNode(T key) { setKey(key); } T N AbstractBinaryNode
4. public N getParent() { return parent; } public N getLeftChild() { return left_child; } public N getRightChild() { return right_child; } public N getGrandParent() { return hasParent() ? parent.getParent() : null; } public N getUncle() { return hasParent() ? parent.getSibling() : null; } public N getSibling() { if (hasParent()) { N parent = getParent(); return parent.isLeftChild((N)this) ? parent.getRightChild() : parent.getLeftChild(); } return null; } this (N)this
5. public void setParent(N node) { parent = node; } public void setLeftChild(N node) { replaceParent(node); left_child = node; } public void setRightChild(N node) { replaceParent(node); right_child = node; } protected void replaceParent(N node) { if (node != null) { if (node.hasParent()) node.getParent().replaceChild(node, null); node.setParent((N)this); } } public void replaceChild(N oldChild, N newChild) { if (isLeftChild(oldChild)) setLeftChild(newChild); else if (isRightChild(oldChild)) setRightChild(newChild); }
6. AbstractBinaryNode.java public class BinaryNode<T extends Comparable<T>> extends AbstractBinaryNode<T, BinaryNode<T>> { public BinaryNode(T key) { super(key); } }
7. public abstract class AbstractBinarySearchTree<T extends Comparable<T>, N extends AbstractBinaryNode<T,N>> { protected N root; public AbstractBinarySearchTree() { setRoot(null); } /** @return a new node with the specific key. */ abstract public N createNode(T key); /** @return the root of this tree. */ public N getRoot() { return root; } /** Sets the root of this tree to the specific node. */ public void setRoot(N node) { if (node != null) node.setParent(null); root = node; } N createNode()
8. protected N findNode(N node, T key) { if (node == null) return null; int diff = key.compareTo(node.getKey()); if (diff < 0) return findNode(node.getLeftChild(), key); else if (diff > 0) return findNode(node.getRightChild(), key); else return node; } public N get(T key) { return findNode(root, key); } public boolean contains(T key) { return get(key) != null; } findNode()
9. Abstract BST - Add 2
10. Abstract BST - Add 2 5
11. Abstract BST - Add 2 5 5
12. Abstract BST - Add 2 5 5 3
13. Abstract BST - Add 2 5 3 5 3
14. Abstract BST - Add 2 5 3 5 3 1
15. Abstract BST - Add 2 5 3 1 5 3 1
16. Abstract BST - Add 2 5 3 1 5 3 1 4
17. Abstract BST - Add 2 5 3 1 4 5 3 1 4
18. Abstract BST - Add 2 5 3 1 4 5 3 1 4 2
19. Abstract BST - Add 2 5 3 1 4 2 5 3 1 4 2
20. Abstract BST - Add 2 5 3 1 4 2 5 3 1 4 2 8
21. Abstract BST - Add 2 5 3 8 1 4 2 5 3 1 4 2 8
22. Abstract BST - Add 2 5 3 8 1 4 2 5 3 1 4 2 8 6
23. Abstract BST - Add 2 5 3 8 1 4 6 2 5 3 1 4 2 8 6
24. Abstract BST - Add 2 5 3 8 1 4 6 2 5 3 1 4 2 8 6 7
25. Abstract BST - Add 2 5 3 8 1 4 6 2 7 5 3 1 4 2 8 6 7
26. public N add(T key) { N node = null; if (root == null) setRoot(node = createNode(key)); else node = addAux(root, key); return node; } private N addAux(N node, T key) { int diff = key.compareTo(node.getKey()); N child, newNode = null; if (diff < 0) { if ((child = node.getLeftChild()) == null) node.setLeftChild(newNode = createNode(key)); else newNode = addAux(child, key); } else if (diff > 0) { if ((child = node.getRightChild()) == null) node.setRightChild(newNode = createNode(key)); else newNode = addAux(child, key); } return newNode; } add()
27. Abstract BST - Remove 3 5 3 8 1 4 6 2 7
28. Abstract BST - Remove 3 5 3 8 1 4 6 2 7 No child.
29. Abstract BST - Remove 3 5 3 8 1 4 6 7 No child.
30. Abstract BST - Remove 3 5 3 8 1 4 6 7 No child. One child.
31. Abstract BST - Remove 3 5 3 8 1 4 7 No child. One child.
32. Abstract BST - Remove 3 5 3 8 1 4 7 No child. One child. Two children?
33. public N remove(T key) { N node = findNode(root, key); if (node != null) { if (node.hasBothChildren()) removeHibbard(node); else removeSelf(node); } return node; } protected N removeSelf(N node) { N parent = node.getParent(); N child = null; if (node.hasLeftChild()) child = node.getLeftChild(); else if (node.hasRightChild()) child = node.getRightChild(); replaceChild(node, child); return parent; } private void replaceChild(N oldNode, N newNode) { if (isRoot(oldNode)) setRoot(newNode); else oldNode.getParent().replaceChild(oldNode, newNode); } removeSelf()
34. protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; }
35. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
36. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
37. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
38. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
39. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
40. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
41. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
42. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
43. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
44. Abstract BST - Remove 4 1 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2
45. Abstract BST - Remove 4 5 4 6 protected N removeHibbard(N node) { N successor = node.getRightChild(); N min = findMinNode(successor); N parent = min.getParent(); min.setLeftChild(node.getLeftChild()); if (min != successor) { parent.setLeftChild(min.getRightChild()); min.setRightChild(successor); } replaceChild(node, min); return parent; } 3 G 0 2