DataStructure——红黑树学习笔记
Posted Avery-Lyu
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1.前言
- 本文伪码和解释参考：
http://blog.csdn.net/v_JULY_v/article/details/6105630
- C实现的源码本文未贴出，请见：
http://blog.csdn.net/v_july_v/article/details/6114226
- July的博客对红黑树的分析很精彩，请见：
http://blog.csdn.net/v_JULY_v/article/category/774945
本文对参考资料有所修订和补完（侵删）。
2.正文
伪码中使用的符号：
1 N：node，当前节点 2 S：sibling，当前节点的兄弟节点 3 P：praent，当前节点的父节点 4 U：uncle，当前节点的叔节点，即父节点的兄弟节点 5 G：graparent，当前节点的祖辈节点，即父节点的父节点 6 ←：赋值 7 ==或=：是否相等 8 ≠：不等 9 x.p：x的父节点 10 N:L或N:R：节点N是父节点的左孩子（大写L，Left），或，节点N是父节点的右孩子（大写R，Right） 11 N:r或N:b：节点N是红色的（小写r，red），或，节点N是黑色的（小写b，black） 12 <N:r>：条件判断，判断N:r是否成立 13 #n：相当于#Case n，即情况n（n=1,2,3.....） 14 L_rt(N)或R_rt(N)：以节点N为轴心，进行左旋转操作（L_rt），或，右旋操作（R_rt）
伪码：
1 //-------------RBTree:Insesrt-----------// 2 RB-INSERT(T, z) 3 y ← nil 4 x ← T.root 5 while x ≠ nil 6 do y ← x 7 if z.key < x.key 8 then x ← x.left 9 else x ← x.right 10 z.p ← y 11 if y == nil 12 then T.root ← z 13 else if z.key < y.key 14 then y.left ← z 15 else y.right ← z 16 z.left ← nil 17 z.right ← nil 18 z.color ← RED 19 RB-INSERT-FIXUP(T, z) 20 21 //-------------RBTree:Insert-FIXUP-----------// 22 RB-INSERT-FIXUP(T, z) 23 while z.p.color == RED //fixup only in case P:r 24 do if z.p == z.p.p.left //P:L 25 then y ← z.p.p.right 26 if y.color == RED //U:r , # Case 27 then z.p.color ← BLACK //P ← b,U ← b,G ← r # 28 y.color ← BLACK 29 z.p.p.color ← RED 30 z ← z.p.p //N ← G 31 else //U:b , # Case -> # Case 32 if z == z.p.right //N:R , 33 then z ← z.p // N ← P,L_rt(T,N) 34 LEFT-ROTATE(T, z) 35 z.p.color ← BLACK //<U:b> , P ← b,G ← r,R_rt(T,G) # Case 36 z.p.p.color ← RED 37 RIGHT-ROTATE(T, z.p.p) 38 else if z.p == z.p.p.right //<P:R> 39 y ← z.p.p.left 40 if y.color == RED //<U:r> , # Case 41 then z.p.color ← BLACK //P ← b,U ← b,G ← r # 42 y.color ← BLACK 43 z.p.p.color ← RED 44 z ← z.p.p //N ← G 45 else //<U:b> , # Case -> # Case 46 if z == z.p.left //<U:b,N:L> , N ← P,R_rt(T,N) 47 then z ← z.p 48 RIGHT-ROTATE(T, z) 49 z.p.color ← BLACK //<U:b> , P ← b,G ← r,L_rt(T,G) # Case 50 z.p.p.color ← RED 51 LEFT-ROTATE(T, z.p.p) 52 T.root.color ← BLACK 53 54 //-------------RBTree:Delete-----------// 55 RB-DELETE(T, z) //y was deleted , x 56 if z.left = NIL or z.right = NIL //N doesnot have child node 57 then y ← z 58 else y ← TREE-SUCCESSOR(z) //TREE-SUCCESSOR(z):find the Lmax in subtree:z 59 if y.left ≠ NIL 60 then x ← y.left 61 else x ← y.right 62 if x ≠ NIL 63 x.p ← y.p 64 if y.p = NIL //in case N is root 65 then T.root ← x 66 else if y = y.p.left //in case single child 67 then y.p.left ← x 68 else y.p.rght ← x 69 if y ≠ z //in case double child 70 then z.key ← y.key //cover but not remove 71 copy y‘s satellite data into z 72 if y.color = BLACK //fixup only when <N:b>=true 73 then RB-DELETE-FIXUP(T, x) 74 return y 75 76 //-------------RBTree:Delete-Fixup-----------// 77 RB-DELETE-FIXUP(T, x) 78 while x ≠ T.root and x.color = BLACK 79 do 80 if x = x.p.left //<N:L> 81 then w ← x.p.right //w ← S:R 82 if w.color = RED //<w:r> #1 83 then w.color ← BLACK //S:b , P:r , L_rt(P) ,w ← S:R 84 x.p.color ← RED 85 LEFT-ROTATE(T, x.p) 86 w ← x.p.right 87 if w.left.color = BLACK and w.right.color = BLACK //<S.left:b & S.right:b> #2 88 then w.color ← RED //S:r , N ← P 89 x ← x.p 90 else if w.right.color = BLACK //<S.right:b> #3 91 then w.left.color ← BLACK //S.left:b , S:r , R_rt(S) , 92 w.color ← RED 93 RIGHT-ROTATE(T, w) 94 w ← x.p.right //new N‘s S cos of the R_rt() 95 w.color ← x.p.color //S.color ← P.color，P:b，S.right:b，L_rt(P), #4 96 x.p.color ← BLACK 97 w.right.color ← BLACK 98 LEFT-ROTATE(T, x.p) 99 x ← T.root //break,exit while{} 100 else 101 w ← x.p.left 102 if w.color = RED 103 then w.color ← BLACK 104 x.p.color ← RED 105 RIGHT-ROTATE(T, x.p) 106 w ← x.p.left 107 if w.left.color = BLACK and w.right.color = BLACK 108 then w.color ← RED 109 x ← x.p 110 else if w.left.color = BLACK 111 then w.right.color ← BLACK 112 w.color ← RED 113 LEFT-ROTATE(T, w) 114 w ← x.p.left 115 w.color ← x.p.color 116 x.p.color ← BLACK 117 w.left.color ← BLACK 118 RIGHT-ROTATE(T, x.p) 119 x ← T.root 120 x.color ← BLACK
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