no11.htm

常用经典算法及讲解：贪婪

color:black;mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>种饮料，对它作出相对评价，将一个数值</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>s</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>作为满意度赋予第</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>种饮料。<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>通常，这个婴儿都会尽量饮用具有最大满意度值的饮料来最大限度地满足她解渴的需要，但是不幸的是：具有最大满意度值的饮料有时并没有足够的量来满足此婴儿解渴的需要。设</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>a</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i</span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>是第</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>种饮料的总量（以盎司为单位），而此婴儿需要</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>t </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>盎司的饮料来解渴，那么，需要饮用</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>n</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>种不同的饮料各多少量才能满足婴儿解渴的需求呢？<span
lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>设各种饮料的满意度已知。令</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>为婴儿将要饮用的第</span><i><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>种饮料的量，则需要解决的问题是：<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>找到一组实数</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i</span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>（</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>1</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>≤</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>i</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>≤</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>n</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>），使</span><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n </span></i><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><i><span lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>= 1</span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>s</span></i><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>x</span></i><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>最大，并满足：</span><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n </span></i><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><i><span lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>i</span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>=1</span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>x</span></i><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>=<i>t </i></span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>及</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>0</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>≤</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i</span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>≤</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>a</span></i><i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>。<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>需要指出的是：如果</span><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n </span></i><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><i><span lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>= 1</span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>a</span></i><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>&lt; <i>t</i></span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>，则不可能找到问题的求解方案，因为即使喝光所有的饮料也不能使婴儿解渴。<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>对上述问题精确的数学描述明确地指出了程序必须完成的工作，根据这些数学公式，可以对输入</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>/ </span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>输出作如下形式的描述：<span
lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>输入：</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n</span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>t</span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>s</span></i><i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>，</span><i><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>a</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i</span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>（其中</span><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1</span><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>≤</span><i><span lang=EN-US style='font-size:
10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i</span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>≤</span><i><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>n</span></i><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>n </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>为整数，</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>t</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>、</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>s</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>、</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>a</span></i><i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i </span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>为正实数）。<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>输出：实数</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i</span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>（</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>1</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>≤</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>i</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>≤</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>n</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>），使</span><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n </span></i><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><i><span lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>i</span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>= 1</span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>s</span></i><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>x</span></i><i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>最大且</span><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n </span></i><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning: