摘要：在上一節(jié)中，在中用了鏈表和紅黑樹兩種方式解決沖突，在中也是用紅黑樹存儲(chǔ)的。其中節(jié)點(diǎn)顏色為黑色紅黑樹的左旋和右旋紅黑樹的插入和刪除，都有可能破壞其特性，就不是一棵紅黑樹了，所以要調(diào)整。
在上一節(jié)中，HashMap在jdk 1.8中用了鏈表和紅黑樹兩種方式解決沖突，在TreeMap中也是用紅黑樹存儲(chǔ)的。下面分析一下紅黑樹的結(jié)構(gòu)和基本操作。
一、紅黑樹的特征和基本操作
上一節(jié)中已經(jīng)描述了紅黑樹的基本概念和特征，下面直接通過(guò)一個(gè)例子分析紅黑樹的構(gòu)造和調(diào)整方法。
1、紅黑樹的數(shù)據(jù)結(jié)構(gòu)
紅黑樹是一棵二叉查找樹，在二叉樹的基礎(chǔ)上增加了節(jié)點(diǎn)的顏色，下面是TreeMap中的紅黑樹定義：
private static final boolean RED = false;
private static final boolean BLACK = true;
static final class Entry implements Map.Entry {
K key;
V value;
Entry left;
Entry right;
Entry parent;
boolean color = BLACK;
/**
* 給定key、value和父節(jié)點(diǎn)，構(gòu)造一個(gè)新的。其中節(jié)點(diǎn)顏色為黑色
*/
Entry(K key, V value, Entry parent) {
this.key = key;
this.value = value;
this.parent = parent;
}
}
2、紅黑樹的左旋和右旋
紅黑樹的插入和刪除，都有可能破壞其特性，就不是一棵紅黑樹了，所以要調(diào)整。調(diào)整的方法又兩種，一種是改變某個(gè)節(jié)點(diǎn)的顏色，另外一種是結(jié)構(gòu)調(diào)整，包括左旋和右旋。
左旋：將X的節(jié)點(diǎn)的右兒子節(jié)點(diǎn)Y變?yōu)槠涓腹?jié)點(diǎn)，并且將Y的左子樹變?yōu)閄的右子樹，變換過(guò)程入下圖
右旋：將X的節(jié)點(diǎn)的左兒子節(jié)點(diǎn)Y變?yōu)槠涓腹?jié)點(diǎn)，并且將Y的右子樹變?yōu)閄的左子樹，變換過(guò)程入下圖
3、插入節(jié)點(diǎn)后調(diào)整紅黑樹
當(dāng)在紅黑樹中插入一個(gè)節(jié)點(diǎn)后，可能會(huì)破壞紅黑樹的規(guī)則，首先再回顧一下紅黑數(shù)的特點(diǎn)：
節(jié)點(diǎn)是紅色或黑色。
根節(jié)點(diǎn)是黑色。
每個(gè)葉子節(jié)點(diǎn)都是黑色的空節(jié)點(diǎn)（NIL節(jié)點(diǎn)）。
每個(gè)紅色節(jié)點(diǎn)的兩個(gè)子節(jié)點(diǎn)都是黑色。(從每個(gè)葉子到根的所有路徑上不能有兩個(gè)連續(xù)的紅色節(jié)點(diǎn))
從任一節(jié)點(diǎn)到其每個(gè)葉子的所有路徑都包含相同數(shù)目的黑色節(jié)點(diǎn)。
從上面的條件可以看出，a肯定是不會(huì)違背的。插入的節(jié)點(diǎn)不在根節(jié)點(diǎn)處，所以b也不會(huì)違背。插入的節(jié)點(diǎn)時(shí)非空節(jié)點(diǎn)，c也不會(huì)違背。最有可能違背的就是d和e。而在我們插入節(jié)點(diǎn)時(shí)，先將要插入的節(jié)點(diǎn)顏色設(shè)置為紅色，這樣也就不會(huì)違背e。所以，插入后只需要調(diào)整不違背e就可以。
插入后調(diào)整需要分三種情況來(lái)處理：
插入的是根節(jié)點(diǎn):
處理方法是直接將根節(jié)點(diǎn)顏色設(shè)置為黑色
插入節(jié)點(diǎn)的父節(jié)點(diǎn)為黑色節(jié)點(diǎn)或父節(jié)點(diǎn)為根節(jié)點(diǎn)
不需要處理
插入節(jié)點(diǎn)的父節(jié)點(diǎn)時(shí)紅色節(jié)點(diǎn)
這種又分為三種情況
下面假設(shè)插入節(jié)點(diǎn)為x，父節(jié)點(diǎn)為xp，祖父節(jié)點(diǎn)為xpp，祖父節(jié)點(diǎn)的左兒子為xppl，祖父節(jié)點(diǎn)的右兒子為xppr
S1：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，且當(dāng)前節(jié)點(diǎn)的祖父節(jié)xpp點(diǎn)的另一個(gè)子節(jié)點(diǎn)（xppl或者xppr）也是紅色
處理邏輯：將父節(jié)點(diǎn)xp設(shè)為紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）設(shè)為黑色，將祖父節(jié)點(diǎn)xpp設(shè)為紅色，將祖父節(jié)點(diǎn)xpp設(shè)為當(dāng)前節(jié)點(diǎn)，繼續(xù)處理。
S2：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）是黑色，且當(dāng)前節(jié)點(diǎn)x是其父節(jié)點(diǎn)xp的右孩子
處理邏輯：父節(jié)點(diǎn)xp作為當(dāng)前節(jié)點(diǎn)x， 以當(dāng)前節(jié)點(diǎn)x為支點(diǎn)進(jìn)行左旋。
S3：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）是黑色，且當(dāng)前節(jié)點(diǎn)是其父節(jié)點(diǎn)xp的左孩子
處理邏輯：將父節(jié)點(diǎn)xp設(shè)置為黑色，祖父節(jié)點(diǎn)xpp設(shè)置為紅色，以祖父節(jié)點(diǎn)xpp為支點(diǎn)進(jìn)行右旋
4、刪除節(jié)點(diǎn)后調(diào)整紅黑樹
未完，待續(xù)。。。
3、構(gòu)造一棵紅黑樹
通過(guò)插入節(jié)點(diǎn)，構(gòu)造紅黑樹
現(xiàn)在給定節(jié)點(diǎn)8 5 3 9 12 1 4 2，依次插入紅黑樹中，具體流程見(jiàn)下圖：
在紅黑樹中刪除節(jié)點(diǎn)
未完，待續(xù)。。。
二、HashMap中的紅黑樹相關(guān)源碼
static final class TreeNode extends LinkedHashMap.Entry {
TreeNode parent; // red-black tree links
TreeNode left;
TreeNode right;
//在節(jié)點(diǎn)刪除后，需解除鏈接
TreeNode prev;
boolean red;
TreeNode(int hash, K key, V val, Node next) {
super(hash, key, val, next);
}
/**
* 返回根節(jié)點(diǎn)
*/
final TreeNode root() {
for (TreeNode r = this, p;;) {
if ((p = r.parent) == null)
return r;
r = p;
}
}
/**
* 確保根節(jié)點(diǎn)就是第一個(gè)節(jié)點(diǎn)
*/
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];
//如果根節(jié)點(diǎn)不是第一個(gè)節(jié)點(diǎn)，進(jìn)行調(diào)整
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);
}
}
/**
* 根據(jù)hash值和key查詢節(jié)點(diǎn)
*/
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;
}
/**
* 根據(jù)hash值和key查詢節(jié)點(diǎn)
*/
final TreeNode getTreeNode(int h, Object k) {
return ((parent != null) ? root() : this).find(h, k, null);
}
/**
* 將鏈表轉(zhuǎn)換為紅黑樹
*/
final void treeify(Node[] tab) {
TreeNode root = null;
//從第一個(gè)節(jié)點(diǎn)開始
for (TreeNode x = this, next; x != null; x = next) {
next = (TreeNode)x.next;
x.left = x.right = null;
//如果root節(jié)點(diǎn)為null，x為根節(jié)點(diǎn)，此節(jié)點(diǎn)為黑色，父節(jié)點(diǎn)為null
if (root == null) {
x.parent = null;
x.red = false;
root = x;
}
else {
//x的key值
K k = x.key;
//x的hash值
int h = x.hash;
Class kc = null;
for (TreeNode p = root;;) {
int dir, ph;
K pk = p.key;
//左邊
if ((ph = p.hash) > h)
dir = -1;
//右邊
else if (ph < h)
dir = 1;
//通過(guò)仲裁方法判斷
else if ((kc == null &&
(kc = comparableClassFor(k)) == null) ||
(dir = compareComparables(kc, k, pk)) == 0)
dir = tieBreakOrder(k, pk);
TreeNode xp = p;
//dir <=0 左子樹搜索，并且判斷左兒子是否為空，表示是否到葉子節(jié)點(diǎn)
if ((p = (dir <= 0) ? p.left : p.right) == null) {
x.parent = xp;
if (dir <= 0)
xp.left = x;
else
xp.right = x;
//插入元素，判斷是否平衡，并且調(diào)整
root = balanceInsertion(root, x);
break;
}
}
}
}
//確保根節(jié)點(diǎn)就是第一個(gè)節(jié)點(diǎn)
moveRootToFront(tab, root);
}
/**
* 紅黑樹轉(zhuǎn)換為鏈表
*/
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;
}
/**
* 插入一個(gè)節(jié)點(diǎn)
*/
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;
//從根據(jù)點(diǎn)開始，和當(dāng)前搜索節(jié)點(diǎn)的hash比較
for (TreeNode p = root;;) {
int dir, ph; K pk;
if ((ph = p.hash) > h)
dir = -1;
else if (ph < h)
dir = 1;
//hash和key都一致
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;
//新建節(jié)點(diǎn)
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;
//插入元素，判斷是否平衡，并且調(diào)整。確保根節(jié)點(diǎn)就是第一個(gè)節(jié)點(diǎn)
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);
}
/* ------------------------------------------------------------ */
// Red-black tree methods, all adapted from CLR
//左旋
static TreeNode rotateLeft(TreeNode root,
TreeNode p) {
TreeNode r, pp, rl;
//以p為左旋支點(diǎn)，且p不為空，右兒子不為空
if (p != null && (r = p.right) != null) {
//將p的右兒子r的左兒子rl變?yōu)閜的右兒子
if ((rl = p.right = r.left) != null)
rl.parent = p;
//處理p、l和p父節(jié)點(diǎn)的關(guān)系
if ((pp = r.parent = p.parent) == null)
(root = r).red = false;
else if (pp.left == p)
pp.left = r;
else
pp.right = r;
//處理p和r的關(guān)系
r.left = p;
p.parent = r;
}
return root;
}
//右旋
static TreeNode rotateRight(TreeNode root,
TreeNode p) {
TreeNode l, pp, lr;
//p:右旋支點(diǎn)，不為空，p的左兒子l不為空
if (p != null && (l = p.left) != null) {
//將左兒子的右子樹變?yōu)閜的左子樹
if ((lr = p.left = l.right) != null)
lr.parent = p;
//p的父節(jié)點(diǎn)變?yōu)閘的父節(jié)點(diǎn)
if ((pp = l.parent = p.parent) == null)
(root = l).red = false;
//如果p為右兒子，則p的父節(jié)點(diǎn)的右兒子變?yōu)閘,否則左兒子變?yōu)閘
else if (pp.right == p)
pp.right = l;
else
pp.left = l;
//p變?yōu)閘的右兒子
l.right = p;
p.parent = l;
}
return root;
}
static TreeNode balanceInsertion(TreeNode root,
TreeNode x) {
//插入節(jié)點(diǎn)初始化為紅色
x.red = true;
//xp:父節(jié)點(diǎn)，xpp:祖父節(jié)點(diǎn)， xppl：祖父節(jié)點(diǎn)的左兒子，xppr:祖父節(jié)點(diǎn)的右兒子
//循環(huán)遍歷
for (TreeNode xp, xpp, xppl, xppr;;) {
//插入的節(jié)點(diǎn)為根節(jié)點(diǎn)，節(jié)點(diǎn)顏色轉(zhuǎn)換為黑色
if ((xp = x.parent) == null) {
x.red = false;
return x;
}
//當(dāng)前節(jié)點(diǎn)的父為黑色節(jié)點(diǎn)或者父節(jié)點(diǎn)為根節(jié)點(diǎn)，直接返回
else if (!xp.red || (xpp = xp.parent) == null)
return root;
//祖父節(jié)點(diǎn)的左兒子是父節(jié)點(diǎn)
if (xp == (xppl = xpp.left)) {
//S1：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，且當(dāng)前節(jié)點(diǎn)的祖父節(jié)xpp點(diǎn)的另一個(gè)子節(jié)點(diǎn)（xppl或者xppr）也是紅色
if ((xppr = xpp.right) != null && xppr.red) {
xppr.red = false;
xp.red = false;
xpp.red = true;
x = xpp;
}
else {
//S2：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）是黑色，且當(dāng)前節(jié)點(diǎn)x是其父節(jié)點(diǎn)xp的右孩子
if (x == xp.right) {
root = rotateLeft(root, x = xp);
xpp = (xp = x.parent) == null ? null : xp.parent;
}
//S3：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）是黑色，且當(dāng)前節(jié)點(diǎn)是其父節(jié)點(diǎn)xp的左孩子
if (xp != null) {
xp.red = false;
if (xpp != null) {
xpp.red = true;
root = rotateRight(root, xpp);
}
}
}
}
else {
//S1：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，且當(dāng)前節(jié)點(diǎn)的祖父節(jié)xpp點(diǎn)的另一個(gè)子節(jié)點(diǎn)（xppl或者xppr）也是紅色
if (xppl != null && xppl.red) {
xppl.red = false;
xp.red = false;
xpp.red = true;
x = xpp;
}
else {
//S2：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）是黑色，且當(dāng)前節(jié)點(diǎn)x是其父節(jié)點(diǎn)xp的右孩子
if (x == xp.left) {
root = rotateRight(root, x = xp);
xpp = (xp = x.parent) == null ? null : xp.parent;
}
//S3：當(dāng)前節(jié)點(diǎn)的父節(jié)點(diǎn)xp是紅色，祖父節(jié)點(diǎn)的兒子節(jié)點(diǎn)（xppl或者xppr）是黑色，且當(dāng)前節(jié)點(diǎn)是其父節(jié)點(diǎn)xp的左孩子
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;
}
}
}
}
}
}
三、總結(jié)
文章版權(quán)歸作者所有，未經(jīng)允許請(qǐng)勿轉(zhuǎn)載,若此文章存在違規(guī)行為，您可以聯(lián)系管理員刪除。
轉(zhuǎn)載請(qǐng)注明本文地址：http://m.hztianpu.com/yun/72103.html
