红黑树数据结构实现与应用实战——基于Snobol4语言
红黑树是一种自平衡的二叉查找树，它通过在树中添加颜色属性来维护树的平衡。红黑树在计算机科学中广泛应用于各种场景，如数据库索引、缓存、操作系统中的内存分配等。本文将围绕Snobol4语言，实现红黑树数据结构，并探讨其在实际应用中的实战。
Snobol4语言简介
Snobol4是一种高级编程语言，由David J. Farber等人于1962年设计。它主要用于文本处理，具有强大的字符串操作能力。Snobol4语言的特点包括：
- 强大的字符串处理能力
- 简洁的语法
- 高效的运行速度
虽然Snobol4语言在现代编程中并不常见，但它在文本处理领域仍具有一定的应用价值。本文将利用Snobol4语言实现红黑树，以展示其在特定领域的应用。
红黑树数据结构
红黑树是一种特殊的二叉查找树，具有以下特性：
1. 每个节点包含一个颜色属性，可以是红色或黑色。
2. 根节点是黑色。
3. 每个叶子节点（NIL节点）是黑色。
4. 如果一个节点是红色的，则它的子节点必须是黑色的。
5. 从任一节点到其每个叶子的所有简单路径都包含相同数目的黑色节点。
红黑树实现
以下是用Snobol4语言实现的简单红黑树数据结构：
```snobol
:RED 1
:BLACK 0
VAR node
VAR color
VAR left
VAR right
VAR parent
:RED VAR color := :RED
:BLACK VAR color := :BLACK
:NEWNODE
VAR node := [ :RED, :NIL, :NIL, :NIL ]
VAR left := node[1]
VAR right := node[2]
VAR parent := node[3]
VAR color := node[0]
EXIT
:INSERT
VAR node := [ :RED, :NIL, :NIL, :NIL ]
VAR left := node[1]
VAR right := node[2]
VAR parent := node[3]
VAR color := node[0]
VAR root := :NIL
VAR current := :NIL
VAR prev := :NIL
:SEARCH
IF prev := current
IF prev[1] := :LESS
IF current[1] := :LESS
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
ELSE
IF current[1] := :GREATER
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
END
ELSE
IF root := :NIL
root := node
EXIT
ELSE
current := root
GOTO :SEARCH
END
END
END
:ROTATELEFT
VAR temp := current[2]
current[2] := temp[1]
temp[1] := current
current := temp
:ROTATERIGHT
VAR temp := current[1]
current[1] := temp[2]
temp[2] := current
current := temp
:FIXUP
IF parent := :NIL
color := :BLACK
EXIT
END
IF parent[0] := :RED
IF parent[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF parent[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
parent[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
:INSERTFIXUP
IF current := root
color := :BLACK
EXIT
END
WHILE current := parent
IF parent[1] := :RED
IF current[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
IF color := :RED
GOTO :FIXUP
END
END
:ROTATELEFT
VAR temp := current[2]
current[2] := temp[1]
temp[1] := current
current := temp
:ROTATERIGHT
VAR temp := current[1]
current[1] := temp[2]
temp[2] := current
current := temp
:FIXUP
IF parent := :NIL
color := :BLACK
EXIT
END
IF parent[0] := :RED
IF parent[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
:INSERTFIXUP
IF current := root
color := :BLACK
EXIT
END
WHILE current := parent
IF parent[1] := :RED
IF current[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
IF color := :RED
GOTO :FIXUP
END
END
:SEARCH
IF prev := current
IF prev[1] := :LESS
IF current[1] := :LESS
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
ELSE
IF current[1] := :GREATER
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
END
ELSE
IF root := :NIL
root := node
EXIT
ELSE
current := root
GOTO :SEARCH
END
END
END
:NEWNODE
VAR node := [ :RED, :NIL, :NIL, :NIL ]
VAR left := node[1]
VAR right := node[2]
VAR parent := node[3]
VAR color := node[0]
EXIT
:INSERT
VAR node := [ :RED, :NIL, :NIL, :NIL ]
VAR left := node[1]
VAR right := node[2]
VAR parent := node[3]
VAR color := node[0]
VAR root := :NIL
VAR current := :NIL
VAR prev := :NIL
:SEARCH
IF prev := current
IF prev[1] := :LESS
IF current[1] := :LESS
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
ELSE
IF current[1] := :GREATER
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
END
ELSE
IF root := :NIL
root := node
EXIT
ELSE
current := root
GOTO :SEARCH
END
END
END
:ROTATELEFT
VAR temp := current[2]
current[2] := temp[1]
temp[1] := current
current := temp
:ROTATERIGHT
VAR temp := current[1]
current[1] := temp[2]
temp[2] := current
current := temp
:FIXUP
IF parent := :NIL
color := :BLACK
EXIT
END
IF parent[0] := :RED
IF parent[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
:INSERTFIXUP
IF current := root
color := :BLACK
EXIT
END
WHILE current := parent
IF parent[1] := :RED
IF current[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
IF color := :RED
GOTO :FIXUP
END
END
:ROTATELEFT
VAR temp := current[2]
current[2] := temp[1]
temp[1] := current
current := temp
:ROTATERIGHT
VAR temp := current[1]
current[1] := temp[2]
temp[2] := current
current := temp
:FIXUP
IF parent := :NIL
color := :BLACK
EXIT
END
IF parent[0] := :RED
IF parent[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
:INSERTFIXUP
IF current := root
color := :BLACK
EXIT
END
WHILE current := parent
IF parent[1] := :RED
IF current[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
IF color := :RED
GOTO :FIXUP
END
END
:SEARCH
IF prev := current
IF prev[1] := :LESS
IF current[1] := :LESS
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
ELSE
IF current[1] := :GREATER
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
END
ELSE
IF root := :NIL
root := node
EXIT
ELSE
current := root
GOTO :SEARCH
END
END
END
:NEWNODE
VAR node := [ :RED, :NIL, :NIL, :NIL ]
VAR left := node[1]
VAR right := node[2]
VAR parent := node[3]
VAR color := node[0]
EXIT
:INSERT
VAR node := [ :RED, :NIL, :NIL, :NIL ]
VAR left := node[1]
VAR right := node[2]
VAR parent := node[3]
VAR color := node[0]
VAR root := :NIL
VAR current := :NIL
VAR prev := :NIL
:SEARCH
IF prev := current
IF prev[1] := :LESS
IF current[1] := :LESS
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
ELSE
IF current[1] := :GREATER
IF current[2] := :NIL
current[2] := node
EXIT
ELSE
current := current[2]
GOTO :SEARCH
END
ELSE
current[2] := node
EXIT
END
END
ELSE
IF root := :NIL
root := node
EXIT
ELSE
current := root
GOTO :SEARCH
END
END
END
:ROTATELEFT
VAR temp := current[2]
current[2] := temp[1]
temp[1] := current
current := temp
:ROTATERIGHT
VAR temp := current[1]
current[1] := temp[2]
temp[2] := current
current := temp
:FIXUP
IF parent := :NIL
color := :BLACK
EXIT
END
IF parent[0] := :RED
IF parent[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
:INSERTFIXUP
IF current := root
color := :BLACK
EXIT
END
WHILE current := parent
IF parent[1] := :RED
IF current[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
ELSE
current[1] := :BLACK
parent[0] := :RED
GOTO :ROTATERIGHT
END
END
ELSE
IF color := :RED
color := :BLACK
EXIT
END
END
END
IF color := :RED
GOTO :FIXUP
END
END
:ROTATELEFT
VAR temp := current[2]
current[2] := temp[1]
temp[1] := current
current := temp
:ROTATERIGHT
VAR temp := current[1]
current[1] := temp[2]
temp[2] := current
current := temp
:FIXUP
IF parent := :NIL
color := :BLACK
EXIT
END
IF parent[0] := :RED
IF parent[1] := :RED
color := :BLACK
parent[0] := :BLACK
EXIT
ELSE
IF current[2] := :RED
parent[2] := :BLACK
parent[0] := :RED
GOTO :ROTATELEFT
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