【数据结构】红黑树的学习
以下内容主要参考wiki上红黑树的相关介绍
定义
是一种自平衡二叉查找树。
所谓的平衡树，意思就是在插入和删除节点的时候，通过旋转rotate树的方式调整树的高度h，将查询n个节点的树内某个节点的时间复杂度保持在O(log n)左右。
二叉树表明红黑树一个节点只会有左右两个子节点。
典型的用途是实现关联数组
关联数组就是K-V形式的数据格式。Java的HashMap中就用到了这个，在HashMap中定义了一个TreeNode，就是红黑树。
性质
- 节点是红色或者黑色
- 根节点是黑色
- 所有叶子都是黑色（叶子是NIL节点）
- 每个红色节点必须有两个黑色的子节点。（从每个叶子到根节点的路径上不能连续出现两个红色节点）
- 从任意节点到其叶子的简单路径上黑色节点的数量相等
旋转知识
树的旋转分为左旋 left rotate和右旋right rotate，如图所示：
左旋
以上图为例，它的过程是：
1. 将B设为P节点的右节点，和Q节点的link断开
2. 将P设为Q节点的左节点
右旋
以上图为例，它的过程是：
1. 将B设为Q节点的左节点，和P节点的link断开
2. 将Q设为P节点的右节点
操作
查询
查询和二叉树一样，不涉及到树结构的变动，没什么好说的。
插入
把要插入的节点标记为红色，因为如果标记为黑色，那么会直接破坏性质5，即路径上多了一个黑色，这个问题很难调整。如果为红色有可能会破坏性质4，这个可以通过树旋转和颜色调换来解决。接下来就是分5种情况来分别进行相关操作。
以下的代码都是从wiki中的代码翻译成Java代码的。
情景一：新节点是根节点的父节点
上来直接当祖宗，这种情况只需要将插入的节点颜色调换为黑色。
public void insert_case1(Node node) {
if (node.getParent() == null) {
node.setColor("BLACK");
} else {
insert_case2(node);
}
}情景二：新节点的父节点是黑色
插入的新节点是红色节点，所以性质5没有破坏，因为父节点是黑色的，所以规则4也没有破坏，符合规则无需修改。
public void insert_case2(Node node) {
if ("BLACK".equals(node.getParent().getColor())) {
return;//仍然有效
} else {
insert_case3(node);
}
}- 情景三：新节点的父节点和叔节点都是都是红色
如图所示，那么这里的骚操作就是把它的父节点和叔节点颜色调换为黑色，然后把祖父节点的颜色改成红色。
public void insert_case3(Node node) {
Node parent = node.getParent();
Node grandparentLeft = parent.getParent().getLeft();
Node grandparentRight = parent.getParent().getRight();
Node uncle = parent == grandparentLeft ? grandparentRight : grandparentLeft;
if (uncle != null && "RED".equals(uncle.getColor())) {
parent.setColor("BLACK");
uncle.setColor("BLACK");
parent.getParent().setColor("RED");
insert_case1(node)
} else {
insert_case4(node);
}
}- 情景四：父节点是红色，叔节点是黑色或者没有。同时新节点是父节点的右节点，父节点是父节点的父节点的左节点，或者新节点是父节点的左节点而父节点是父节点的父节点的右节点，这个时候进行左旋或者右旋操作。
即父子不同侧，按照父节点侧进行旋转。
然后进入情景五的问题，用情景五的方式解决。
public void insert_case4(Node node) {
if (node == node.getParent().getRight() && node.getParent() == node.getParent().getParent().getLeft()) {
//左旋
node.getParent().setRight(node.getLeft());
Node parent = node.getParent();
node.getParent.getParent().setLeft(node);
node.setLeft(parent);
} else if (node == node.getParent().getLeft() && node.getParent() == node.getParent().getParent().getRight()) {
//右旋
node.getParent().setLeft(node.getRight());
Node parent = node.getParent();
node.getParent.getParent().setRight(node);
node.setRight(parent);
}
insert_case5(Node node);
}- 情景五：父节点是红色，叔节点是黑色或者没有。同时新节点是父节点的左节点，父节点也是父节点的父节点的左节点，或者新节点是父节点的右节点，父节点也是父节点的父节点的右侧，这是进行右旋或者左旋操作。
即父子同侧，按反方向进行树旋转。
旋转完成后，原父节点颜色改成黑色，原父节点的父节点颜色改成红色。操作完成。
public void insert_case5(Node node) {
node.getParent().setColor("BLACK");
node.getParent().getParent().setColor("RED");
if (node == node.getParent().getLeft() && node.getParent() == node.getParent().getParent().getLeft()) {
//右旋
node.getParent().getParent().setLeft(node.getParent().getRight());
node.getParent().setRight(node.getParent().getParent());
} else if (node == node.getParent().getRight() && node.getParent() == node.getParent().getParent().getRight()) {
//左旋
node.getParent().getParent().setRight(node.getParent().getLeft());
node.getParent().setLeft(node.getParent().getParent());
}
}至此，增加节点的操作结束。这里的操作都是针对单个节点的，对于整树需要进行递归操作。
删除
如果要删除的节点是有两个儿子的节点，这里的儿子不是NIL叶子节点
那么这个操作就是查找该节点左子树中最大元素或者是右子树中最小元素。在一个有序的树中，最大元素和最小元素的子节点肯定是两个NIL，所以可以将他们的值赋给准备删除的节点，并删除这个最大值或者是最小值节点，这样在不违背任何性质的条件下完成节点的删除。
如果要删除的节点只有一个儿子，两个子节点都是NIL的则取其中一个子节点为该节点的子节点。
如果要删除的节点是红色的，那么它的父节点和子节点都是黑色的（因为性质4），所以可以直接删除这个节点，并让该节点的子节点代替它的位置。
如果要删除的节点是黑色的，它的唯一子节点是红色的，那么可以直接删除这个节点，让子节点代替它的位置。因为少了一个黑色会违背性质5，需要将替代的这个子节点改成黑色。
如果要删除的节点和子节点都是黑色，这种情况很复杂。首先还是删除该节点，然后让子节点代替它的位置。这部分用代码表示为：
void
delete_one_child(struct node *n)
{
/*
* Precondition: n has at most one non-null child.
* 判断子节点是否是NIL，如果是NIL，那么如果该节点是父节点的左节点，子节点取左侧的NIL，反之亦反。即父子同侧。
*/
struct node *child = is_leaf(n->right)? n->left : n->right;
//交换父子位置
replace_node(n, child);
//如果该节点是黑色的，但是子节点是红色的，这就是上面第二种情况，将子节点改成黑色即可。
if(n->color == BLACK){
if(child->color == RED)
child->color = BLACK;
else
delete_case1 (child);//需要参考下列的额情况一来处理
}
free (n);
}但是因为删除了一个黑色节点，可能会导致违背性质5，因此需要分6种情况来分析。后续中出现的N表示删除节点的子节点，现在已经替代删除节点的位置，P是删除节点的父节点，S是删除节点的兄弟节点，SL是兄弟节点的左子节点，SR是兄弟节点的右子节点。下面所列的情况都是N是P的左节点的情况下，如果是右节点就是进行反向操作。
- 情景一：N是新的根节点，也就是说删除的节点是根节点，那么所有的路径都删除了一个黑色节点，性质5依然成立。不需要改动
void delete_case1(struct node *n) { if(n->parent != NULL) delete_case2 (n); }- 情景二：S是红色的，那么进行左旋。然后进行情景四五六处理。
void delete_case2(struct node *n) { struct node *s = sibling (n); if(s->color == RED){ n->parent->color = RED; s->color = BLACK; if(n == n->parent->left) rotate_left(n->parent); else rotate_right(n->parent); } delete_case3 (n); }- 情景三：P、S、SL、SR都是黑色的。把S改成红色，此时的P作为这部分的树是黑色的，然后按照情景一进行处理。
void delete_case3(struct node *n) { struct node *s = sibling (n); if((n->parent->color == BLACK)&& (s->color == BLACK)&& (s->left->color == BLACK)&& (s->right->color == BLACK)) { s->color = RED; delete_case1(n->parent); } else delete_case4 (n); }- 情景四：S、SL、SR是黑色，P是红色，这种情况只需要将S和P的颜色互换一下即可。
void delete_case4(struct node *n) { struct node *s = sibling (n); if（(n->parent->color == RED)&& (s->color == BLACK)&& (s->left->color == BLACK)&& (s->right->color == BLACK)) { s->color = RED; n->parent->color = BLACK; } else delete_case5 (n); }- 情景五：S和SR是黑色，SL是红色。这个时候要在S进行右旋转，这样SL成了S的父节点，然后将SL和S的颜色互换。接着就进入情景六。
void delete_case5(struct node *n) { struct node *s = sibling (n); if（s->color == BLACK){ /* this if statement is trivial, due to Case 2(even though Case two changed the sibling to a sibling's child, the sibling's child can't be red, since no red parent can have a red child). */ // the following statements just force the red to be on the left of the left of the parent, // or right of the right, so case six will rotate correctly. if((n == n->parent->left)&& (s->right->color == BLACK)&& (s->left->color == RED)) { // this last test is trivial too due to cases 2-4. s->color = RED; s->left->color = BLACK; rotate_right (s); } else if((n == n->parent->right)&& (s->left->color == BLACK)&& (s->right->color == RED)) {// this last test is trivial too due to cases 2-4. s->color = RED; s->right->color = BLACK; rotate_left (s); } } delete_case6 (n); }- 情景六：S是黑色，SR是红色。这时对P做左旋转，并且将S的颜色改成P的颜色，P的颜色改成黑色，SR的颜色改成黑色。这样树就平衡了。
void delete_case6(struct node *n) { struct node *s = sibling (n); s->color = n->parent->color; n->parent->color = BLACK; if(n == n->parent->left){ s->right->color = BLACK; rotate_left(n->parent); } else { s->left->color = BLACK; rotate_right(n->parent); } }
参考代码
c++
wiki上提供的就是c++的代码
#define BLACK 1
#define RED 0
#include <iostream>
using namespace std;
class bst {
private:
struct Node {
int value;
bool color;
Node *leftTree, *rightTree, *parent;
Node() : value(0), color(RED), leftTree(NULL), rightTree(NULL), parent(NULL) { }
Node* grandparent() {
if(parent == NULL){
return NULL;
}
return parent->parent;
}
Node* uncle() {
if(grandparent() == NULL) {
return NULL;
}
if(parent == grandparent()->rightTree)
return grandparent()->leftTree;
else
return grandparent()->rightTree;
}
Node* sibling() {
if(parent->leftTree == this)
return parent->rightTree;
else
return parent->leftTree;
}
};
void rotate_right(Node *p){
Node *gp = p->grandparent();
Node *fa = p->parent;
Node *y = p->rightTree;
fa->leftTree = y;
if(y != NIL)
y->parent = fa;
p->rightTree = fa;
fa->parent = p;
if(root == fa)
root = p;
p->parent = gp;
if(gp != NULL){
if(gp->leftTree == fa)
gp->leftTree = p;
else
gp->rightTree = p;
}
}
void rotate_left(Node *p){
if(p->parent == NULL){
root = p;
return;
}
Node *gp = p->grandparent();
Node *fa = p->parent;
Node *y = p->leftTree;
fa->rightTree = y;
if(y != NIL)
y->parent = fa;
p->leftTree = fa;
fa->parent = p;
if(root == fa)
root = p;
p->parent = gp;
if(gp != NULL){
if(gp->leftTree == fa)
gp->leftTree = p;
else
gp->rightTree = p;
}
}
void inorder(Node *p){
if(p == NIL)
return;
if(p->leftTree)
inorder(p->leftTree);
cout << p->value << " ";
if(p->rightTree)
inorder(p->rightTree);
}
string outputColor (bool color) {
return color ? "BLACK" : "RED";
}
Node* getSmallestChild(Node *p){
if(p->leftTree == NIL)
return p;
return getSmallestChild(p->leftTree);
}
bool delete_child(Node *p, int data){
if(p->value > data){
if(p->leftTree == NIL){
return false;
}
return delete_child(p->leftTree, data);
} else if(p->value < data){
if(p->rightTree == NIL){
return false;
}
return delete_child(p->rightTree, data);
} else if(p->value == data){
if(p->rightTree == NIL){
delete_one_child (p);
return true;
}
Node *smallest = getSmallestChild(p->rightTree);
swap(p->value, smallest->value);
delete_one_child (smallest);
return true;
}else{
return false;
}
}
void delete_one_child(Node *p){
Node *child = p->leftTree == NIL ? p->rightTree : p->leftTree;
if(p->parent == NULL && p->leftTree == NIL && p->rightTree == NIL){
p = NULL;
root = p;
return;
}
if(p->parent == NULL){
delete p;
child->parent = NULL;
root = child;
root->color = BLACK;
return;
}
if(p->parent->leftTree == p){
p->parent->leftTree = child;
} else {
p->parent->rightTree = child;
}
child->parent = p->parent;
if(p->color == BLACK){
if(child->color == RED){
child->color = BLACK;
} else
delete_case (child);
}
delete p;
}
void delete_case(Node *p){
if(p->parent == NULL){
p->color = BLACK;
return;
}
if(p->sibling()->color == RED) {
p->parent->color = RED;
p->sibling()->color = BLACK;
if(p == p->parent->leftTree)
rotate_left(p->sibling());
else
rotate_right(p->sibling());
}
if(p->parent->color == BLACK && p->sibling()->color == BLACK
&& p->sibling()->leftTree->color == BLACK && p->sibling()->rightTree->color == BLACK) {
p->sibling()->color = RED;
delete_case(p->parent);
} else if(p->parent->color == RED && p->sibling()->color == BLACK
&& p->sibling()->leftTree->color == BLACK && p->sibling()->rightTree->color == BLACK) {
p->sibling()->color = RED;
p->parent->color = BLACK;
} else {
if(p->sibling()->color == BLACK) {
if(p == p->parent->leftTree && p->sibling()->leftTree->color == RED
&& p->sibling()->rightTree->color == BLACK) {
p->sibling()->color = RED;
p->sibling()->leftTree->color = BLACK;
rotate_right(p->sibling()->leftTree);
} else if(p == p->parent->rightTree && p->sibling()->leftTree->color == BLACK
&& p->sibling()->rightTree->color == RED) {
p->sibling()->color = RED;
p->sibling()->rightTree->color = BLACK;
rotate_left(p->sibling()->rightTree);
}
}
p->sibling()->color = p->parent->color;
p->parent->color = BLACK;
if(p == p->parent->leftTree){
p->sibling()->rightTree->color = BLACK;
rotate_left(p->sibling());
} else {
p->sibling()->leftTree->color = BLACK;
rotate_right(p->sibling());
}
}
}
void insert(Node *p, int data){
if(p->value >= data){
if(p->leftTree != NIL)
insert(p->leftTree, data);
else {
Node *tmp = new Node();
tmp->value = data;
tmp->leftTree = tmp->rightTree = NIL;
tmp->parent = p;
p->leftTree = tmp;
insert_case (tmp);
}
} else {
if(p->rightTree != NIL)
insert(p->rightTree, data);
else {
Node *tmp = new Node();
tmp->value = data;
tmp->leftTree = tmp->rightTree = NIL;
tmp->parent = p;
p->rightTree = tmp;
insert_case (tmp);
}
}
}
void insert_case(Node *p){
if(p->parent == NULL){
root = p;
p->color = BLACK;
return;
}
if(p->parent->color == RED){
if(p->uncle()->color == RED) {
p->parent->color = p->uncle()->color = BLACK;
p->grandparent()->color = RED;
insert_case(p->grandparent());
} else {
if(p->parent->rightTree == p && p->grandparent()->leftTree == p->parent) {
rotate_left (p);
rotate_right (p);
p->color = BLACK;
p->leftTree->color = p->rightTree->color = RED;
} else if(p->parent->leftTree == p && p->grandparent()->rightTree == p->parent) {
rotate_right (p);
rotate_left (p);
p->color = BLACK;
p->leftTree->color = p->rightTree->color = RED;
} else if(p->parent->leftTree == p && p->grandparent()->leftTree == p->parent) {
p->parent->color = BLACK;
p->grandparent()->color = RED;
rotate_right(p->parent);
} else if(p->parent->rightTree == p && p->grandparent()->rightTree == p->parent) {
p->parent->color = BLACK;
p->grandparent()->color = RED;
rotate_left(p->parent);
}
}
}
}
void DeleteTree(Node *p){
if(!p || p == NIL){
return;
}
DeleteTree(p->leftTree);
DeleteTree(p->rightTree);
delete p;
}
public:
bst() {
NIL = new Node();
NIL->color = BLACK;
root = NULL;
}
~bst() {
if (root)
DeleteTree (root);
delete NIL;
}
void inorder() {
if(root == NULL)
return;
inorder (root);
cout << endl;
}
void insert (int x) {
if(root == NULL){
root = new Node();
root->color = BLACK;
root->leftTree = root->rightTree = NIL;
root->value = x;
} else {
insert(root, x);
}
}
bool delete_value (int data) {
return delete_child(root, data);
}
private:
Node *root, *NIL;
};Java
Java的实现在java.util.HashMap类中就有定义，TreeNode这个内部类就是红黑树。
/**
* Entry for Tree bins. Extends LinkedHashMap.Entry (which in turn
* extends Node) so can be used as extension of either regular or
* linked node.
*/
static final class TreeNode extends LinkedHashMap.Entry {
TreeNode parent; // red-black tree links
TreeNode left;
TreeNode right;
TreeNode prev; // needed to unlink next upon deletion
boolean red;
TreeNode(int hash, K key, V val, Node next) {
super(hash, key, val, next);
}
/**
* Returns root of tree containing this node.
*/
final TreeNode root() {
for (TreeNode r = this, p;;) {
if ((p = r.parent) == null)
return r;
r = p;
}
}
/**
* Ensures that the given root is the first node of its bin.
*/
static void moveRootToFront(Node[] tab, TreeNode root) {
int n;
if (root != null && tab != null && (n = tab.length) > 0) {
int index = (n - 1) & root.hash;
TreeNode first = (TreeNode)tab[index];
if (root != first) {
Node rn;
tab[index] = root;
TreeNode rp = root.prev;
if ((rn = root.next) != null)
((TreeNode)rn).prev = rp;
if (rp != null)
rp.next = rn;
if (first != null)
first.prev = root;
root.next = first;
root.prev = null;
}
assert checkInvariants(root);
}
}
/**
* Finds the node starting at root p with the given hash and key.
* The kc argument caches comparableClassFor(key) upon first use
* comparing keys.
*/
final TreeNode find(int h, Object k, Class kc) {
TreeNode p = this;
do {
int ph, dir; K pk;
TreeNode pl = p.left, pr = p.right, q;
if ((ph = p.hash) > h)
p = pl;
else if (ph < h)
p = pr;
else if ((pk = p.key) == k || (k != null && k.equals(pk)))
return p;
else if (pl == null)
p = pr;
else if (pr == null)
p = pl;
else if ((kc != null ||
(kc = comparableClassFor(k)) != null) &&
(dir = compareComparables(kc, k, pk)) != 0)
p = (dir < 0) ? pl : pr;
else if ((q = pr.find(h, k, kc)) != null)
return q;
else
p = pl;
} while (p != null);
return null;
}
/**
* Calls find for root node.
*/
final TreeNode getTreeNode(int h, Object k) {
return ((parent != null) ? root() : this).find(h, k, null);
}
/**
* Tie-breaking utility for ordering insertions when equal
* hashCodes and non-comparable. We don't require a total
* order, just a consistent insertion rule to maintain
* equivalence across rebalancings. Tie-breaking further than
* necessary simplifies testing a bit.
*/
static int tieBreakOrder(Object a, Object b) {
int d;
if (a == null || b == null ||
(d = a.getClass().getName().
compareTo(b.getClass().getName())) == 0)
d = (System.identityHashCode(a) <= System.identityHashCode(b) ?
-1 : 1);
return d;
}
/**
* Forms tree of the nodes linked from this node.
* @return root of tree
*/
final void treeify(Node[] tab) {
TreeNode root = null;
for (TreeNode x = this, next; x != null; x = next) {
next = (TreeNode)x.next;
x.left = x.right = null;
if (root == null) {
x.parent = null;
x.red = false;
root = x;
}
else {
K k = x.key;
int h = x.hash;
Class kc = null;
for (TreeNode p = root;;) {
int dir, ph;
K pk = p.key;
if ((ph = p.hash) > h)
dir = -1;
else if (ph < h)
dir = 1;
else if ((kc == null &&
(kc = comparableClassFor(k)) == null) ||
(dir = compareComparables(kc, k, pk)) == 0)
dir = tieBreakOrder(k, pk);
TreeNode xp = p;
if ((p = (dir <= 0) ? p.left : p.right) == null) {
x.parent = xp;
if (dir <= 0)
xp.left = x;
else
xp.right = x;
root = balanceInsertion(root, x);
break;
}
}
}
}
moveRootToFront(tab, root);
}
/**
* Returns a list of non-TreeNodes replacing those linked from
* this node.
*/
final Node untreeify(HashMap map) {
Node hd = null, tl = null;
for (Node q = this; q != null; q = q.next) {
Node p = map.replacementNode(q, null);
if (tl == null)
hd = p;
else
tl.next = p;
tl = p;
}
return hd;
}
/**
* Tree version of putVal.
*/
final TreeNode putTreeVal(HashMap map, Node[] tab,
int h, K k, V v) {
Class kc = null;
boolean searched = false;
TreeNode root = (parent != null) ? root() : this;
for (TreeNode p = root;;) {
int dir, ph; K pk;
if ((ph = p.hash) > h)
dir = -1;
else if (ph < h)
dir = 1;
else if ((pk = p.key) == k || (k != null && k.equals(pk)))
return p;
else if ((kc == null &&
(kc = comparableClassFor(k)) == null) ||
(dir = compareComparables(kc, k, pk)) == 0) {
if (!searched) {
TreeNode q, ch;
searched = true;
if (((ch = p.left) != null &&
(q = ch.find(h, k, kc)) != null) ||
((ch = p.right) != null &&
(q = ch.find(h, k, kc)) != null))
return q;
}
dir = tieBreakOrder(k, pk);
}
TreeNode xp = p;
if ((p = (dir <= 0) ? p.left : p.right) == null) {
Node xpn = xp.next;
TreeNode x = map.newTreeNode(h, k, v, xpn);
if (dir <= 0)
xp.left = x;
else
xp.right = x;
xp.next = x;
x.parent = x.prev = xp;
if (xpn != null)
((TreeNode)xpn).prev = x;
moveRootToFront(tab, balanceInsertion(root, x));
return null;
}
}
}
/**
* Removes the given node, that must be present before this call.
* This is messier than typical red-black deletion code because we
* cannot swap the contents of an interior node with a leaf
* successor that is pinned by "next" pointers that are accessible
* independently during traversal. So instead we swap the tree
* linkages. If the current tree appears to have too few nodes,
* the bin is converted back to a plain bin. (The test triggers
* somewhere between 2 and 6 nodes, depending on tree structure).
*/
final void removeTreeNode(HashMap map, Node[] tab,
boolean movable) {
int n;
if (tab == null || (n = tab.length) == 0)
return;
int index = (n - 1) & hash;
TreeNode first = (TreeNode)tab[index], root = first, rl;
TreeNode succ = (TreeNode)next, pred = prev;
if (pred == null)
tab[index] = first = succ;
else
pred.next = succ;
if (succ != null)
succ.prev = pred;
if (first == null)
return;
if (root.parent != null)
root = root.root();
if (root == null || root.right == null ||
(rl = root.left) == null || rl.left == null) {
tab[index] = first.untreeify(map); // too small
return;
}
TreeNode p = this, pl = left, pr = right, replacement;
if (pl != null && pr != null) {
TreeNode s = pr, sl;
while ((sl = s.left) != null) // find successor
s = sl;
boolean c = s.red; s.red = p.red; p.red = c; // swap colors
TreeNode sr = s.right;
TreeNode pp = p.parent;
if (s == pr) { // p was s's direct parent
p.parent = s;
s.right = p;
}
else {
TreeNode sp = s.parent;
if ((p.parent = sp) != null) {
if (s == sp.left)
sp.left = p;
else
sp.right = p;
}
if ((s.right = pr) != null)
pr.parent = s;
}
p.left = null;
if ((p.right = sr) != null)
sr.parent = p;
if ((s.left = pl) != null)
pl.parent = s;
if ((s.parent = pp) == null)
root = s;
else if (p == pp.left)
pp.left = s;
else
pp.right = s;
if (sr != null)
replacement = sr;
else
replacement = p;
}
else if (pl != null)
replacement = pl;
else if (pr != null)
replacement = pr;
else
replacement = p;
if (replacement != p) {
TreeNode pp = replacement.parent = p.parent;
if (pp == null)
root = replacement;
else if (p == pp.left)
pp.left = replacement;
else
pp.right = replacement;
p.left = p.right = p.parent = null;
}
TreeNode r = p.red ? root : balanceDeletion(root, replacement);
if (replacement == p) { // detach
TreeNode pp = p.parent;
p.parent = null;
if (pp != null) {
if (p == pp.left)
pp.left = null;
else if (p == pp.right)
pp.right = null;
}
}
if (movable)
moveRootToFront(tab, r);
}
/**
* Splits nodes in a tree bin into lower and upper tree bins,
* or untreeifies if now too small. Called only from resize;
* see above discussion about split bits and indices.
*
* @param map the map
* @param tab the table for recording bin heads
* @param index the index of the table being split
* @param bit the bit of hash to split on
*/
final void split(HashMap map, Node[] tab, int index, int bit) {
TreeNode b = this;
// Relink into lo and hi lists, preserving order
TreeNode loHead = null, loTail = null;
TreeNode hiHead = null, hiTail = null;
int lc = 0, hc = 0;
for (TreeNode e = b, next; e != null; e = next) {
next = (TreeNode)e.next;
e.next = null;
if ((e.hash & bit) == 0) {
if ((e.prev = loTail) == null)
loHead = e;
else
loTail.next = e;
loTail = e;
++lc;
}
else {
if ((e.prev = hiTail) == null)
hiHead = e;
else
hiTail.next = e;
hiTail = e;
++hc;
}
}
if (loHead != null) {
if (lc <= UNTREEIFY_THRESHOLD)
tab[index] = loHead.untreeify(map);
else {
tab[index] = loHead;
if (hiHead != null) // (else is already treeified)
loHead.treeify(tab);
}
}
if (hiHead != null) {
if (hc <= UNTREEIFY_THRESHOLD)
tab[index + bit] = hiHead.untreeify(map);
else {
tab[index + bit] = hiHead;
if (loHead != null)
hiHead.treeify(tab);
}
}
}
/* ------------------------------------------------------------ */
// Red-black tree methods, all adapted from CLR
static TreeNode rotateLeft(TreeNode root,
TreeNode p) {
TreeNode r, pp, rl;
if (p != null && (r = p.right) != null) {
if ((rl = p.right = r.left) != null)
rl.parent = p;
if ((pp = r.parent = p.parent) == null)
(root = r).red = false;
else if (pp.left == p)
pp.left = r;
else
pp.right = r;
r.left = p;
p.parent = r;
}
return root;
}
static TreeNode rotateRight(TreeNode root,
TreeNode p) {
TreeNode l, pp, lr;
if (p != null && (l = p.left) != null) {
if ((lr = p.left = l.right) != null)
lr.parent = p;
if ((pp = l.parent = p.parent) == null)
(root = l).red = false;
else if (pp.right == p)
pp.right = l;
else
pp.left = l;
l.right = p;
p.parent = l;
}
return root;
}
static TreeNode balanceInsertion(TreeNode root,
TreeNode x) {
x.red = true;
for (TreeNode xp, xpp, xppl, xppr;;) {
if ((xp = x.parent) == null) {
x.red = false;
return x;
}
else if (!xp.red || (xpp = xp.parent) == null)
return root;
if (xp == (xppl = xpp.left)) {
if ((xppr = xpp.right) != null && xppr.red) {
xppr.red = false;
xp.red = false;
xpp.red = true;
x = xpp;
}
else {
if (x == xp.right) {
root = rotateLeft(root, x = xp);
xpp = (xp = x.parent) == null ? null : xp.parent;
}
if (xp != null) {
xp.red = false;
if (xpp != null) {
xpp.red = true;
root = rotateRight(root, xpp);
}
}
}
}
else {
if (xppl != null && xppl.red) {
xppl.red = false;
xp.red = false;
xpp.red = true;
x = xpp;
}
else {
if (x == xp.left) {
root = rotateRight(root, x = xp);
xpp = (xp = x.parent) == null ? null : xp.parent;
}
if (xp != null) {
xp.red = false;
if (xpp != null) {
xpp.red = true;
root = rotateLeft(root, xpp);
}
}
}
}
}
}
static TreeNode balanceDeletion(TreeNode root,
TreeNode x) {
for (TreeNode xp, xpl, xpr;;) {
if (x == null || x == root)
return root;
else if ((xp = x.parent) == null) {
x.red = false;
return x;
}
else if (x.red) {
x.red = false;
return root;
}
else if ((xpl = xp.left) == x) {
if ((xpr = xp.right) != null && xpr.red) {
xpr.red = false;
xp.red = true;
root = rotateLeft(root, xp);
xpr = (xp = x.parent) == null ? null : xp.right;
}
if (xpr == null)
x = xp;
else {
TreeNode sl = xpr.left, sr = xpr.right;
if ((sr == null || !sr.red) &&
(sl == null || !sl.red)) {
xpr.red = true;
x = xp;
}
else {
if (sr == null || !sr.red) {
if (sl != null)
sl.red = false;
xpr.red = true;
root = rotateRight(root, xpr);
xpr = (xp = x.parent) == null ?
null : xp.right;
}
if (xpr != null) {
xpr.red = (xp == null) ? false : xp.red;
if ((sr = xpr.right) != null)
sr.red = false;
}
if (xp != null) {
xp.red = false;
root = rotateLeft(root, xp);
}
x = root;
}
}
}
else { // symmetric
if (xpl != null && xpl.red) {
xpl.red = false;
xp.red = true;
root = rotateRight(root, xp);
xpl = (xp = x.parent) == null ? null : xp.left;
}
if (xpl == null)
x = xp;
else {
TreeNode sl = xpl.left, sr = xpl.right;
if ((sl == null || !sl.red) &&
(sr == null || !sr.red)) {
xpl.red = true;
x = xp;
}
else {
if (sl == null || !sl.red) {
if (sr != null)
sr.red = false;
xpl.red = true;
root = rotateLeft(root, xpl);
xpl = (xp = x.parent) == null ?
null : xp.left;
}
if (xpl != null) {
xpl.red = (xp == null) ? false : xp.red;
if ((sl = xpl.left) != null)
sl.red = false;
}
if (xp != null) {
xp.red = false;
root = rotateRight(root, xp);
}
x = root;
}
}
}
}
}
/**
* Recursive invariant check
*/
static boolean checkInvariants(TreeNode t) {
TreeNode tp = t.parent, tl = t.left, tr = t.right,
tb = t.prev, tn = (TreeNode)t.next;
if (tb != null && tb.next != t)
return false;
if (tn != null && tn.prev != t)
return false;
if (tp != null && t != tp.left && t != tp.right)
return false;
if (tl != null && (tl.parent != t || tl.hash > t.hash))
return false;
if (tr != null && (tr.parent != t || tr.hash < t.hash))
return false;
if (t.red && tl != null && tl.red && tr != null && tr.red)
return false;
if (tl != null && !checkInvariants(tl))
return false;
if (tr != null && !checkInvariants(tr))
return false;
return true;
}
}