/// <summary>
/// B+树节点
/// </summary>
/// <param name="tree">包含该节点的树</param>
/// <param name="parent">节点的父节点</param>
/// <param name="indexInParent">在父节点中的索引</param>
/// <param name="isLeaf">是否为叶子节点</param>
public BPlusTreeNode(BPlusTreeLong tree, BPlusTreeNode parent, int indexInParent, bool isLeaf)
{
if(tree == null)
throw new ArgumentNullException("tree");
this.Tree = tree;
this.Parent = parent;
this.IsLeaf = isLeaf;
this.IndexInParent = -1;
this.BlockNumber = StoredConstants.NullBlockNumber;
this.Capacity = tree.NodeCapacity;
this.Dirty = true;
this.Clear();
// 存在父节点
if (parent != null && indexInParent >= 0)
{
// B+树 父节点中键值数与子节点数量相等
if (indexInParent > this.Capacity)
{
throw new BPlusTreeException("parent index too large");
}
// 建立与父节点关系
this.Parent.ChildNodes[indexInParent] = this;
this.BlockNumber = this.Parent.ChildValues[indexInParent];
this.IndexInParent = indexInParent;
}
}
/// <summary>
/// 加载指定插入的索引点的节点对象
/// </summary>
/// <param name="insertPosition">指定插入的索引点</param>
/// <returns>节点对象</returns>
private BPlusTreeNode LoadNodeAtIndex(int insertPosition)
{
if (this.IsLeaf) // 只对中间节点应用有效
{
throw new BPlusTreeException("cannot materialize child for leaf");
}
// 获取指定位置对应子节点的块序号
long childBlockNumber = this.ChildValues[insertPosition];
if (childBlockNumber == StoredConstants.NullBlockNumber)
{
throw new BPlusTreeException("can't search null subtree at position " + insertPosition + " in " + this.BlockNumber);
}
// 节点对象已经存在吗
BPlusTreeNode node = this.ChildNodes[insertPosition];
if (node != null)
{
return node;
}
// 如果不存在则从块中加载
node = new BPlusTreeNode(this.Tree, this, insertPosition, true); // dummy isLeaf item
node.LoadFromBlock(childBlockNumber);
this.ChildNodes[insertPosition] = node;
// 该节点不在是终端节点
this.Tree.ForgetTerminalNode(this); // 我已经有了一个具体化的子节点，我不再是终端节点
return node;
}
/// <summary>
/// 查找指定索引处的下一个键值，如果没有则遍历右子树，如果仍没找到则返回空
/// </summary>
/// <param name="atIndex">开始查找的索引</param>
/// <param name="foundInLeaf">找到键值的叶子节点</param>
/// <param name="foundKey">找到的键值</param>
private void TraverseToFollowingKey(int atIndex, out BPlusTreeNode foundInLeaf, out string foundKey)
{
foundInLeaf = null;
foundKey = null;
bool lookInParent = false;
if (this.IsLeaf)
{
lookInParent = (atIndex >= this.Capacity) || (this.ChildKeys[atIndex] == null);
}
else
{
lookInParent = (atIndex > this.Capacity) || (atIndex > 0 && this.ChildKeys[atIndex - 1] == null);
}
if (lookInParent)
{
// if it's anywhere it's in the next child of parent
if (this.Parent != null && this.IndexInParent >= 0)
{
this.Parent.TraverseToFollowingKey(this.IndexInParent + 1, out foundInLeaf, out foundKey);
return;
}
else
{
return; // no such following key
}
}
if (this.IsLeaf)
{
// leaf, we found it.
foundInLeaf = this;
foundKey = this.ChildKeys[atIndex];
return;
}
else
{
// nonleaf, look in child (if there is one)
if (atIndex == 0 || this.ChildKeys[atIndex - 1] != null)
{
BPlusTreeNode child = this.LoadNodeAtIndex(atIndex);
child.TraverseToFollowingKey(0, out foundInLeaf, out foundKey);
}
}
}
/// <summary>
/// 在节点中插入键值对并作为叶子节点
/// </summary>
/// <param name="key">叶子节点的键</param>
/// <param name="value">键对应的值</param>
/// <param name="splitFirstKey">if not null then the smallest key in the new split leaf</param>
/// <param name="splitNode">if not null then the node was split and this is the leaf to the right.</param>
/// <returns>smallest key item in keys, or null if no change</returns>
public string InsertLeaf(string key, long value, out string splitFirstKey, out BPlusTreeNode splitNode)
{
splitFirstKey = null;
splitNode = null;
if (!this.IsLeaf)
{
throw new BPlusTreeException("bad call to insert leaf, this is not a leaf");
}
// 标示节点已被更改
this.Soil();
// 查找新键的位置 键可能已经存在
int insertPosition = this.FindAtOrNextPosition(key, false);
bool doSplit = false;
// 节点未满
if (insertPosition < this.Capacity)
{
// 如果键已存在，则更改其对应值及位置，不支持重复的条目
if (this.ChildKeys[insertPosition] == null || this.Tree.Compare(this.ChildKeys[insertPosition], key) == 0)
{
this.ChildKeys[insertPosition] = key;
this.ChildValues[insertPosition] = value;
// 返回键序列中的最小值，如果无更改则返回空
if (insertPosition == 0)
{
return key;
}
else
{
return null;
}
}
// 插入点为比指定键稍大的键
}
else
{
// 节点已满，准备分割节点
doSplit = true;
}
// 查看是否还有空位置
int nullIndex = insertPosition;
while (nullIndex < this.ChildKeys.Length && this.ChildKeys[nullIndex] != null)
{
nullIndex++;
}
if (nullIndex >= this.ChildKeys.Length)
{
doSplit = true;
}
// 做分割的准备 数组增加1
if (doSplit)
{
this.PrepareBeforeSplit();
}
// 将新数据插入至数组中，将已存在的值向右移动
string nextKey = this.ChildKeys[insertPosition];
long nextValue = this.ChildValues[insertPosition];
this.ChildKeys[insertPosition] = key;
this.ChildValues[insertPosition] = value;
while (nextKey != null)
{
key = nextKey;
value = nextValue;
insertPosition++;
nextKey = this.ChildKeys[insertPosition];
nextValue = this.ChildValues[insertPosition];
this.ChildKeys[insertPosition] = key;
this.ChildValues[insertPosition] = value;
}
// 如果需要分割
if (doSplit)
{
// 从中间开始分割 折半
int splitPoint = this.ChildKeys.Length / 2;
int splitLength = this.ChildKeys.Length - splitPoint;
// 新创建的分割出的节点，始终是右节点
splitNode = new BPlusTreeNode(this.Tree, this.Parent, -1, this.IsLeaf);
// 将指定分割点左侧的数据拷贝至新的节点
Array.Copy(this.ChildKeys, splitPoint, splitNode.ChildKeys, 0, splitLength);
Array.Copy(this.ChildValues, splitPoint, splitNode.ChildValues, 0, splitLength);
Array.Copy(this.ChildNodes, splitPoint, splitNode.ChildNodes, 0, splitLength);
// 记录分割节点的第一个键，右节点的第一个键
splitFirstKey = splitNode.ChildKeys[0];
// 存储新节点至块文件
splitNode.DumpToNewBlock();
// 分割完毕 恢复之前的准备 处理分割点右侧数据，保留左侧数据，删除右侧数据
this.RepairAfterSplit(splitPoint);
// 记录新的节点
this.Tree.RecordTerminalNode(splitNode); // InsertLeaf
// 新节点及其父节点需要处理
splitNode.Soil();
}
if (insertPosition == 0)
{
return key; // smallest key changed.
}
else
{
return null; // no change in smallest key
}
}
/// <summary>
/// 重新组织分割树，新的根节点将有两个子节点
/// </summary>
/// <param name="oldRoot">原根节点</param>
/// <param name="splitFirstKey">新根节点的第一个Key</param>
/// <param name="splitNode">新分割出的节点</param>
/// <param name="tree">指定的树</param>
/// <returns>新根节点</returns>
public static BPlusTreeNode BinaryRoot(BPlusTreeNode oldRoot, string splitFirstKey, BPlusTreeNode splitNode, BPlusTreeLong tree)
{
if (oldRoot == null)
throw new ArgumentNullException("oldRoot");
if (splitNode == null)
throw new ArgumentNullException("splitNode");
// 已不是叶子节点
BPlusTreeNode newRoot = MakeRoot(tree, false);
// 新的跟记录分割节点的第一个Key
newRoot.ChildKeys[0] = splitFirstKey;
// 新旧节点分别为新的根节点的索引 0 1 位置
oldRoot.ResetParent(newRoot, 0);
splitNode.ResetParent(newRoot, 1);
// new root is stored elsewhere
return newRoot;
}
/// <summary>
/// 重置节点的父节点
/// </summary>
/// <param name="newParent">父节点</param>
/// <param name="indexInParent">在父节点中的索引</param>
private void ResetParent(BPlusTreeNode newParent, int indexInParent)
{
// keys and existing parent structure must be updated elsewhere.
this.Parent = newParent;
this.IndexInParent = indexInParent;
newParent.ChildValues[indexInParent] = this.BlockNumber; // 中间节点存储的值为子节点的块序号
newParent.ChildNodes[indexInParent] = this;
// parent is no longer terminal
this.Tree.ForgetTerminalNode(this.Parent); // 父节点已经有了一个具体化的子节点，父节点不再是终端节点
}
/// <summary>
/// 合并叶子节点，当节点的使用率不足50%时，则需要合并
/// </summary>
/// <param name="left">左节点</param>
/// <param name="right">右节点</param>
/// <param name="canDeleteRightNode">是否可以删除右节点</param>
public static void MergeLeaves(BPlusTreeNode left, BPlusTreeNode right, out bool canDeleteRightNode)
{
if (left == null)
throw new ArgumentNullException("left");
if (right == null)
throw new ArgumentNullException("right");
canDeleteRightNode = false;
string[] allKeys = new string[left.Capacity * 2];
long[] allValues = new long[left.Capacity * 2];
int index = 0;
for (int i = 0; i < left.Capacity; i++)
{
if (left.ChildKeys[i] == null)
{
break;
}
allKeys[index] = left.ChildKeys[i];
allValues[index] = left.ChildValues[i];
index++;
}
for (int i = 0; i < right.Capacity; i++)
{
if (right.ChildKeys[i] == null)
{
break;
}
allKeys[index] = right.ChildKeys[i];
allValues[index] = right.ChildValues[i];
index++;
}
// 如果左节点的容量足够，则可删除右节点
if (index <= left.Capacity)
{
canDeleteRightNode = true;
left.Clear();
for (int i = 0; i < index; i++)
{
left.ChildKeys[i] = allKeys[i];
left.ChildValues[i] = allValues[i];
}
left.Soil();
right.Free();
return;
}
// 左节点的容量不够了
left.Clear();
right.Clear();
left.Soil();
right.Soil();
int rightContent = index / 2;
int leftContent = index - rightContent;
int newIndex = 0;
for (int i = 0; i < leftContent; i++)
{
left.ChildKeys[i] = allKeys[newIndex];
left.ChildValues[i] = allValues[newIndex];
newIndex++;
}
for (int i = 0; i < rightContent; i++)
{
right.ChildKeys[i] = allKeys[newIndex];
right.ChildValues[i] = allValues[newIndex];
newIndex++;
}
}
/// <summary>
/// 在节点中插入键值对
/// </summary>
/// <param name="key">叶子节点的键</param>
/// <param name="value">键对应的值</param>
/// <param name="splitFirstKey">if not null then the smallest key in the new split leaf</param>
/// <param name="splitNode">if not null then the node was split and this is the leaf to the right.</param>
/// <returns>
/// null unless the smallest key under this node has changed, in which case it returns the smallest key.
/// </returns>
public string Insert(string key, long value, out string splitFirstKey, out BPlusTreeNode splitNode)
{
if (this.IsLeaf)
{
return this.InsertLeaf(key, value, out splitFirstKey, out splitNode);
}
// 我不是叶子 我是中间节点 找到Key对应的位置 在子节点中插入键值对
splitFirstKey = null;
splitNode = null;
// 查找新键的位置 由于是中间节点 则新键的位置必须存在
int insertPosition = this.FindAtOrNextPosition(key, false);
// 非叶子节点中的值数组存储叶子节点的块序号
long insertValue = this.ChildValues[insertPosition];
if (insertValue == StoredConstants.NullBlockNumber)
{
throw new BPlusTreeException("key not followed by block number in non-leaf");
}
// 加载子节点
BPlusTreeNode insertChild = this.LoadNodeAtIndex(insertPosition);
string childSplitFirstKey;
BPlusTreeNode childSplitNode;
// 在子节点中插入新的键值对
string childInsert = insertChild.Insert(key, value, out childSplitFirstKey, out childSplitNode);
// 发现子节点已满，也需要分割
if (childSplitNode != null)
{
// 我即将被更改
this.Soil(); // redundant -- a child will have a change so this node will need to be copied
// 为新的子节点创建位置索引，即下一个
int newChildPosition = insertPosition + 1;
// 自己是否已满
bool doSplit = false;
// 如果我作为中间节点容量也满了，则中间节点也需要被分割
if (this.ChildValues[this.Capacity] != StoredConstants.NullBlockNumber)
{
doSplit = true;
}
if (doSplit)
{
// 做分割准备
this.PrepareBeforeSplit();
}
// bubble over the current values to make space for new child
// 新节点位置上及其右侧内容全部向右移动1位，为新节点空出位置
for (int i = this.ChildKeys.Length - 2; i >= newChildPosition - 1; i--)
{
int iPlus1 = i + 1;
int iPlus2 = iPlus1 + 1;
this.ChildKeys[iPlus1] = this.ChildKeys[i];
this.ChildValues[iPlus2] = this.ChildValues[iPlus1];
this.ChildNodes[iPlus2] = this.ChildNodes[iPlus1];
}
// record the new child
// 新节点的位置存放新节点的第一个键
this.ChildKeys[newChildPosition - 1] = childSplitFirstKey;
// 被分割出的子节点的父节点为自己
childSplitNode.ResetParent(this, newChildPosition);
// 如果我作为中间节点容量也满了，则中间节点也需要被分割
if (doSplit)
{
// 从中间开始分割 折半
int splitPoint = this.ChildNodes.Length / 2 - 1;
// 分割出的新节点的第一个Key
splitFirstKey = this.ChildKeys[splitPoint];
// 新建节点 包含分割点右侧所有数据
splitNode = new BPlusTreeNode(this.Tree, this.Parent, -1, this.IsLeaf);
splitNode.Clear(); // redundant.
// 记录已经扩充的数据结构
long[] values = this.ChildValues;
string[] keys = this.ChildKeys;
BPlusTreeNode[] nodes = this.ChildNodes;
// 重置和清空数据
this.Clear();
// 将分割点左侧的数据拷贝至此节点
Array.Copy(keys, 0, this.ChildKeys, 0, splitPoint);
Array.Copy(values, 0, this.ChildValues, 0, splitPoint + 1);
Array.Copy(nodes, 0, this.ChildNodes, 0, splitPoint + 1);
// 将分割点右侧的数据拷贝至新的分割节点
int remainingKeys = this.Capacity - splitPoint;
Array.Copy(keys, splitPoint + 1, splitNode.ChildKeys, 0, remainingKeys);
Array.Copy(values, splitPoint + 1, splitNode.ChildValues, 0, remainingKeys + 1);
Array.Copy(nodes, splitPoint + 1, splitNode.ChildNodes, 0, remainingKeys + 1);
// 重置新节点中所有的子节点的父节点
splitNode.ResetAllChildrenParent();
// 存储新节点
splitNode.DumpToNewBlock();
splitNode.CheckIfTerminal();
splitNode.Soil();
this.CheckIfTerminal();
} // end do split
// 重置节点中所有的子节点的父节点
this.ResetAllChildrenParent();
}
// 返回最小的那个键
if (insertPosition == 0)
{
return childInsert; // the smallest key may have changed
}
else
{
return null; // no change in smallest key
}
}
/// <summary>
/// 合并节点，当节点的使用率不足50%时，则需要合并
/// </summary>
/// <param name="left">左节点</param>
/// <param name="keyBetween">左右节点的中间键</param>
/// <param name="right">右节点</param>
/// <param name="rightLeastKey">合并后的键的最小值</param>
/// <param name="canDeleteRightNode">是否可以删除右节点</param>
public static void Merge(BPlusTreeNode left, string keyBetween, BPlusTreeNode right, out string rightLeastKey, out bool canDeleteRightNode)
{
if (left == null)
throw new ArgumentNullException("left");
if (right == null)
throw new ArgumentNullException("right");
rightLeastKey = null; // only if DeleteRight
// 合并叶子节点
if (left.IsLeaf || right.IsLeaf)
{
if (!(left.IsLeaf && right.IsLeaf))
{
throw new BPlusTreeException("can't merge leaf with non-leaf");
}
// 合并子节点
MergeLeaves(left, right, out canDeleteRightNode);
rightLeastKey = right.ChildKeys[0];
return;
}
// 合并非叶子节点
canDeleteRightNode = false;
if (left.ChildValues[0] == StoredConstants.NullBlockNumber || right.ChildValues[0] == StoredConstants.NullBlockNumber)
{
throw new BPlusTreeException("cannot merge empty non-leaf with non-leaf");
}
string[] allKeys = new string[left.Capacity * 2 + 1];
long[] allValues = new long[left.Capacity * 2 + 2];
BPlusTreeNode[] allNodes = new BPlusTreeNode[left.Capacity * 2 + 2];
// 拷贝左节点的数据
int index = 0;
allValues[0] = left.ChildValues[0];
allNodes[0] = left.ChildNodes[0];
for (int i = 0; i < left.Capacity; i++)
{
if (left.ChildKeys[i] == null)
{
break;
}
allKeys[index] = left.ChildKeys[i];
allValues[index + 1] = left.ChildValues[i + 1];
allNodes[index + 1] = left.ChildNodes[i + 1];
index++;
}
// 拷贝中间键
allKeys[index] = keyBetween;
index++;
// 拷贝右节点的数据
allValues[index] = right.ChildValues[0];
allNodes[index] = right.ChildNodes[0];
int rightCount = 0;
for (int i = 0; i < right.Capacity; i++)
{
if (right.ChildKeys[i] == null)
{
break;
}
allKeys[index] = right.ChildKeys[i];
allValues[index + 1] = right.ChildValues[i + 1];
allNodes[index + 1] = right.ChildNodes[i + 1];
index++;
rightCount++;
}
// 如果数量小于左节点的能力，则右节点可以删除掉
if (index <= left.Capacity)
{
// it will all fit in one node
canDeleteRightNode = true;
for (int i = 0; i < index; i++)
{
left.ChildKeys[i] = allKeys[i];
left.ChildValues[i] = allValues[i];
left.ChildNodes[i] = allNodes[i];
}
left.ChildValues[index] = allValues[index];
left.ChildNodes[index] = allNodes[index];
left.ResetAllChildrenParent();
left.Soil();
right.Free();
return;
}
// otherwise split the content between the nodes
left.Clear();
right.Clear();
left.Soil();
right.Soil();
int leftContent = index / 2;
int rightContent = index - leftContent - 1;
rightLeastKey = allKeys[leftContent];
int outputIndex = 0;
for (int i = 0; i < leftContent; i++)
{
left.ChildKeys[i] = allKeys[outputIndex];
left.ChildValues[i] = allValues[outputIndex];
left.ChildNodes[i] = allNodes[outputIndex];
outputIndex++;
}
rightLeastKey = allKeys[outputIndex];
left.ChildValues[outputIndex] = allValues[outputIndex];
left.ChildNodes[outputIndex] = allNodes[outputIndex];
outputIndex++;
rightCount = 0;
for (int i = 0; i < rightContent; i++)
{
right.ChildKeys[i] = allKeys[outputIndex];
right.ChildValues[i] = allValues[outputIndex];
right.ChildNodes[i] = allNodes[outputIndex];
outputIndex++;
rightCount++;
}
right.ChildValues[rightCount] = allValues[outputIndex];
right.ChildNodes[rightCount] = allNodes[outputIndex];
left.ResetAllChildrenParent();
right.ResetAllChildrenParent();
}
/// <summary>
/// 将当前节点的容量扩大(+1)，为插入和分割做准备
/// </summary>
private void PrepareBeforeSplit()
{
int superSize = this.Capacity + 1;
string[] keys = new string[superSize];
long[] positions = new long[superSize + 1];
BPlusTreeNode[] materialized = new BPlusTreeNode[superSize + 1];
Array.Copy(this.ChildKeys, 0, keys, 0, this.Capacity);
keys[this.Capacity] = null;
Array.Copy(this.ChildValues, 0, positions, 0, this.Capacity + 1);
positions[this.Capacity + 1] = StoredConstants.NullBlockNumber;
Array.Copy(this.ChildNodes, 0, materialized, 0, this.Capacity + 1);
materialized[this.Capacity + 1] = null;
this.ChildValues = positions;
this.ChildKeys = keys;
this.ChildNodes = materialized;
}
/// <summary>
/// Find near-index of comparekey in leaf under this node.
/// </summary>
/// <param name="compareKey">the key to look for</param>
/// <param name="inLeaf">the leaf where found</param>
/// <param name="lookPastOnly">If true then only look for a greater item, not an exact match.</param>
/// <returns>index of match in leaf</returns>
private int FindAtOrNextPositionInLeaf(string compareKey, out BPlusTreeNode inLeaf, bool lookPastOnly)
{
int keyPosition = this.FindAtOrNextPosition(compareKey, lookPastOnly);
// 如果自己即是叶子节点
if (this.IsLeaf)
{
inLeaf = this;
return keyPosition;
}
// 尝试在子节点中查找
BPlusTreeNode child = this.LoadNodeAtIndex(keyPosition);
return child.FindAtOrNextPositionInLeaf(compareKey, out inLeaf, lookPastOnly);
}
/// <summary>
/// 由树记录节点是否为终端节点，终端节点没有子节点，而根或中间节点有子节点
/// </summary>
/// <param name="nonTerminalNode">这个节点已经不是终端节点</param>
public void ForgetTerminalNode(BPlusTreeNode nonTerminalNode)
{
if (!this._TerminalNodeToId.ContainsKey(nonTerminalNode))
{
// silently ignore (?)
return;
}
int id = (int)this._TerminalNodeToId[nonTerminalNode];
if (id == this._LowerTerminalNodeCount)
{
this._LowerTerminalNodeCount++;
}
this._IdToTerminalNode.Remove(id);
this._TerminalNodeToId.Remove(nonTerminalNode);
}
/// <summary>
/// 由树记录节点是否为终端节点，终端节点没有子节点，而根或中间节点有子节点
/// </summary>
/// <param name="terminalNode">这个节点是终端节点</param>
public void RecordTerminalNode(BPlusTreeNode terminalNode)
{
if (terminalNode == this.RootNode)
{
return; // never record the root node
}
if (this._TerminalNodeToId.ContainsKey(terminalNode))
{
return; // don't record it again
}
int id = this._TerminalNodeCount;
this._TerminalNodeCount++;
this._TerminalNodeToId[terminalNode] = id;
this._IdToTerminalNode[id] = terminalNode;
}
