?? 螺旋方陣--fevernova的博客.htm
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lang=EN-US
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style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN>printf("%4d",t)；
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style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN>}
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style="mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN>printf("\n")；
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lang=EN-US
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style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN>}
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style="mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體">}
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<P class=MsoNormal style="tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: 宋體">
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<P class=MsoNormal style="tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
style="FONT-SIZE: 12pt; COLOR: blue; FONT-FAMILY: 宋體">第<SPAN
lang=EN-US>5種解法：遞歸方法。
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style="TEXT-INDENT: 24pt; mso-char-indent-count: 2.0; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體">分析：根據本題圖形的特點，我們可以構造一個遞歸算法。我們可以將邊長為<SPAN
lang=EN-US>N的圖形分為兩部分：第一部分最外層的框架，第二部分為中間的邊長為N-2的圖形。
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style="TEXT-INDENT: 24pt; mso-char-indent-count: 2.0; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體">對于邊長為<SPAN
lang=EN-US>N的正方型，若其中每個元素的行號為i（1≤i≤N），列號為j（1≤j≤N），第1行第1列元素表示為a<SUB>1,1</SUB>（a11=1），則有：
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style="MARGIN-LEFT: 30.85pt; TEXT-INDENT: -30.85pt; mso-char-indent-count: -2.57; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN>對于最外層的框架可以用以下數學模型描述：
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lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes">
</SPAN>上邊：<SPAN style="mso-spacerun: yes">
</SPAN>a<SUB>1,j</SUB>=a<SUB>1,1</SUB>+j-1<SPAN
style="mso-spacerun: yes">
</SPAN>(j≠1)
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lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes">
</SPAN>右邊：<SPAN style="mso-spacerun: yes">
</SPAN>a<SUB>i,N</SUB>=a<SUB>1,1</SUB>+N+i-2<SPAN
style="mso-spacerun: yes">
</SPAN>(i≠1)
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style="MARGIN-LEFT: 30.85pt; TEXT-INDENT: -30.85pt; mso-char-indent-count: -2.57; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes">
</SPAN>下邊：<SPAN style="mso-spacerun: yes">
</SPAN>a<SUB>i,1</SUB>=a<SUB>1,1</SUB>+4N-i-3<SPAN
style="mso-spacerun: yes"> </SPAN>(i≠1)
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style="MARGIN-LEFT: 30.85pt; TEXT-INDENT: -30.85pt; mso-char-indent-count: -2.57; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes">
</SPAN>左邊：<SPAN style="mso-spacerun: yes">
</SPAN>a<SUB>N,j</SUB>=a<SUB>1,1</SUB>+3N-2-j<SPAN
style="mso-spacerun: yes"> </SPAN>(j≠1)
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<P class=MsoPlainText
style="MARGIN-LEFT: 30.85pt; TEXT-INDENT: -30.85pt; mso-char-indent-count: -2.57; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes"> </SPAN>對于內層的邊長為N-2的圖形可以用以下數學模型描述：
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style="MARGIN-LEFT: 30.85pt; TEXT-INDENT: -30.85pt; mso-char-indent-count: -2.57; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
style="mso-spacerun: yes"> </SPAN><SPAN
style="mso-spacerun: yes">
</SPAN>左上角元素：a<SUB>i,i</SUB>=a<SUB>i-1,i-1</SUB>+4(N-2i-1)<SPAN
style="mso-spacerun: yes"> </SPAN>(i＞1)
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style="TEXT-INDENT: 24pt; mso-char-indent-count: 2.0; mso-char-indent-size: 12pt; tab-stops: 595.4pt 641.2pt 687.0pt 732.8pt"><SPAN
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體">若令：<SPAN
lang=EN-US>a<SUB>i,j</SUB>=fun(a<SUB>i-1,i-1</SUB>+4(N-2i-1)，當：i＜(N+1)/2且j＜(N+1)/2時，min=MIN(i,j)，則有：
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lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 宋體"><SPAN
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