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📁 一些算法小技巧 有利于学习C语言 在C语言和JAVA中都可以用的
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<title>贪婪（贪心）算法 Greedy Algorithm </title>
<meta name=Description content="2005/9/19: 2.3.2 k阶常系数线性非齐次递归方程 ：">
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 <div v:shape="_x0000_s104450" class=T><span style='position:absolute;
 top:1.75%;left:13.48%;width:101.12%'><span lang=ZH-CN style='font-family:"Times New Roman";
 mso-ascii-font-family:"Times New Roman";mso-ansi-language:EN-US'>2.3.2 k</span><span
 lang=ZH-CN style='mso-ansi-language:EN-US'>阶常系数线性非齐次递归</span></span><span
 style='position:absolute;top:11.5%;left:13.48%;width:85.58%'><span lang=ZH-CN
 style='mso-ansi-language:EN-US'>方程</span><span lang=ZH-CN style='font-family:
 "Times New Roman";mso-ascii-font-family:"Times New Roman";mso-ansi-language:
 EN-US'> </span><span lang=ZH-CN style='mso-ansi-language:EN-US'>：</span><span
 lang=ZH-CN style='color:yellow;mso-ansi-language:EN-US;mso-special-format:
 lastCR;display:none'>&#13;</span></span></div>
 <div v:shape="_x0000_s104451" class=B>
 <div style='position:absolute;top:21.75%;left:13.48%;width:81.46%;height:6.25%'><span
 style='position:absolute;top:0%;left:4.59%;width:95.4%'><span
 style='color:yellow'><span style='mso-special-format:bullet;color:#FFCC66;
 mso-color-index:3;position:absolute;left:-4.81%;top:.1em;font-family:Symbol;
 font-size:90%'>¨</span></span><span lang=ZH-CN style='color:yellow;mso-ansi-language:
 EN-US'>形式：&#13;</span></span></div>
 <div style='position:absolute;top:29.0%;left:13.48%;width:87.64%;height:4.25%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:63%;mso-ansi-language:EN-US'><span
 style='mso-tab-count:1;width:4.27%'> </span></span><span lang=EN-US
 style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;mso-fareast-language:
 ZH-CN'><b>f(n) = a</b></span><span lang=EN-US style='font-family:宋体;
 mso-ascii-font-family:宋体;font-size:41%;position:relative;top:.37em;mso-text-raise:
 -25%;mso-fareast-language:ZH-CN'><b>1</b></span><span lang=EN-US
 style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;mso-fareast-language:
 ZH-CN'><b>f(n-1) + a</b></span><span lang=EN-US style='font-family:宋体;
 mso-ascii-font-family:宋体;font-size:41%;position:relative;top:.37em;mso-text-raise:
 -25%;mso-fareast-language:ZH-CN'><b>2</b></span><span lang=EN-US
 style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;mso-fareast-language:
 ZH-CN'><b>f(n-2)+</b></span><span lang=EN-US style='font-family:"Times New Roman";
 mso-ascii-font-family:宋体;mso-hansi-font-family:"Times New Roman";font-size:
 63%;mso-fareast-language:ZH-CN'><b>…</b></span><span lang=EN-US
 style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;mso-fareast-language:
 ZH-CN'><b>+a</b></span><span lang=EN-US style='font-family:宋体;mso-ascii-font-family:
 宋体;font-size:41%;position:relative;top:.37em;mso-text-raise:-25%;mso-fareast-language:
 ZH-CN'><b>k</b></span><span lang=EN-US style='font-family:宋体;mso-ascii-font-family:
 宋体;font-size:63%;mso-fareast-language:ZH-CN'><b>f(n-k) </b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;
 color:yellow;mso-fareast-language:ZH-CN'><b>+ g(n)</b></span><span lang=ZH-CN
 style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;mso-ansi-language:
 EN-US'><b> <span style='mso-tab-count:1;width:3.54%'> </span>①&#13;</b></span></div>
 <div style='position:absolute;top:34.5%;left:13.48%;width:87.64%;height:4.0%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:63%;mso-ansi-language:EN-US'><b><span
 style='mso-tab-count:1;width:4.27%'> </span>f(i) = b</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:41%;
 position:relative;top:.37em;mso-text-raise:-25%;mso-fareast-language:ZH-CN'><b>i</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;
 mso-fareast-language:ZH-CN'><b><span style='mso-tab-count:3;width:27.49%'> </span></b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;
 color:yellow;mso-fareast-language:ZH-CN'><b>(初始条件) <span style='mso-tab-count:
 2;width:16.66%'> </span></b></span><span lang=EN-US style='mso-ascii-font-family:
 宋体;font-size:63%;mso-fareast-language:ZH-CN'><b>②</b></span><span lang=ZH-CN
 style='mso-ascii-font-family:宋体;font-size:63%;color:yellow;mso-ansi-language:
 EN-US;display:none'><b>&#13;</b></span></div>
 <div style='position:absolute;top:40.75%;left:13.48%;width:81.46%;height:6.25%'><span
 style='position:absolute;top:0%;left:4.59%;width:95.4%'><span
 style='color:yellow'><span style='mso-special-format:bullet;color:#FFCC66;
 mso-color-index:3;position:absolute;left:-4.81%;top:.1em;font-family:Symbol;
 font-size:90%'>¨</span></span><span lang=ZH-CN style='color:yellow;mso-ansi-language:
 EN-US'>通解形式：&#13;</span></span></div>
 <div style='position:absolute;top:48.75%;left:13.48%;width:88.38%;height:6.75%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 "Times New Roman";mso-ascii-font-family:"Times New Roman";color:yellow;
 mso-ansi-language:EN-US'><span style='mso-tab-count:1;width:4.24%'> </span> </span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;
 mso-fareast-language:ZH-CN'><b>f(n) = f</b></span><span lang=EN-US
 style='font-family:"Times New Roman";mso-ascii-font-family:宋体;mso-hansi-font-family:
 "Times New Roman";font-size:63%;mso-fareast-language:ZH-CN'><b>’</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;
 mso-fareast-language:ZH-CN'><b>(n) + f</b></span><span lang=EN-US
 style='font-family:宋体;mso-ascii-font-family:宋体;font-size:41%;position:relative;
 top:-.45em;mso-text-raise:30%;mso-fareast-language:ZH-CN'><b>*</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:63%;
 mso-fareast-language:ZH-CN'><b>(n)<span style='mso-tab-count:1;width:9.05%'> </span></b></span><span
 lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:宋体;
 mso-hansi-font-family:"Times New Roman";font-size:63%;mso-fareast-language:
 ZH-CN'><b>……</b></span><span lang=ZH-CN style='mso-ascii-font-family:宋体;
 font-size:63%;mso-ansi-language:EN-US'><b>齐次通解＋非齐次特解</b></span><span
 lang=ZH-CN style='color:yellow;mso-ansi-language:EN-US;display:none'>&#13;</span></div>
 <div style='position:absolute;top:58.0%;left:13.48%;width:81.46%;height:6.25%'><span
 style='position:absolute;top:0%;left:4.59%;width:95.4%'><span
 style='color:yellow'><span style='mso-special-format:bullet;color:#FFCC66;
 mso-color-index:3;position:absolute;left:-4.81%;top:.1em;font-family:Symbol;
 font-size:90%'>¨</span></span><span lang=ZH-CN style='color:yellow;mso-ansi-language:
 EN-US'>解题思路：&#13;</span></span></div>
 <div style='position:absolute;top:65.75%;left:13.48%;width:81.46%;height:4.75%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:75%;mso-ansi-language:EN-US'><b>1）用 x</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:50%;
 position:relative;top:-.45em;mso-text-raise:30%;mso-fareast-language:ZH-CN'><b>n
 </b></span><span lang=ZH-CN style='mso-ascii-font-family:宋体;font-size:75%;
 mso-ansi-language:EN-US'><b>取代f(n):&#13;</b></span></div>
 <div style='position:absolute;top:72.25%;left:13.48%;width:81.46%;height:4.75%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:75%;mso-ansi-language:EN-US'><b>2）两边同除以x</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:50%;
 position:relative;top:-.45em;mso-text-raise:30%;mso-fareast-language:ZH-CN'><b>(n-k)</b></span><span
 lang=EN-US style='font-family:宋体;mso-ascii-font-family:宋体;font-size:75%;
 mso-fareast-language:ZH-CN'><b><span style="mso-spacerun:
 yes">&nbsp;</span>，并移到左端得：&#13;</b></span></div>
 <div style='position:absolute;top:78.5%;left:13.48%;width:81.46%;height:4.75%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:75%;mso-ansi-language:EN-US'><b>3）求出方程得根得递归方程通解&#13;</b></span></div>
 <div style='position:absolute;top:85.0%;left:13.48%;width:81.46%;height:4.75%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=EN-US style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:75%;color:yellow;mso-fareast-language:
 ZH-CN'><b>4）根据P45，确定特解（含待定系数）&#13;</b></span></div>
 <div style='position:absolute;top:91.25%;left:13.48%;width:81.46%;height:4.75%'><span
 style='mso-special-format:nobullet;display:none;color:#FFCC66;mso-color-index:
 3;font-family:Symbol;font-size:90%'>¨</span><span lang=ZH-CN style='font-family:
 宋体;mso-ascii-font-family:宋体;font-size:75%;color:yellow;mso-ansi-language:EN-US'><b>5）代入方程求出待定系数，即得通解。</b></span><span
 lang=ZH-CN style='mso-ascii-font-family:宋体;font-size:63%;mso-ansi-language:
 EN-US;mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
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