由于CSDN单篇帖子的字数限制，补充上一篇快速排序1中的对向双指针算法的图解：

2.2.2 对向双指针

在对向双指针的排序方式中，以key值为序列中点元素为例。图解如下：

待排序数组

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3
5
7
4
6
8
2
1
9

取中点元素6，为key值，在对向双指针的排序中，key值所在的位置有可能被交换，所以需要在排序开始时保存key值保存到数组外部的变量中

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记录key值
6
3
5
7
4
key
6
8
2
1
9

从左右两端对向查找符合条件的数，使用left指针从左向右查找大于等于key值的数，使用right指针从右向左查找小于等于key值的数，直到满足结束条件”left>right“

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key
6
left->
3
5
7
4
6
8
2
1
<-right
9

left指针查找到第一个大于等于key:6的数为7，right指针查找到第一个小于等于key:6的数为1

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key
6
3
5
left->
7
4
6
8
2
<-right
1
9

交换两者之后，left和right继续查找，left找到大于等于key:6的数6，right找到小于等于key:6的数2

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key
6
3
5
1
4
left->
6
8
<-right
2
7
9

交换两者之后，left和right继续查找，left找到大于等于key:6的数8，right找到小于等于key:6的数2，此时满足结束条件“left>right”，第一轮排序结束

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key
6
3
5
1
4
<-right
2
left->
8
6
7
9

区间以left和right指针的位置，分成了“小值/key/大值”的形式（也有可能形成“小值/大值”的形式）

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大值8679
小值35142
9
7
6
left->
8
<-right
2
4
1
5
3

左右区间再分别进行递归快排

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子递归:对右区间排序
子递归:对左区间排序
key
6
<-right
9
7
key
6
left->
8
key
1
<-right
2
4
key
1
5
left->
3

左区间找到3和1，右区间找到8和6

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该位置的第二轮排序
该位置第二轮排序
key
6
9
7
<-right
6
left->
8
key
1
2
4
<-right
1
5
left->
3

分别交换之后，继续查找，左区间满足“left>right”完成该位置的第二轮排序，形成”小值/大值“的形式；右区间满足“left>right”完成该位置的第二轮排序，形成”小值/大值“的形式

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该位置的第二轮排序后:小值6/大值879
该位置第二轮排序后:小值1/大值4352
key
6
9
7
left->
8
<-right
6
key
1
2
5
3
left->
4
<-right
1

左区间进行第三轮排序，key为3；右区间进行第三轮排序，key为7

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该位置的第二轮排序
该位置第二轮排序
该位置的第三轮排序
该位置第三轮排序
6
key
7
<-right
9
key
7
left->
8
1
key
3
<-right
2
5
key
3
left->
4

左区间找到4和2；右区间找到8和7

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该位置的第二轮排序
该位置第二轮排序
该位置的第三轮排序
该位置第三轮排序
6
key
7
9
<-right
7
left->
8
1
key
3
<-right
2
5
3
left->
4

分别交换之后，继续查找，左区间找到3和3；右区间满足“left>right”完成该位置的第三轮排序

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该位置的第二轮排序
该位置第二轮排序
该位置的第三轮排序后:小值7/大值89
该位置第三轮排序
6
key
7
9
<-right
8
left->
7
1
key
3
4
5
left->
<-right
3
2

左区间交换找到的数（3与自身交换）之后，满足“left>right”完成该位置的第三轮排序；右区间进行第四轮排序，key为8

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该位置的第二轮排序
该位置第二轮排序
该位置的第三轮排序
该位置的第四轮排序
该位置第三轮排序后
6
7
key
8
<-right
9
left->
8
1
key
3
4
left->
5
3
<-right
2

左区间进行第四轮排序，key为5；右区间满足“left>right”完成第四轮排序，至此右区间已有序

#mermaid-svg-eH5GGJZN1rRFBC4t {font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:16px;fill:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t .error-icon{fill:#552222;}#mermaid-svg-eH5GGJZN1rRFBC4t .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-eH5GGJZN1rRFBC4t .edge-thickness-normal{stroke-width:2px;}#mermaid-svg-eH5GGJZN1rRFBC4t .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-eH5GGJZN1rRFBC4t .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-eH5GGJZN1rRFBC4t .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-eH5GGJZN1rRFBC4t .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-eH5GGJZN1rRFBC4t .marker{fill:#333333;stroke:#333333;}#mermaid-svg-eH5GGJZN1rRFBC4t .marker.cross{stroke:#333333;}#mermaid-svg-eH5GGJZN1rRFBC4t svg{font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-eH5GGJZN1rRFBC4t .label{font-family:"trebuchet ms",verdana,arial,sans-serif;color:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t .cluster-label text{fill:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t .cluster-label span{color:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t .label text,#mermaid-svg-eH5GGJZN1rRFBC4t span{fill:#333;color:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t .node rect,#mermaid-svg-eH5GGJZN1rRFBC4t .node circle,#mermaid-svg-eH5GGJZN1rRFBC4t .node ellipse,#mermaid-svg-eH5GGJZN1rRFBC4t .node polygon,#mermaid-svg-eH5GGJZN1rRFBC4t .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-eH5GGJZN1rRFBC4t .node .label{text-align:center;}#mermaid-svg-eH5GGJZN1rRFBC4t .node.clickable{cursor:pointer;}#mermaid-svg-eH5GGJZN1rRFBC4t .arrowheadPath{fill:#333333;}#mermaid-svg-eH5GGJZN1rRFBC4t .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-eH5GGJZN1rRFBC4t .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-eH5GGJZN1rRFBC4t .edgeLabel{background-color:#e8e8e8;text-align:center;}#mermaid-svg-eH5GGJZN1rRFBC4t .edgeLabel rect{opacity:0.5;background-color:#e8e8e8;fill:#e8e8e8;}#mermaid-svg-eH5GGJZN1rRFBC4t .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-eH5GGJZN1rRFBC4t .cluster text{fill:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t .cluster span{color:#333;}#mermaid-svg-eH5GGJZN1rRFBC4t div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-eH5GGJZN1rRFBC4t :root{--mermaid-font-family:"trebuchet ms",verdana,arial,sans-serif;}

右区间第二轮排序后
子递归:对左区间排序
该位置的第三轮排序
该位置的第四轮排序:小值8/大值9
该位置第三轮排序
该位置第四轮排序
6
7
key
8
left->
9
<-right
8
2
1
3
key
5
<-right
4
left->
5

左区间找到5和4

#mermaid-svg-axqhwRq4Ppu3qG8C {font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:16px;fill:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C .error-icon{fill:#552222;}#mermaid-svg-axqhwRq4Ppu3qG8C .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-axqhwRq4Ppu3qG8C .edge-thickness-normal{stroke-width:2px;}#mermaid-svg-axqhwRq4Ppu3qG8C .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-axqhwRq4Ppu3qG8C .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-axqhwRq4Ppu3qG8C .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-axqhwRq4Ppu3qG8C .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-axqhwRq4Ppu3qG8C .marker{fill:#333333;stroke:#333333;}#mermaid-svg-axqhwRq4Ppu3qG8C .marker.cross{stroke:#333333;}#mermaid-svg-axqhwRq4Ppu3qG8C svg{font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-axqhwRq4Ppu3qG8C .label{font-family:"trebuchet ms",verdana,arial,sans-serif;color:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C .cluster-label text{fill:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C .cluster-label span{color:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C .label text,#mermaid-svg-axqhwRq4Ppu3qG8C span{fill:#333;color:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C .node rect,#mermaid-svg-axqhwRq4Ppu3qG8C .node circle,#mermaid-svg-axqhwRq4Ppu3qG8C .node ellipse,#mermaid-svg-axqhwRq4Ppu3qG8C .node polygon,#mermaid-svg-axqhwRq4Ppu3qG8C .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-axqhwRq4Ppu3qG8C .node .label{text-align:center;}#mermaid-svg-axqhwRq4Ppu3qG8C .node.clickable{cursor:pointer;}#mermaid-svg-axqhwRq4Ppu3qG8C .arrowheadPath{fill:#333333;}#mermaid-svg-axqhwRq4Ppu3qG8C .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-axqhwRq4Ppu3qG8C .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-axqhwRq4Ppu3qG8C .edgeLabel{background-color:#e8e8e8;text-align:center;}#mermaid-svg-axqhwRq4Ppu3qG8C .edgeLabel rect{opacity:0.5;background-color:#e8e8e8;fill:#e8e8e8;}#mermaid-svg-axqhwRq4Ppu3qG8C .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-axqhwRq4Ppu3qG8C .cluster text{fill:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C .cluster span{color:#333;}#mermaid-svg-axqhwRq4Ppu3qG8C div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-axqhwRq4Ppu3qG8C :root{--mermaid-font-family:"trebuchet ms",verdana,arial,sans-serif;}

右区间已有序
子递归:对左区间排序
该位置第三轮排序
该位置第四轮排序
9
8
7
6
2
1
3
key
5
<-right
4
left->
5

交换两者，继续查找，此时左区间满足“left>right”完成第四轮排序，形成”小值/大值“的形式，至此左区间已有序

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右区间已有序
子递归:对左区间排序
该位置第三轮排序
该位置第四轮排序
9
8
7
6
2
1
3
key
5
left->
5
<-right
4

整个序列排序完成

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9

  1. 快速排序：https://blog.csdn.net/SeeDoubleU/article/details/122421967 ↩︎

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