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📁 插入算法
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<HTML><HEAD><TITLE>插入排序(Inseretion Sort)</TITLE>
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<TABLE class=MsoNormalTable style="WIDTH: 98%" cellSpacing=0 cellPadding=0 
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    style="PADDING-RIGHT: 0cm; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; PADDING-TOP: 0cm">
      <P class=MsoNormal style="TEXT-ALIGN: center" align=center><B><SPAN 
      style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体">插入排序</SPAN></B><B><SPAN 
      lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: Arial">(Inseretion 
      Sort)</SPAN></B></P></TD></TR>
  <TR>
    <TD 
    style="PADDING-RIGHT: 0cm; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; PADDING-TOP: 0cm">
      <P class=MsoNormal style="TEXT-ALIGN: left" align=left><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">&nbsp;&nbsp;&nbsp; 
      </SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">插入排序的基本思想是，经过</SPAN><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">i-1</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">遍处理后</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">,a<SUB>1</SUB>,a<SUB>2</SUB>,..,a<SUB>i-1</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">己排好序。第</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">i</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">遍处理仅将</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">插入</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>1</SUB>,a<SUB>2</SUB>,..,a<SUB>i-1</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">的适当位置，使得</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>1</SUB>,a<SUB>2</SUB>,..,a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">又是排好序的序列。要达到这个目的，我们可以用顺序比较的方法。首先比较</SPAN><SPAN 
      lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">和</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i-1</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，如果</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i-1</SUB> ≤ 
      a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，则</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>1</SUB>,a<SUB>2</SUB>,..,a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">已排好序，第</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">i</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">遍处理就结束了；否则交换</SPAN><SPAN 
      lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">与</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i-1</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">的位置，继续比较</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i-1</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">和</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i-2</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，直到找到某一个位置</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">j(1≤j≤i-1)</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，使得</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>j</SUB> ≤ 
      a<SUB>j+1</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">时为止。图</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">1</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">演示了对</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">4</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">个元素进行插入排序的过程。</SPAN></P>
      <P class=MsoNormal style="TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><A 
      href="file:///F:/算法/insert2.gif"><SPAN style="TEXT-DECORATION: none"><IMG 
      height=32 src="插入排序(Inseretion Sort).files/image002.gif" width=32 
      border=0></SPAN></A></SPAN></P>
      <P class=MsoNormal style="TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">图</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">1 </SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">对</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">4</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">个元素进行插入排序</SPAN></P>
      <P class=MsoNormal style="MARGIN-BOTTOM: 12pt; TEXT-ALIGN: left" 
      align=left><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">在下面的插入排序算法中，为了写程序方便我们可以引入一个哨兵元素</SPAN><SPAN 
      lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>0</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，它小于</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>1</SUB>,a<SUB>2</SUB>,..,a<SUB>n</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">中任一记录。所以，我们设元素的类型</SPAN><SPAN 
      lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">TElement</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">中有一个常量</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">-∞</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，它比可能出现的任何记录都小。如果常量</SPAN><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">-∞</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">不好事先确定，就必须在决定</SPAN><SPAN 
      lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">是否向前移动之前检查当前位置是否为</SPAN><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">1</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">，若当前位置已经为</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">1</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">时就应结束第</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">i</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">遍的处理。另一个办法是在第</SPAN><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">i</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">遍处理开始时，就将</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>i</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">放入</SPAN><SPAN lang=EN-US 
      style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">a<SUB>0</SUB></SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">中，这样也可以保证在适当的时候结束第</SPAN><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">i</SPAN><SPAN 
      style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体">遍处理。</SPAN></P>
      <P class=MsoNormal style="TEXT-ALIGN: left" align=left><SPAN 
      style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 宋体">例：</SPAN><SPAN 
      lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> </SPAN></P>
      <TABLE class=MsoNormalTable style="WIDTH: 50%" cellSpacing=0 cellPadding=0 
      width="50%" border=1>
        <TBODY>
        <TR>
          <TD 
          style="PADDING-RIGHT: 0cm; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; WIDTH: 12%; PADDING-TOP: 0cm" 
          width="12%">
            <P class=MsoNormal style="TEXT-ALIGN: center" align=center><SPAN 
            style="FONT-SIZE: 9pt; FONT-FAMILY: 宋体">初始序列：</SPAN></P></TD>
          <TD 
          style="PADDING-RIGHT: 0cm; PADDING-LEFT: 0cm; BACKGROUND: blue; PADDING-BOTTOM: 0cm; WIDTH: 12%; PADDING-TOP: 0cm" 
          width="12%">
            <P class=MsoNormal style="TEXT-ALIGN: center" align=center><SPAN
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