B-树的java实现
理论部分见：B-树的理论学习
JAVA实现
定义树结点类
/**
* B-树的结点类
*/
private static class Node {
/**
* 关键字列表
*/
private final List<Object> keyList;
/**
* 孩子结点列表
*/
private final List<Node> childNodesList;
/**
* 是否叶子结点
*/
private boolean isLeaf;
/**
* 双亲结点
*/
private Node parentNode;
/**
* 键值比较函数对象，如果采用倒序或者其它排序方式，传入该对象
*/
private Comparator<Object> kComparator;
public Node() {
this.keyList = new LinkedList<>();
this.childNodesList = new LinkedList<>();
this.isLeaf = false;
}
/**
* 自定义K排序方式的构造函数
*/
public Node(Comparator<Object> kComparator) {
this();
this.kComparator = kComparator;
}
/**
* 比较两个key，如果没有传入自定义排序方式则采用默认的升序
*/
private int compare(Object key1, Object key2) {
return this.kComparator == null ? ((Comparable<Object>) key2).compareTo(key1) : kComparator.compare(key1, key2);
}
public void setIsLeaf(boolean isLeaf) {
this.isLeaf = isLeaf;
}
public boolean getIsLeaf() {
return this.isLeaf;
}
public void setParentNode(Node parentNode) {
this.parentNode = parentNode;
}
public Node getParentNode() {
return parentNode;
}
/**
* 结点中关键字的个数
*/
public int keySize() {
return this.keyList.size();
}
/**
* 采用二分查找在结点内查找关键字
*/
public SearchResult searchResult(Object key) {
int begin = 0;
int end = this.keySize() - 1;
int mid = (begin + end) / 2;
boolean isExist = false;
int index = 0;
//二分查找
while (begin < end) {
mid = (begin + end) / 2;
Object midValue = this.keyList.get(mid);
int compareRe = compare(midValue, key);
//找到了
if (compareRe == 0) {
break;
} else {
if (compareRe > 0) {
//在中点右边
begin = mid + 1;
} else {
end = mid - 1;
}
}
}
//二分查找结束，判断结果;三个元素以上才是正经二分，只有两个或一个元素属于边界条件要着重考虑
if (begin < end) {
//找到了
isExist = true;
index = mid;
} else if (begin == end) {
Object midKey = this.keyList.get(begin);
int comRe = compare(midKey, key);
if (comRe == 0) {
isExist = true;
index = begin;
} else if (comRe > 0) {
index = begin + 1;
} else {
index = begin;
}
} else {
index = begin;
}
return new SearchResult(isExist, index, null);
}
}定义查询key的结果类
/**
* 关键字查询结果类
*/
private static class SearchResult {
/**
* 关键字所在结点
*/
private final Node node;
/**
* 是否存在
*/
private final boolean isExist;
/**
* 下标
*/
private final int index;
public SearchResult(boolean isExist, int index, Node node) {
this.isExist = isExist;
this.index = index;
this.node = node;
}
public boolean isExist() {
return isExist;
}
public int getIndex() {
return index;
}
public Node getNode() {
return node;
}
}定义树类
public class MyBTree {
...
...
...
/**
* 默认3阶树
*/
private final Integer DEFAULT_ORDER = 3;
/**
* 树阶
*/
private int order = DEFAULT_ORDER;
/**
* 结点中关键字个数的最大值
*/
private int maxKeySize = order - 1;
/**
* 结点的最小关键字数
*/
private int nonLeafMinKeys = (int) Math.ceil(order / 2.0) - 1;
/**
* 根结点
*/
private Node root;
/**
* 比较函数对象
*/
private Comparator<Object> kComparator;
/**
* 构造一棵自然排序的B树
*/
MyBTree() {
Node root = new Node();
this.root = root;
root.setIsLeaf(true);
}
/**
* 构造一棵order阶 的B树
*/
MyBTree(int order) {
this();
this.order = order;
this.maxKeySize = order - 1;
this.nonLeafMinKeys = (int) Math.ceil(order / 2.0) - 1;
}
...
...
...
}类图
Node和SearchResult是Btree的子类，由入口main方法执行验证。若有BUG，可以留言。
完整
package tree.b;
import java.util.*;
public class MyBTree<K> {
/**
* 关键字查询结果类
*/
private static class SearchResult {
/**
* 关键字所在结点
*/
private final Node node;
/**
* 是否存在
*/
private final boolean isExist;
/**
* 下标
*/
private final int index;
public SearchResult(boolean isExist, int index, Node node) {
this.isExist = isExist;
this.index = index;
this.node = node;
}
public boolean isExist() {
return isExist;
}
public int getIndex() {
return index;
}
public Node getNode() {
return node;
}
}
/**
* B-树的结点类
*/
private static class Node {
/**
* 关键字列表
*/
private final List<Object> keyList;
/**
* 孩子结点列表
*/
private final List<Node> childNodesList;
/**
* 是否叶子结点
*/
private boolean isLeaf;
/**
* 双亲结点
*/
private Node parentNode;
/**
* 键值比较函数对象，如果采用倒序或者其它排序方式，传入该对象
*/
private Comparator<Object> kComparator;
public Node() {
this.keyList = new LinkedList<>();
this.childNodesList = new LinkedList<>();
this.isLeaf = false;
}
/**
* 自定义K排序方式的构造函数
*/
public Node(Comparator<Object> kComparator) {
this();
this.kComparator = kComparator;
}
/**
* 比较两个key，如果没有传入自定义排序方式则采用默认的升序
*/
private int compare(Object key1, Object key2) {
return this.kComparator == null ? ((Comparable<Object>) key2).compareTo(key1) : kComparator.compare(key1, key2);
}
public void setIsLeaf(boolean isLeaf) {
this.isLeaf = isLeaf;
}
public boolean getIsLeaf() {
return this.isLeaf;
}
public void setParentNode(Node parentNode) {
this.parentNode = parentNode;
}
public Node getParentNode() {
return parentNode;
}
/**
* 结点中关键字的个数
*/
public int keySize() {
return this.keyList.size();
}
/**
* 采用二分查找在结点内查找关键字
*/
public SearchResult searchResult(Object key) {
int begin = 0;
int end = this.keySize() - 1;
int mid = (begin + end) / 2;
boolean isExist = false;
int index = 0;
//二分查找
while (begin < end) {
mid = (begin + end) / 2;
Object midValue = this.keyList.get(mid);
int compareRe = compare(midValue, key);
//找到了
if (compareRe == 0) {
break;
} else {
if (compareRe > 0) {
//在中点右边
begin = mid + 1;
} else {
end = mid - 1;
}
}
}
//二分查找结束，判断结果;三个元素以上才是正经二分，只有两个或一个元素属于边界条件要着重考虑
if (begin < end) {
//找到了
isExist = true;
index = mid;
} else if (begin == end) {
Object midKey = this.keyList.get(begin);
int comRe = compare(midKey, key);
if (comRe == 0) {
isExist = true;
index = begin;
} else if (comRe > 0) {
index = begin + 1;
} else {
index = begin;
}
} else {
index = begin;
}
return new SearchResult(isExist, index, null);
}
}
/**
* 默认3阶树
*/
private final Integer DEFAULT_ORDER = 3;
/**
* 树阶
*/
private int order = DEFAULT_ORDER;
/**
* 结点中关键字个数的最大值
*/
private int maxKeySize = order - 1;
/**
* 结点的最小关键字数
*/
private int nonLeafMinKeys = (int) Math.ceil(order / 2.0) - 1;
/**
* 根结点
*/
private Node root;
/**
* 比较函数对象
*/
private Comparator<Object> kComparator;
/**
* 构造一棵自然排序的B树
*/
MyBTree() {
Node root = new Node();
this.root = root;
root.setIsLeaf(true);
}
/**
* 构造一棵order阶 的B树
*/
MyBTree(int order) {
this();
this.order = order;
this.maxKeySize = order - 1;
this.nonLeafMinKeys = (int) Math.ceil(order / 2.0) - 1;
}
/**
* 在以node为根的树内搜索key项
*/
private SearchResult search(Node node, Object key) {
SearchResult re = node.searchResult(key);
if (re.isExist()) {
return new SearchResult(true, re.getIndex(), node);
} else {
// 叶子结点
if (node.getIsLeaf()) {
return new SearchResult(false, re.getIndex(), node);
}
int index = re.getIndex();
//递归搜索子结点--index是在查询结点内关键字的下标 也是子结点的下标
return search(node.childNodesList.get(index), key);
}
}
public boolean insertKey(Object key) {
// 查询key在树中的结点情况
SearchResult searchResult = search(root, key);
if (searchResult.isExist()) {
//已存在key，直接返回
return false;
}
// 找出根结点
if (null == searchResult.getNode().parentNode) {
return insertKey(root, searchResult.getIndex(), key);
} else {
return insertKey(searchResult.getNode(), searchResult.getIndex(), key);
}
}
private boolean insertKey(Node node, int index, Object key) {
node.keyList.add(index, key);
if (node.keyList.size() > maxKeySize) {
// 分裂
splitNode(node);
}
return true;
}
/**
* 分裂结点
*/
private void splitNode(Node node) {
//取结点中间key下标
int midIndex = node.keyList.size() / 2;
Object key = node.keyList.get(midIndex);
Node newNode = new Node();
// 新结点采用原来结点是否是叶子结点的值
newNode.setIsLeaf(node.getIsLeaf());
// 新结点取源结点的(midIndex,node.keyList.size()-1]的关键字
for (int i = midIndex + 1; i < node.keyList.size(); i++) {
newNode.keyList.add(node.keyList.get(i));
}
// 源结点只留下标为[0,midIndex)的关键字
if (node.keyList.size() > midIndex) {
node.keyList.subList(midIndex, node.keyList.size()).clear();
}
// 若叶子结点，需要将原来结点的孩子结点也进行分裂，新结点取(midIndex,node.keyList.size()-1]的孩子结点
if (!node.isLeaf) {
for (int i = midIndex + 1; i < node.childNodesList.size(); i++) {
newNode.childNodesList.add(node.childNodesList.get(i));
// 修改孩子结点的双亲结点为新结点
node.childNodesList.get(i).setParentNode(newNode);
}
// 源结点只留下标为[0,midIndex]的孩子结点
if (node.childNodesList.size() > midIndex + 1) {
node.childNodesList.subList(midIndex + 1, node.childNodesList.size()).clear();
}
}
Node father = node.getParentNode();
if (null == father) {
// 若结点的双亲结点为null,说明是根结点进行的分裂，需要新增结点作为根结点
father = new Node();
father.childNodesList.add(node);
father.setIsLeaf(false);
father.keyList.add(key);
father.childNodesList.add(newNode);
node.parentNode = father;
newNode.parentNode = father;
} else {
newNode.parentNode = father;
SearchResult re = father.searchResult(key);
father.keyList.add(re.getIndex(), key);
father.childNodesList.add(re.getIndex() + 1, newNode);
// 若双亲的关键字个数超出最大允许值，则继续分裂
if (father.keyList.size() > maxKeySize) {
splitNode(father);
}
}
if (father.getParentNode() == null) {
this.root = father;
}
}
public boolean deleteKey(Object key) {
SearchResult searchResult = search(root, key);
// 没有找到key 直接结束
if (!searchResult.isExist()) {
return false;
}
Node keyInNode = searchResult.getNode();
// 是否是叶子结点
if (!keyInNode.getIsLeaf()) {
// 非叶子结点，取第i个孩子结点中的最大关键字
Node keyChildNode = keyInNode.childNodesList.get(searchResult.getIndex());
//如果孩子结点不是叶子结点，去找这个子树到叶子结点中最大的关键字，与key互换位置
if (!keyChildNode.getIsLeaf()) {
keyChildNode = getMaxLeaf(keyChildNode);
}
Object childMinkey = keyChildNode.keyList.get(keyChildNode.keyList.size() - 1);
keyInNode.keyList.add(searchResult.getIndex(), childMinkey);
keyInNode.keyList.remove(key);
keyChildNode.keyList.remove(childMinkey);
keyChildNode.keyList.add(key);
keyInNode = keyChildNode;
}
return deleteKey(keyInNode, key);
}
/**
* 获取node结点到最右侧子结点的叶子结点
* @param node
* @return
*/
private Node getMaxLeaf(Node node) {
Node keyChildNode = node.childNodesList.get(node.childNodesList.size() - 1);
if (!keyChildNode.getIsLeaf()) {
getMaxLeaf(keyChildNode);
}
return keyChildNode;
}
public boolean deleteKey(Node node, Object key) {
// 如果需要删除关键字的结点，原本的关键字个数超过Math.ceil(order / 2.0) - 1
if (node.keyList.size() > nonLeafMinKeys) {
node.keyList.remove(key);
return true;
}
// 如果需要删除关键字的结点，原本的关键字个数不超过Math.ceil(order / 2.0) - 1
if (node.keyList.size() == nonLeafMinKeys) {
doManageNode(node, key);
}
return true;
}
private void doManageNode(Node node, Object key) {
if (null == node.parentNode) {
return;
}
// 找兄弟结点中是否存在关键字个数超过Math.ceil(order / 2.0) - 1的
int nodeIndex = node.parentNode.childNodesList.indexOf(node);
Node leftNode = null;
Node rightNode = null;
if (0 <= nodeIndex && nodeIndex < node.parentNode.childNodesList.size() - 1) {
rightNode = node.parentNode.childNodesList.get(nodeIndex + 1);
}
if (0 < nodeIndex) {
leftNode = node.parentNode.childNodesList.get(nodeIndex - 1);
}
if (null != leftNode && leftNode.keyList.size() > nonLeafMinKeys) {
node.parentNode.keyList.add(nodeIndex - 1, leftNode.keyList.get(leftNode.keyList.size() - 1));
node.keyList.add(0, node.parentNode.keyList.get(node.parentNode.keyList.size() - 1));
node.parentNode.keyList.remove(node.parentNode.keyList.size() - 1);
node.keyList.remove(key);
leftNode.keyList.remove(leftNode.keyList.get(leftNode.keyList.size() - 1));
return;
}
if (null != rightNode && rightNode.keyList.size() > nonLeafMinKeys) {
node.parentNode.keyList.add(nodeIndex + 1, rightNode.keyList.get(0));
node.keyList.add(node.parentNode.keyList.get(nodeIndex));
node.parentNode.keyList.remove(nodeIndex);
node.keyList.remove(key);
rightNode.keyList.remove(rightNode.keyList.get(0));
return;
}
// 左右兄弟结点的关键字个数都不足的话，合并兄弟结点，下放一个双亲结点的关键字
if (leftNode != null) {
//合并结点
node = merge(leftNode, node);
node.keyList.remove(key);
if (node.parentNode.keyList.size() < nonLeafMinKeys && null != node.parentNode.parentNode) {
// 寻找结点合并
doManageNode(node.parentNode, null);
}
if (null == node.parentNode.parentNode && node.parentNode.keyList.isEmpty()) {
root = node;
}
return;
}
if (rightNode != null) {
//合并结点
node = merge(node, rightNode);
node.keyList.remove(key);
if (node.parentNode.keyList.size() < nonLeafMinKeys && null != node.parentNode.parentNode) {
// 寻找结点合并
doManageNode(node.parentNode, null);
}
if (null == node.parentNode.parentNode && node.parentNode.keyList.isEmpty()) {
root = node;
}
}
}
private Node merge(Node leftNode, Node rightNode) {
int index = leftNode.parentNode.childNodesList.indexOf(leftNode);
leftNode.keyList.add(leftNode.parentNode.keyList.get(index));
leftNode.parentNode.keyList.remove(index);
leftNode.keyList.addAll(rightNode.keyList);
if (!rightNode.isLeaf) {
leftNode.childNodesList.addAll(rightNode.childNodesList);
}
leftNode.parentNode.childNodesList.remove(rightNode);
return leftNode;
}
public static void main(String[] args) {
List<Integer> save = new ArrayList<Integer>(30);
MyBTree<Integer> btree = new MyBTree<>(3);
save.add(45);
save.add(24);
save.add(90);
save.add(3);
save.add(27);
save.add(70);
save.add(100);
save.add(62);
for (int r : save) {
System.out.print(r + " ");
btree.insertKey(r);
}
System.out.println("");
System.out.println("----------------------");
btree.output();
System.out.println("----------------------");
btree.deleteKey(45);
btree.output();
}
public void output() {
Queue<Node> queue = new LinkedList<>();
queue.offer(this.root);
while (!queue.isEmpty()) {
Node node = queue.poll();
for (int i = 0; i < node.keyList.size(); ++i) {
System.out.print(node.keyList.get(i) + " ");
}
System.out.println();
if (!node.getIsLeaf()) {
for (int i = 0; i <= node.childNodesList.size() - 1; ++i) {
queue.offer(node.childNodesList.get(i));
}
}
}
}
}
本文章为转载内容，我们尊重原作者对文章享有的著作权。如有内容错误或侵权问题，欢迎原作者联系我们进行内容更正或删除文章。
