写在前面：
一，本文侧重诠释对算法的思考记录过程，忽略其他诸如代码简洁、字符编码等细节问题。
二，本文结合 红黑树插入过程图示 这篇一起看，有助于理解。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 | package main import "fmt" type Node struct {<!-- --> Data int Left *Node Right *Node Color int Parent *Node } //红黑树（Red-Black Tree）是每个节点都带有颜色属性的二叉排序（查找）树，具备以下特性： //1,节点是红色或黑色 //2,根节点是黑色的 //3,每个叶子节点都是黑色的空节点（NIL），也就是说，叶子节点不存储数据 //4,任何相邻的节点都不能同时为红色，也就是说，红色节点是被黑色节点隔开的 //5,每个节点，从该节点到达其可达叶子节点的所有路径，都包含相同数目的黑色节点 type RbTree struct {<!-- --> Tree *Node } const ( RED = 1 BLACK = 0 ) //中序遍历 func (t *RbTree) MidOrderTraverse(tree *Node) {<!-- --> if tree == nil {<!-- --> return } if tree.Left != nil {<!-- --> t.MidOrderTraverse(tree.Left) } fmt.Println(tree) if tree.Right != nil {<!-- --> t.MidOrderTraverse(tree.Right) } } //插入节点 func (t *RbTree) Insert(data int) {<!-- --> //如果是空树，就插入到根节点 if t.Tree == nil {<!-- --> t.Tree = &Node{<!-- -->Data: data} return } tree := t.Tree for tree != nil {<!-- --> if data < tree.Data {<!-- --> if tree.Left == nil {<!-- --> tree.Left = &Node{<!-- -->Data: data, Color: RED, Parent: tree} t.ChangeColor(tree.Left) return } tree = tree.Left } else if data > tree.Data {<!-- --> if tree.Right == nil {<!-- --> tree.Right = &Node{<!-- -->Data: data, Color: RED, Parent: tree} t.ChangeColor(tree.Right) return } tree = tree.Right } } } func (t *RbTree) ChangeColor(tree *Node) {<!-- --> flag := false //被关注节点和其父节点是否在同一侧 //被关注节点的父节点不是根节点 if tree.Parent.Parent != nil {<!-- --> isLeft := t.IsLeft(tree) parentLeft := t.IsLeft(tree.Parent) uncle := t.GetUncle(tree) if isLeft && parentLeft {<!-- --> //被关注节点和其父节点同在左侧 flag = true } else if !isLeft && !parentLeft {<!-- --> //被关注节点和其父节点同在右侧 flag = true } //case1：被关注节点的父节点和叔叔/伯伯节点都是红色 if uncle != nil && tree.Parent.Color == RED && uncle.Color == RED {<!-- --> tree.Parent.Color = BLACK uncle.Color = BLACK if tree.Parent.Parent.Parent != nil {<!-- --> //祖父不是根节点 tree.Parent.Parent.Color = RED tree = tree.Parent.Parent //关注节点变成祖父节点 if tree.Parent.Parent != nil {<!-- --> isLeft = t.IsLeft(tree) parentLeft = t.IsLeft(tree.Parent) uncle = t.GetUncle(tree) if isLeft && parentLeft {<!-- --> flag = true } else if !isLeft && !parentLeft {<!-- --> flag = true } } } } //case2：关注节点和其父节点都是红色，但不在同一侧（同为左侧或同为右侧），且叔叔/伯伯节点是黑色 if tree.Parent.Parent != nil && tree.Parent.Color == RED && (uncle == nil || uncle.Color == BLACK) && !flag {<!-- --> if parentLeft {<!-- --> //父节点在左侧 tree = t.LeftRotate(tree.Parent).Left isLeft = true flag = true } else {<!-- --> tree = t.RightRotate(tree.Parent).Right isLeft = false flag = true } } //case3：关注节点和其父节点都是红色，且在同一侧（同为左侧或同为右侧），且叔叔/伯伯节点是黑色 if tree.Parent.Parent != nil && tree.Parent.Color == RED && (uncle == nil || uncle.Color == BLACK) && flag {<!-- --> tree.Parent.Color = BLACK tree.Parent.Parent.Color = RED if parentLeft {<!-- --> //父节点在左侧 tree = t.RightRotate(tree.Parent.Parent) } else {<!-- --> tree = t.LeftRotate(tree.Parent.Parent) } } else if tree.Parent.Parent != nil && uncle != nil && tree.Parent.Color == RED && uncle.Color == RED {<!-- --> //case1 t.ChangeColor(tree) } } } func (t *RbTree) IsLeft(tree *Node) bool {<!-- --> isLeft := false if tree.Parent != nil && tree.Parent.Left == tree {<!-- --> isLeft = true } return isLeft } func (t *RbTree) GetUncle(tree *Node) *Node {<!-- --> var uncle *Node if tree.Parent.Parent != nil {<!-- --> uncle = tree.Parent.Parent.Left if tree.Parent.Parent.Left == tree.Parent {<!-- --> uncle = tree.Parent.Parent.Right } } return uncle } //右旋 func (t *RbTree) RightRotate(tree *Node) *Node {<!-- --> subTree := tree.Left isLeft := false if tree.Parent != nil {<!-- --> subTree.Parent = tree.Parent //更新新子树的父节点 if tree.Parent.Left == tree {<!-- --> isLeft = true } } else {<!-- --> subTree.Parent = nil } tree.Left = subTree.Right //原来左节点的右子树挂到老的根节点的左子树 if subTree.Right != nil {<!-- --> subTree.Right.Parent = tree } tree.Parent = subTree //原来的左节点变成老的根节点的父节点 subTree.Right = tree //原来的根节点变成原来左节点的右子树 tree = subTree if tree.Parent == nil {<!-- --> //旋转的是整棵树的根节点 t.Tree = tree } else {<!-- --> if isLeft {<!-- --> //更新老的子树根节点父节点指针指向新的根节点 tree.Parent.Left = tree } else {<!-- --> tree.Parent.Right = tree } } return tree } //左旋 func (t *RbTree) LeftRotate(tree *Node) *Node {<!-- --> subTree := tree.Right isLeft := false if tree.Parent != nil {<!-- --> subTree.Parent = tree.Parent if tree.Parent.Left == tree {<!-- --> isLeft = true } } else {<!-- --> subTree.Parent = nil } tree.Right = subTree.Left if subTree.Left != nil {<!-- --> subTree.Left.Parent = tree } tree.Parent = subTree subTree.Left = tree tree = subTree if tree.Parent == nil {<!-- --> t.Tree = tree } else {<!-- --> if isLeft {<!-- --> tree.Parent.Left = tree } else {<!-- --> tree.Parent.Right = tree } } return tree } //测试数据 func main() {<!-- --> treeObj := &RbTree{<!-- -->} treeObj.Insert(99) // treeObj.Insert(78) // treeObj.Insert(120) // treeObj.Insert(66) // treeObj.Insert(83) // treeObj.Insert(57) // treeObj.Insert(52) // treeObj.Insert(61) // treeObj.Insert(64) // treeObj.Insert(59) // treeObj.Insert(60) // treeObj.Insert(70) // treeObj.Insert(75) // treeObj.Insert(72) // treeObj.Insert(74) treeObj.MidOrderTraverse(treeObj.Tree) } |