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| package bbm.tree;
public class BTree { private static final int t = 5; Node root;
public BTree() { Node root = new Node(); root.leaf = true; this.root = root; }
private SearchResult search(Node x, int key) { int i = 0; while (i < x.keySize && key > x.keys[i]) { i++; } if (i < x.keySize && key == x.keys[i]) { return new SearchResult(x, i); } else if (x.leaf) { return null; } else { return search(x.children[i], key); } }
public SearchResult search(int key) { return search(root, key); }
private void splitChild(Node x, int i) { Node z = new Node(); Node y = x.children[i]; z.leaf = y.leaf; z.keySize = t - 1; for (int j = 0; j < t - 1; j++) { z.keys[j] = y.keys[t + j]; y.keys[t + j] = 0; } if (!y.leaf) { for (int j = 0; j < t; j++) { z.children[j] = y.children[t + j]; y.children[t + j] = null; } } y.keySize = t - 1; for (int j = x.keySize; j >= i + 1; j--) { x.children[j + 1] = x.children[j]; } x.children[i + 1] = z; for (int j = x.keySize - 1; j >= i; j--) { x.keys[j + 1] = x.keys[j]; } x.keys[i] = y.keys[t - 1]; y.keys[t - 1] = 0; x.keySize = x.keySize + 1; }
public void insert(int k) { Node r = root; if (root.keySize == 2 * t - 1) { Node s = new Node(); root = s; s.leaf = false; s.keySize = 0; s.children[0] = r; splitChild(s, 0); insertNonFull(s, k); } else { insertNonFull(r, k); } verify(); }
private void insertNonFull(Node x, int k) { int i = x.keySize - 1; if (x.leaf) { while (i >= 0 && k < x.keys[i]) { x.keys[i + 1] = x.keys[i]; i--; } x.keys[i + 1] = k; x.keySize += 1; } else { while (i >= 0 && k < x.keys[i]) { i--; } i = i + 1; if (x.children[i].keySize == 2 * t - 1) { splitChild(x, i); if (k > x.keys[i]) { i++; } } insertNonFull(x.children[i], k); } }
public void delete(int k) { Node r = root; if (r.keySize == 1 && !r.leaf) { Node y = r.children[0]; Node z = r.children[1]; if (y.keySize == z.keySize && y.keySize == t - 1) { mergeChild(r, 0, y, z); root = y; deleteNonOne(y, k); } else { deleteNonOne(r, k); } } else { deleteNonOne(r, k); } verify(); }
private void mergeChild(Node r, int i, Node y, Node z) { y.keySize = 2 * t - 1; for (int j = t; j < 2 * t - 1; j++) { y.keys[j] = z.keys[j - t]; } y.keys[t - 1] = r.keys[i]; if (!y.leaf) { for (int j = t; j < 2 * t; j++) { y.children[j] = z.children[j - t]; } } for (int j = i + 1; j < r.keySize; j++) { r.children[j] = r.children[j + 1]; } for (int j = i; j < r.keySize - 1; j++) { r.keys[j] = r.keys[j + 1]; }
r.keySize -= 1; r.keys[r.keySize] = 0; r.children[r.keySize + 1] = null; }
private void deleteNonOne(Node x, int k) { int i = 0; if (x.leaf) { while (i < x.keySize && k > x.keys[i]) { i++; } if (i < x.keySize && k == x.keys[i]) { for (int j = i + 1; j < x.keySize; j++) { x.keys[j - 1] = x.keys[j]; } x.keySize -= 1; x.keys[x.keySize] = 0; } else { System.out.println(k + ": key not exist in tree"); } } else { while (i < x.keySize && k > x.keys[i]) { i++; } Node y = x.children[i]; Node z = null; if (i < x.keySize) { z = x.children[i + 1]; } if (i < x.keySize && k == x.keys[i]) { if (y.keySize > t - 1) { int newK = searchPredecessor(y); deleteNonOne(y, newK); x.keys[i] = newK; } else if (z.keySize > t - 1) { int newK = searchSuccessor(z); deleteNonOne(z, newK); x.keys[i] = newK; } else { mergeChild(x, i, y, z); deleteNonOne(y, k); } } else { Node p = null; if (i > 0) { p = x.children[i - 1]; } if (y.keySize == t - 1) { if (i > 0 && p.keySize > t - 1) { shift2RightChild(x, i - 1, p, y); } else if (i < x.keySize && z.keySize > t - 1) { shift2LeftChild(x, i, y, z); } else if (i > 0) { mergeChild(x, i - 1, p, y); y = p; } else { mergeChild(x, i, y, z); } } deleteNonOne(y, k); } } }
private void shift2LeftChild(Node x, int i, Node left, Node right) { left.keys[left.keySize] = x.keys[i]; left.keySize += 1; x.keys[i] = right.keys[0]; right.keySize -= 1; for (int j = 0; j < right.keySize; j++) { right.keys[j] = right.keys[j + 1]; } right.keys[right.keySize] = 0; if (!right.leaf) { left.children[left.keySize] = right.children[0]; for (int j = 0; j <= right.keySize; j++) { right.children[j] = right.children[j + 1]; } right.children[right.keySize + 1] = null; } }
private void shift2RightChild(Node x, int i, Node left, Node right) { right.keySize += 1; for (int j = right.keySize - 1; j > 0; j--) { right.keys[j] = right.keys[j - 1]; } right.keys[0] = x.keys[i]; x.keys[i] = left.keys[left.keySize - 1]; if (!right.leaf) { for (int j = right.keySize - 1; j >= 0; j--) { right.children[j + 1] = right.children[j]; } right.children[0] = left.children[left.keySize]; left.children[left.keySize] = null; } left.keySize -= 1; left.keys[left.keySize] = 0; }
private void verify() { if (root == null) { return; } verifyFromNode(root); }
private void verifyFromNode(Node x) { if (x != root && x.keySize < (t - 1)) { throw new RuntimeException("节点关键字小于 t-1"); } if (x.keySize > (2 * t - 1)) { throw new RuntimeException("节点关键字大于 2 * t - 1"); } for (int i = 1; i < x.keySize; i++) { if (x.keys[i - 1] > x.keys[i]) { throw new RuntimeException("节点 keys 不是升序"); } } if (!x.leaf) { for (int i = 0; i < x.keySize; i++) { if (x.children[i].keys[x.children[i].keySize - 1] > x.keys[i]) { throw new RuntimeException("左子节点的 max key 比当前 key 大"); } if (x.children[i + 1].keys[0] < x.keys[i]) { throw new RuntimeException("右子节点的 min key 比当前 key 小"); } } } }
private int searchPredecessor(Node z) { Node x = z; int i = x.keySize; while (!x.leaf) { x = x.children[i]; i = x.keySize; } return x.keys[x.keySize - 1]; }
private int searchSuccessor(Node z) { Node x = z; while (!x.leaf) { x = x.children[0]; } return x.keys[0]; }
public Node getRoot() { return root; }
public static class Node { int[] keys = new int[2 * t - 1]; int keySize; Node[] children = new Node[2 * t]; boolean leaf; }
public static class SearchResult { Node node; int index;
public SearchResult(Node node, int index) { this.node = node; this.index = index; } } }
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