M阶B+树的定义：
- 任意非叶子结点最多有M个子节点；且M>2；
- 除根结点以外的非叶子结点至少有 M/2个子节点；
- 根结点至少有2个子节点；
- 除根节点外每个结点存放至少M/2和至多M个关键字；（至少2个关键字）
- 非叶子结点的子树指针与关键字个数相同；
- 所有结点的关键字：K[1], K[2], …, K[M]；且K[i] < K[i+1]；
- 非叶子结点的子树指针P[i]，指向关键字值属于[K[i], K[i+1])的子树；
- 所有叶子结点位于同一层；
- 为所有叶子结点增加一个链指针；
- 所有关键字都在叶子结点出现；
B+树是对B树的一种变形树，它与B树的差异在于：
- 有k个子结点的结点必然有k个关键码；
- 非叶结点仅具有索引作用，跟记录有关的信息均存放在叶结点中。
- 树的所有叶结点构成一个有序链表，可以按照关键码排序的次序遍历全部记录。
如下图，是一个B+树:
下图是B+树的插入动画：
代码如下：
BPlusTree定义如下：
/** * B+树的定义： * 1.任意非叶子结点最多有M个子节点；且M>2；M为B+树的阶数 * 2.除根结点以外的非叶子结点至少有 (M+1)/2个子节点； * 3.根结点至少有2个子节点； * 4.除根节点外每个结点存放至少（M-1）/2和至多M-1个关键字；（至少1个关键字） * 5.非叶子结点的子树指针比关键字多1个； * 6.非叶子节点的所有key按升序存放，假设节点的关键字分别为K[0], K[1] … K[M-2],指向子女的指针分别为P[0], P[1]…P[M-1]。则有： * P[0] < K[0] <= P[1] < K[1] …..< K[M-2] <= P[M-1] * 7.所有叶子结点位于同一层； * 8.为所有叶子结点增加一个链指针； * 9.所有关键字都在叶子结点出现 */ @SuppressWarnings("all") public class BPlusTree<K extends Comparable<K>, V> { // 根节点 protected BPlusNode<K, V> root; // 阶数，M值 protected int order; // 叶子节点的链表头 protected BPlusNode<K, V> head; // 树高 protected int height = 0; public BPlusNode<K, V> getHead() { return head; } public void setHead(BPlusNode<K, V> head) { this.head = head; } public BPlusNode<K, V> getRoot() { return root; } public void setRoot(BPlusNode<K, V> root) { this.root = root; } public int getOrder() { return order; } public void setOrder(int order) { this.order = order; } public void setHeight(int height) { this.height = height; } public int getHeight() { return height; } public V get(K key) { return root.get(key); } public V remove(K key) { return root.remove(key, this); } public void insertOrUpdate(K key, V value) { root.insertOrUpdate(key, value, this); } public BPlusTree(int order) { if (order < 3) { System.out.print("order must be greater than 2"); System.exit(0); } this.order = order; root = new BPlusNode<K, V>(true, true); head = root; } public void printBPlusTree() { this.root.printBPlusTree(0); } }
BplusNode定义如下：
@SuppressWarnings("all")
public class BPlusNode<K extends Comparable<K>, V> {
// 是否为叶子节点
protected boolean isLeaf;
// 是否为根节点
protected boolean isRoot;
// 父节点
protected BPlusNode<K, V> parent;
// 叶节点的前节点
protected BPlusNode<K, V> previous;
// 叶节点的后节点
protected BPlusNode<K, V> next;
// 节点的关键字列表
protected List<Entry<K, V>> entries;
// 子节点列表
protected List<BPlusNode<K, V>> children;
public BPlusNode(boolean isLeaf) {
this.isLeaf = isLeaf;
entries = new ArrayList();
if (!isLeaf) {
children = new ArrayList();
}
}
public BPlusNode(boolean isLeaf, boolean isRoot) {
this(isLeaf);
this.isRoot = isRoot;
}
public V get(K key) {
//如果是叶子节点
if (isLeaf) {
int low = 0, high = entries.size() - 1, mid;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
return entries.get(mid).getValue();
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
//未找到所要查询的对象
return null;
}
//如果不是叶子节点
//如果key小于节点最左边的key，沿第一个子节点继续搜索
if (key.compareTo(entries.get(0).getKey()) < 0) {
return children.get(0).get(key);
//如果key大于等于节点最右边的key，沿最后一个子节点继续搜索
} else if (key.compareTo(entries.get(entries.size() - 1).getKey()) >= 0) {
return children.get(children.size() - 1).get(key);
//否则沿比key大的前一个子节点继续搜索
} else {
int low = 0, high = entries.size() - 1, mid = 0;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
return children.get(mid + 1).get(key);
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
return children.get(low).get(key);
}
}
public void insertOrUpdate(K key, V value, BPlusTree<K, V> tree) {
//如果是叶子节点
if (isLeaf) {
//不需要分裂，直接插入或更新
if (contains(key) != -1 || entries.size() < tree.getOrder()) {
insertOrUpdate(key, value);
if (tree.getHeight() == 0) {
tree.setHeight(1);
}
return;
}
//需要分裂
//分裂成左右两个节点
BPlusNode<K, V> left = new BPlusNode<K, V>(true);
BPlusNode<K, V> right = new BPlusNode<K, V>(true);
//设置链接
if (previous != null) {
previous.next = left;
left.previous = previous;
}
if (next != null) {
next.previous = right;
right.next = next;
}
if (previous == null) {
tree.setHead(left);
}
left.next = right;
right.previous = left;
previous = null;
next = null;
//复制原节点关键字到分裂出来的新节点
copy2Nodes(key, value, left, right, tree);
//如果不是根节点
if (parent != null) {
//调整父子节点关系
int index = parent.children.indexOf(this);
parent.children.remove(this);
left.parent = parent;
right.parent = parent;
parent.children.add(index, left);
parent.children.add(index + 1, right);
parent.entries.add(index, right.entries.get(0));
entries = null; //删除当前节点的关键字信息
children = null; //删除当前节点的孩子节点引用
//父节点插入或更新关键字
parent.updateInsert(tree);
parent = null; //删除当前节点的父节点引用
//如果是根节点
} else {
isRoot = false;
BPlusNode<K, V> parent = new BPlusNode<K, V>(false, true);
tree.setRoot(parent);
left.parent = parent;
right.parent = parent;
parent.children.add(left);
parent.children.add(right);
parent.entries.add(right.entries.get(0));
entries = null;
children = null;
}
return;
}
//如果不是叶子节点
//如果key小于等于节点最左边的key，沿第一个子节点继续搜索
if (key.compareTo(entries.get(0).getKey()) < 0) {
children.get(0).insertOrUpdate(key, value, tree);
//如果key大于节点最右边的key，沿最后一个子节点继续搜索
} else if (key.compareTo(entries.get(entries.size() - 1).getKey()) >= 0) {
children.get(children.size() - 1).insertOrUpdate(key, value, tree);
//否则沿比key大的前一个子节点继续搜索
} else {
int low = 0, high = entries.size() - 1, mid = 0;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
children.get(mid + 1).insertOrUpdate(key, value, tree);
break;
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
if (low > high) {
children.get(low).insertOrUpdate(key, value, tree);
}
}
}
private void copy2Nodes(K key, V value, BPlusNode<K, V> left,
BPlusNode<K, V> right, BPlusTree<K, V> tree) {
//左右两个节点关键字长度
int leftSize = (tree.getOrder() + 1) / 2 + (tree.getOrder() + 1) % 2;
boolean b = false;//用于记录新元素是否已经被插入
for (int i = 0; i < entries.size(); i++) {
if (leftSize != 0) {
leftSize--;
if (!b && entries.get(i).getKey().compareTo(key) > 0) {
left.entries.add(new SimpleEntry<K, V>(key, value));
b = true;
i--;
} else {
left.entries.add(entries.get(i));
}
} else {
if (!b && entries.get(i).getKey().compareTo(key) > 0) {
right.entries.add(new SimpleEntry<K, V>(key, value));
b = true;
i--;
} else {
right.entries.add(entries.get(i));
}
}
}
if (!b) {
right.entries.add(new SimpleEntry<K, V>(key, value));
}
}
/**
* 插入节点后中间节点的更新
*/
protected void updateInsert(BPlusTree<K, V> tree) {
//如果子节点数超出阶数，则需要分裂该节点
if (children.size() > tree.getOrder()) {
//分裂成左右两个节点
BPlusNode<K, V> left = new BPlusNode<K, V>(false);
BPlusNode<K, V> right = new BPlusNode<K, V>(false);
//左右两个节点子节点的长度
int leftSize = (tree.getOrder() + 1) / 2 + (tree.getOrder() + 1) % 2;
int rightSize = (tree.getOrder() + 1) / 2;
//复制子节点到分裂出来的新节点，并更新关键字
for (int i = 0; i < leftSize; i++) {
left.children.add(children.get(i));
children.get(i).parent = left;
}
for (int i = 0; i < rightSize; i++) {
right.children.add(children.get(leftSize + i));
children.get(leftSize + i).parent = right;
}
for (int i = 0; i < leftSize - 1; i++) {
left.entries.add(entries.get(i));
}
for (int i = 0; i < rightSize - 1; i++) {
right.entries.add(entries.get(leftSize + i));
}
//如果不是根节点
if (parent != null) {
//调整父子节点关系
int index = parent.children.indexOf(this);
parent.children.remove(this);
left.parent = parent;
right.parent = parent;
parent.children.add(index, left);
parent.children.add(index + 1, right);
parent.entries.add(index, entries.get(leftSize - 1));
entries = null;
children = null;
//父节点更新关键字
parent.updateInsert(tree);
parent = null;
//如果是根节点
} else {
isRoot = false;
BPlusNode<K, V> parent = new BPlusNode<K, V>(false, true);
tree.setRoot(parent);
tree.setHeight(tree.getHeight() + 1);
left.parent = parent;
right.parent = parent;
parent.children.add(left);
parent.children.add(right);
parent.entries.add(entries.get(leftSize - 1));
entries = null;
children = null;
}
}
}
/**
* 删除节点后中间节点的更新
*/
protected void updateRemove(BPlusTree<K, V> tree) {
// 如果子节点数小于M / 2或者小于2，则需要合并节点
if (children.size() < tree.getOrder() / 2 || children.size() < 2) {
if (isRoot) {
// 如果是根节点并且子节点数大于等于2，OK
if (children.size() >= 2) return;
// 否则与子节点合并
BPlusNode<K, V> root = children.get(0);
tree.setRoot(root);
tree.setHeight(tree.getHeight() - 1);
root.parent = null;
root.isRoot = true;
entries = null;
children = null;
return;
}
//计算前后节点
int currIdx = parent.children.indexOf(this);
int prevIdx = currIdx - 1;
int nextIdx = currIdx + 1;
BPlusNode<K, V> previous = null, next = null;
if (prevIdx >= 0) {
previous = parent.children.get(prevIdx);
}
if (nextIdx < parent.children.size()) {
next = parent.children.get(nextIdx);
}
// 如果前节点子节点数大于M / 2并且大于2，则从其处借补
if (previous != null
&& previous.children.size() > tree.getOrder() / 2
&& previous.children.size() > 2) {
//前叶子节点末尾节点添加到首位
int idx = previous.children.size() - 1;
BPlusNode<K, V> borrow = previous.children.get(idx);
previous.children.remove(idx);
borrow.parent = this;
children.add(0, borrow);
int preIndex = parent.children.indexOf(previous);
entries.add(0, parent.entries.get(preIndex));
parent.entries.set(preIndex, previous.entries.remove(idx - 1));
return;
}
// 如果后节点子节点数大于M / 2并且大于2，则从其处借补
if (next != null
&& next.children.size() > tree.getOrder() / 2
&& next.children.size() > 2) {
//后叶子节点首位添加到末尾
BPlusNode<K, V> borrow = next.children.get(0);
next.children.remove(0);
borrow.parent = this;
children.add(borrow);
int preIndex = parent.children.indexOf(this);
entries.add(parent.entries.get(preIndex));
parent.entries.set(preIndex, next.entries.remove(0));
return;
}
// 同前面节点合并
if (previous != null
&& (previous.children.size() <= tree.getOrder() / 2
|| previous.children.size() <= 2)) {
for (int i = 0; i < children.size(); i++) {
previous.children.add(children.get(i));
}
for (int i = 0; i < previous.children.size(); i++) {
previous.children.get(i).parent = this;
}
int indexPre = parent.children.indexOf(previous);
previous.entries.add(parent.entries.get(indexPre));
for (int i = 0; i < entries.size(); i++) {
previous.entries.add(entries.get(i));
}
children = previous.children;
entries = previous.entries;
//更新父节点的关键字列表
parent.children.remove(previous);
previous.parent = null;
previous.children = null;
previous.entries = null;
parent.entries.remove(parent.children.indexOf(this));
if ((!parent.isRoot
&& (parent.children.size() >= tree.getOrder() / 2
&& parent.children.size() >= 2))
|| parent.isRoot && parent.children.size() >= 2) {
return;
}
parent.updateRemove(tree);
return;
}
// 同后面节点合并
if (next != null
&& (next.children.size() <= tree.getOrder() / 2
|| next.children.size() <= 2)) {
for (int i = 0; i < next.children.size(); i++) {
BPlusNode<K, V> child = next.children.get(i);
children.add(child);
child.parent = this;
}
int index = parent.children.indexOf(this);
entries.add(parent.entries.get(index));
for (int i = 0; i < next.entries.size(); i++) {
entries.add(next.entries.get(i));
}
parent.children.remove(next);
next.parent = null;
next.children = null;
next.entries = null;
parent.entries.remove(parent.children.indexOf(this));
if ((!parent.isRoot && (parent.children.size() >= tree.getOrder() / 2
&& parent.children.size() >= 2))
|| parent.isRoot && parent.children.size() >= 2) {
return;
}
parent.updateRemove(tree);
return;
}
}
}
public V remove(K key, BPlusTree<K, V> tree) {
//如果是叶子节点
if (isLeaf) {
//如果不包含该关键字，则直接返回
if (contains(key) == -1) {
return null;
}
//如果既是叶子节点又是根节点，直接删除
if (isRoot) {
if (entries.size() == 1) {
tree.setHeight(0);
}
return remove(key);
}
//如果关键字数大于M / 2，直接删除
if (entries.size() > tree.getOrder() / 2 && entries.size() > 2) {
return remove(key);
}
//如果自身关键字数小于M / 2，并且前节点关键字数大于M / 2，则从其处借补
if (previous != null &&
previous.parent == parent
&& previous.entries.size() > tree.getOrder() / 2
&& previous.entries.size() > 2) {
//添加到首位
int size = previous.entries.size();
entries.add(0, previous.entries.remove(size - 1));
int index = parent.children.indexOf(previous);
parent.entries.set(index, entries.get(0));
return remove(key);
}
//如果自身关键字数小于M / 2，并且后节点关键字数大于M / 2，则从其处借补
if (next != null
&& next.parent == parent
&& next.entries.size() > tree.getOrder() / 2
&& next.entries.size() > 2) {
entries.add(next.entries.remove(0));
int index = parent.children.indexOf(this);
parent.entries.set(index, next.entries.get(0));
return remove(key);
}
//同前面节点合并
if (previous != null
&& previous.parent == parent
&& (previous.entries.size() <= tree.getOrder() / 2
|| previous.entries.size() <= 2)) {
V returnValue = remove(key);
for (int i = 0; i < entries.size(); i++) {
//将当前节点的关键字添加到前节点的末尾
previous.entries.add(entries.get(i));
}
entries = previous.entries;
parent.children.remove(previous);
previous.parent = null;
previous.entries = null;
//更新链表
if (previous.previous != null) {
BPlusNode<K, V> temp = previous;
temp.previous.next = this;
previous = temp.previous;
temp.previous = null;
temp.next = null;
} else {
tree.setHead(this);
previous.next = null;
previous = null;
}
parent.entries.remove(parent.children.indexOf(this));
if ((!parent.isRoot && (parent.children.size() >= tree.getOrder() / 2
&& parent.children.size() >= 2))
|| parent.isRoot && parent.children.size() >= 2) {
return returnValue;
}
parent.updateRemove(tree);
return returnValue;
}
//同后面节点合并
if (next != null
&& next.parent == parent
&& (next.entries.size() <= tree.getOrder() / 2
|| next.entries.size() <= 2)) {
V returnValue = remove(key);
for (int i = 0; i < next.entries.size(); i++) {
//从首位开始添加到末尾
entries.add(next.entries.get(i));
}
next.parent = null;
next.entries = null;
parent.children.remove(next);
//更新链表
if (next.next != null) {
BPlusNode<K, V> temp = next;
temp.next.previous = this;
next = temp.next;
temp.previous = null;
temp.next = null;
} else {
next.previous = null;
next = null;
}
//更新父节点的关键字列表
parent.entries.remove(parent.children.indexOf(this));
if ((!parent.isRoot && (parent.children.size() >= tree.getOrder() / 2
&& parent.children.size() >= 2))
|| parent.isRoot && parent.children.size() >= 2) {
return returnValue;
}
parent.updateRemove(tree);
return returnValue;
}
}
/*如果不是叶子节点*/
//如果key小于等于节点最左边的key，沿第一个子节点继续搜索
if (key.compareTo(entries.get(0).getKey()) < 0) {
return children.get(0).remove(key, tree);
//如果key大于节点最右边的key，沿最后一个子节点继续搜索
} else if (key.compareTo(entries.get(entries.size() - 1).getKey()) >= 0) {
return children.get(children.size() - 1).remove(key, tree);
//否则沿比key大的前一个子节点继续搜索
} else {
int low = 0, high = entries.size() - 1, mid = 0;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
return children.get(mid + 1).remove(key, tree);
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
return children.get(low).remove(key, tree);
}
}
// 判断当前节点是否包含该关键字
protected int contains(K key) {
int low = 0, high = entries.size() - 1, mid;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
return mid;
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
return -1;
}
// 插入到当前节点的关键字中
protected void insertOrUpdate(K key, V value) {
//二叉查找，插入
int low = 0, high = entries.size() - 1, mid;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
entries.get(mid).setValue(value);
break;
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
if (low > high) {
entries.add(low, new SimpleEntry<K, V>(key, value));
}
}
// 删除节点
protected V remove(K key) {
int low = 0, high = entries.size() - 1, mid;
int comp;
while (low <= high) {
mid = (low + high) / 2;
comp = entries.get(mid).getKey().compareTo(key);
if (comp == 0) {
return entries.remove(mid).getValue();
} else if (comp < 0) {
low = mid + 1;
} else {
high = mid - 1;
}
}
return null;
}
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append("isRoot: ");
sb.append(isRoot);
sb.append(", ");
sb.append("isLeaf: ");
sb.append(isLeaf);
sb.append(", ");
sb.append("keys: ");
for (Entry<K, V> entry : entries) {
sb.append(entry.getKey());
sb.append(", ");
}
sb.append(", ");
return sb.toString();
}
public void printBPlusTree(int index) {
if (this.isLeaf) {
System.out.print("层级：" + index + ",叶子节点，keys为: ");
for (int i = 0; i < entries.size(); ++i)
System.out.print(entries.get(i) + " ");
System.out.println();
} else {
System.out.print("层级：" + index + ",非叶子节点，keys为: ");
for (int i = 0; i < entries.size(); ++i)
System.out.print(entries.get(i) + " ");
System.out.println();
for (int i = 0; i < children.size(); ++i)
children.get(i).printBPlusTree(index + 1);
}
}
}
测试类：
public class BPlusTreeTest { // 测试 public static void main(String[] args) { int size = 10; int order = 3; testRandomInsert(size, order); testOrderInsert(size, order); testRandomSearch(size, order); testOrderSearch(size, order); testRandomRemove(size, order); testOrderRemove(size, order); } private static void testOrderRemove(int size, int order) { BPlusTree<Integer, Integer> tree = new BPlusTree<Integer, Integer>(order); System.out.println("\nTest order remove " + size + " datas, of order:" + order); System.out.println("Begin order insert..."); for (int i = 0; i < size; i++) { tree.insertOrUpdate(i, i); } tree.printBPlusTree(); System.out.println("Begin order remove..."); long current = System.currentTimeMillis(); for (int j = 0; j < size; j++) { if (tree.remove(j) == null) { System.err.println("得不到数据:" + j); break; } } long duration = System.currentTimeMillis() - current; System.out.println("time elpsed for duration: " + duration); tree.printBPlusTree(); System.out.println(tree.getHeight()); } private static void testRandomRemove(int size, int order) { BPlusTree<Integer, Integer> tree = new BPlusTree<Integer, Integer>(order); System.out.println("\nTest random remove " + size + " datas, of order:" + order); Random random = new Random(); boolean[] a = new boolean[size + 10]; List<Integer> list = new ArrayList<Integer>(); int randomNumber = 0; System.out.println("Begin random insert..."); for (int i = 0; i < size; i++) { randomNumber = random.nextInt(size); a[randomNumber] = true; list.add(randomNumber); tree.insertOrUpdate(randomNumber, randomNumber); } tree.printBPlusTree(); System.out.println("Begin random remove..."); long current = System.currentTimeMillis(); for (int j = 0; j < size; j++) { randomNumber = list.get(j); if (a[randomNumber]) { if (tree.remove(randomNumber) == null) { System.err.println("得不到数据:" + randomNumber); break; } else { a[randomNumber] = false; } } } long duration = System.currentTimeMillis() - current; System.out.println("time elpsed for duration: " + duration); tree.printBPlusTree(); System.out.println(tree.getHeight()); } private static void testOrderSearch(int size, int order) { BPlusTree<Integer, Integer> tree = new BPlusTree<Integer, Integer>(order); System.out.println("\nTest order search " + size + " datas, of order:" + order); System.out.println("Begin order insert..."); for (int i = 0; i < size; i++) { tree.insertOrUpdate(i, i); } tree.printBPlusTree(); System.out.println("Begin order search..."); long current = System.currentTimeMillis(); for (int j = 0; j < size; j++) { if (tree.get(j) == null) { System.err.println("得不到数据:" + j); break; } } long duration = System.currentTimeMillis() - current; System.out.println("time elpsed for duration: " + duration); } private static void testRandomSearch(int size, int order) { BPlusTree<Integer, Integer> tree = new BPlusTree<Integer, Integer>(order); System.out.println("\nTest random search " + size + " datas, of order:" + order); Random random = new Random(); boolean[] a = new boolean[size + 10]; int randomNumber = 0; System.out.println("Begin random insert..."); for (int i = 0; i < size; i++) { randomNumber = random.nextInt(size); a[randomNumber] = true; tree.insertOrUpdate(randomNumber, randomNumber); } tree.printBPlusTree(); System.out.println("Begin random search..."); long current = System.currentTimeMillis(); for (int j = 0; j < size; j++) { randomNumber = random.nextInt(size); if (a[randomNumber]) { if (tree.get(randomNumber) == null) { System.err.println("得不到数据:" + randomNumber); break; } } } long duration = System.currentTimeMillis() - current; System.out.println("time elpsed for duration: " + duration); } private static void testRandomInsert(int size, int order) { BPlusTree<Integer, Integer> tree = new BPlusTree<Integer, Integer>(order); System.out.println("\nTest random insert " + size + " datas, of order:" + order); Random random = new Random(); int randomNumber = 0; long current = System.currentTimeMillis(); for (int i = 0; i < size; i++) { randomNumber = random.nextInt(size * 10); System.out.print(randomNumber + " "); tree.insertOrUpdate(randomNumber, randomNumber); } long duration = System.currentTimeMillis() - current; System.out.println("time elpsed for duration: " + duration); tree.printBPlusTree(); System.out.println(tree.getHeight()); } private static void testOrderInsert(int size, int order) { BPlusTree<Integer, Integer> tree = new BPlusTree<Integer, Integer>(order); System.out.println("\nTest order insert " + size + " datas, of order:" + order); long current = System.currentTimeMillis(); for (int i = 0; i < size; i++) { tree.insertOrUpdate(i, i); } long duration = System.currentTimeMillis() - current; System.out.println("time elpsed for duration: " + duration); tree.printBPlusTree(); } }