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	<title>수학의정석/집합의연산/이영호 - Revision history</title>
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		<updated>2021-02-07T05:30:15Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;어렵다. 알고리즘 구현이 어렵다...&lt;br /&gt;
새로운 방법을 생각해내 구현을 하긴 했지만 배열을 malloc으로 했으면 더 좋았을걸이라는 생각이 계속 든다.&lt;br /&gt;
set 1-&amp;gt; a&lt;br /&gt;
set 2-&amp;gt; a&lt;br /&gt;
       (a ab) b&lt;br /&gt;
set 3-&amp;gt; a      ab       b&lt;br /&gt;
       (a ac) (ab, abc) (b, bc)    c&lt;br /&gt;
set 4-&amp;gt;         a           ac               ab            abc             b            bc            c&lt;br /&gt;
            (a    ad)     (ac    acd)    (ab     abd)    (abc   abcd)     (b    bd)   (bc     bcd)   (c   cd)         d&lt;br /&gt;
&lt;br /&gt;
가만히 보니 재귀호출을 생각해볼 수도 있었겠다.&lt;br /&gt;
&lt;br /&gt;
set1에서는 a하나&lt;br /&gt;
set2에서는 set1과 set1+set2    set2&lt;br /&gt;
set3에서는 set2와 set2+set3    set3&lt;br /&gt;
&lt;br /&gt;
이렇게 나가게된다.&lt;br /&gt;
이것을 아래에 구현 했다. 복잡하지만.&lt;br /&gt;
&lt;br /&gt;
만약 이것을 malloc으로 구현하려했다면 메모리 크기를 구해야하므로&lt;br /&gt;
메모리의 크기는 Ssub(n) = 2Ssub(n-1) + asub(n-1) + 1 이 된다.&lt;br /&gt;
S -&amp;gt; 크기(메모리, 각각의 수의 갯수), a -&amp;gt; 항(subset)의 갯수&lt;br /&gt;
&lt;br /&gt;
input은 9 {1,2,3,4,5,6,7,8,9}로 테스트를 해 보았다. 결과는 아래.&lt;br /&gt;
set9에서 0.03초 set10에서 0.12초, set12에서 2.4초가 나왔다.&lt;br /&gt;
&lt;br /&gt;
 #include &amp;amp;lt;stdio.h&amp;amp;gt;&lt;br /&gt;
 #include &amp;amp;lt;time.h&amp;amp;gt;&lt;br /&gt;
 #include &amp;amp;lt;string.h&amp;amp;gt;&lt;br /&gt;
 &lt;br /&gt;
 int print(char *set, int size);&lt;br /&gt;
 &lt;br /&gt;
 int main()&lt;br /&gt;
 {&lt;br /&gt;
                 int size;&lt;br /&gt;
                 int i;&lt;br /&gt;
                 clock_t time_in;&lt;br /&gt;
                 scanf(&amp;quot; %d&amp;quot;, &amp;amp;amp;size);&lt;br /&gt;
                 char set[size];&lt;br /&gt;
                 time_in = clock();&lt;br /&gt;
                 for(i=0; i&amp;amp;lt;size; i++)&lt;br /&gt;
                                 scanf(&amp;quot; %d&amp;quot;, &amp;amp;amp;(set[i]));&lt;br /&gt;
 &lt;br /&gt;
                 print(set, size);&lt;br /&gt;
                 printf(&amp;quot;CLOCK_TIME = %d\n&amp;quot;, clock() - time_in);&lt;br /&gt;
 &lt;br /&gt;
                 return 0;&lt;br /&gt;
 }&lt;br /&gt;
 &lt;br /&gt;
 int print(char *set, int size)&lt;br /&gt;
 {&lt;br /&gt;
                 int count;&lt;br /&gt;
                 int i, j, t;&lt;br /&gt;
                 char buf[3000];&lt;br /&gt;
                 char temp[3000];&lt;br /&gt;
                 char next;&lt;br /&gt;
 &lt;br /&gt;
                 for(i = 1; i &amp;amp;lt;= size; i++){&lt;br /&gt;
                                 next = set[i-1];&lt;br /&gt;
 &lt;br /&gt;
                                 if(next == &amp;#039;\0&amp;#039;) break;&lt;br /&gt;
 &lt;br /&gt;
                                 if(i == 1){&lt;br /&gt;
                                                 buf[0] = next;&lt;br /&gt;
                                                 buf[1] = &amp;#039;\0&amp;#039;;&lt;br /&gt;
                                                 continue;&lt;br /&gt;
                                 }&lt;br /&gt;
 &lt;br /&gt;
                                 for(j = 0, count = 0; buf[j] != &amp;#039;\0&amp;#039;;){&lt;br /&gt;
                                                 if(buf[j] == 99){&lt;br /&gt;
                                                                 temp[count++] = 99;&lt;br /&gt;
                                                                 j++;&lt;br /&gt;
                                                 }&lt;br /&gt;
                                                 else{&lt;br /&gt;
                                                                 for(t = 0; buf[j+t] != 99 &amp;amp;amp;&amp;amp;amp; buf[j+t] != &amp;#039;\0&amp;#039;; t++)&lt;br /&gt;
                                                                                 temp[count++] = buf[j+t];&lt;br /&gt;
                                                                 temp[count++] = 99;&lt;br /&gt;
                                                                 for(t = 0; buf[j+t] != 99 &amp;amp;amp;&amp;amp;amp; buf[j+t] != &amp;#039;\0&amp;#039;; t++)&lt;br /&gt;
                                                                                 temp[count++] = buf[j+t];&lt;br /&gt;
                                                                 temp[count++] = next;&lt;br /&gt;
                                                                 j+=t;&lt;br /&gt;
                                                 }&lt;br /&gt;
                                 }&lt;br /&gt;
                                                                 temp[count++] = 99;&lt;br /&gt;
                                 temp[count++] = next;&lt;br /&gt;
                                 temp[count] = &amp;#039;\0&amp;#039;;&lt;br /&gt;
                                 memcpy(buf, temp, strlen(temp));&lt;br /&gt;
                                 buf[strlen(temp)] = &amp;#039;\0&amp;#039;;&lt;br /&gt;
                 }&lt;br /&gt;
 &lt;br /&gt;
                                 printf(&amp;quot;{&amp;quot;);&lt;br /&gt;
                 for(i = 0; i &amp;amp;lt; strlen(buf); i++){&lt;br /&gt;
                                 if(buf[i] == 99)&lt;br /&gt;
                                                 printf(&amp;quot;\b},{&amp;quot;);&lt;br /&gt;
                                 else if(buf[i] == &amp;#039;\0&amp;#039;)&lt;br /&gt;
                                                 break;&lt;br /&gt;
                                 else&lt;br /&gt;
                                                 printf(&amp;quot;%d,&amp;quot;, buf[i]);&lt;br /&gt;
                 }&lt;br /&gt;
                                 printf(&amp;quot;\b}\n&amp;quot;);&lt;br /&gt;
 &lt;br /&gt;
                 return 0;&lt;br /&gt;
 }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
subset 들. set은 {1,2,3,4,5,6,7,8,9}이다.&lt;br /&gt;
갯수는 2^9 - 1로 511개.&lt;br /&gt;
{1},{1,9},{1,8},{1,8,9},{1,7},{1,7,9},{1,7,8},{1,7,8,9},{1,6},{1,6,9},{1,6,8},{1,6,8,9},{1,6,7},{1,6,7,9},{1,6,7,8},{1,6,7,8,9},{1,5},{1,5,9},{1,5,8},{1,5,8,9},{1,5,7},{1,5,7,9},{1,5,7,8},{1,5,7,8,9},{1,5,6},{1,5,6,9},{1,5,6,8},{1,5,6,8,9},{1,5,6,7},{1,5,6,7,9},{1,5,6,7,8},{1,5,6,7,8,9},{1,4},{1,4,9},{1,4,8},{1,4,8,9},{1,4,7},{1,4,7,9},{1,4,7,8},{1,4,7,8,9},{1,4,6},{1,4,6,9},{1,4,6,8},{1,4,6,8,9},{1,4,6,7},{1,4,6,7,9},{1,4,6,7,8},{1,4,6,7,8,9},{1,4,5},{1,4,5,9},{1,4,5,8},{1,4,5,8,9},{1,4,5,7},{1,4,5,7,9},{1,4,5,7,8},{1,4,5,7,8,9},{1,4,5,6},{1,4,5,6,9},{1,4,5,6,8},{1,4,5,6,8,9},{1,4,5,6,7},{1,4,5,6,7,9},{1,4,5,6,7,8},{1,4,5,6,7,8,9},{1,3},{1,3,9},{1,3,8},{1,3,8,9},{1,3,7},{1,3,7,9},{1,3,7,8},{1,3,7,8,9},{1,3,6},{1,3,6,9},{1,3,6,8},{1,3,6,8,9},{1,3,6,7},{1,3,6,7,9},{1,3,6,7,8},{1,3,6,7,8,9},{1,3,5},{1,3,5,9},{1,3,5,8},{1,3,5,8,9},{1,3,5,7},{1,3,5,7,9},{1,3,5,7,8},{1,3,5,7,8,9},{1,3,5,6},{1,3,5,6,9},{1,3,5,6,8},{1,3,5,6,8,9},{1,3,5,6,7},{1,3,5,6,7,9},{1,3,5,6,7,8},{1,3,5,6,7,8,9},{1,3,4},{1,3,4,9},{1,3,4,8},{1,3,4,8,9},{1,3,4,7},{1,3,4,7,9},{1,3,4,7,8},{1,3,4,7,8,9},{1,3,4,6},{1,3,4,6,9},{1,3,4,6,8},{1,3,4,6,8,9},{1,3,4,6,7},{1,3,4,6,7,9},{1,3,4,6,7,8},{1,3,4,6,7,8,9},{1,3,4,5},{1,3,4,5,9},{1,3,4,5,8},{1,3,4,5,8,9},{1,3,4,5,7},{1,3,4,5,7,9},{1,3,4,5,7,8},{1,3,4,5,7,8,9},{1,3,4,5,6},{1,3,4,5,6,9},{1,3,4,5,6,8},{1,3,4,5,6,8,9},{1,3,4,5,6,7},{1,3,4,5,6,7,9},{1,3,4,5,6,7,8},{1,3,4,5,6,7,8,9},{1,2},{1,2,9},{1,2,8},{1,2,8,9},{1,2,7},{1,2,7,9},{1,2,7,8},{1,2,7,8,9},{1,2,6},{1,2,6,9},{1,2,6,8},{1,2,6,8,9},{1,2,6,7},{1,2,6,7,9},{1,2,6,7,8},{1,2,6,7,8,9},{1,2,5},{1,2,5,9},{1,2,5,8},{1,2,5,8,9},{1,2,5,7},{1,2,5,7,9},{1,2,5,7,8},{1,2,5,7,8,9},{1,2,5,6},{1,2,5,6,9},{1,2,5,6,8},{1,2,5,6,8,9},{1,2,5,6,7},{1,2,5,6,7,9},{1,2,5,6,7,8},{1,2,5,6,7,8,9},{1,2,4},{1,2,4,9},{1,2,4,8},{1,2,4,8,9},{1,2,4,7},{1,2,4,7,9},{1,2,4,7,8},{1,2,4,7,8,9},{1,2,4,6},{1,2,4,6,9},{1,2,4,6,8},{1,2,4,6,8,9},{1,2,4,6,7},{1,2,4,6,7,9},{1,2,4,6,7,8},{1,2,4,6,7,8,9},{1,2,4,5},{1,2,4,5,9},{1,2,4,5,8},{1,2,4,5,8,9},{1,2,4,5,7},{1,2,4,5,7,9},{1,2,4,5,7,8},{1,2,4,5,7,8,9},{1,2,4,5,6},{1,2,4,5,6,9},{1,2,4,5,6,8},{1,2,4,5,6,8,9},{1,2,4,5,6,7},{1,2,4,5,6,7,9},{1,2,4,5,6,7,8},{1,2,4,5,6,7,8,9},{1,2,3},{1,2,3,9},{1,2,3,8},{1,2,3,8,9},{1,2,3,7},{1,2,3,7,9},{1,2,3,7,8},{1,2,3,7,8,9},{1,2,3,6},{1,2,3,6,9},{1,2,3,6,8},{1,2,3,6,8,9},{1,2,3,6,7},{1,2,3,6,7,9},{1,2,3,6,7,8},{1,2,3,6,7,8,9},{1,2,3,5},{1,2,3,5,9},{1,2,3,5,8},{1,2,3,5,8,9},{1,2,3,5,7},{1,2,3,5,7,9},{1,2,3,5,7,8},{1,2,3,5,7,8,9},{1,2,3,5,6},{1,2,3,5,6,9},{1,2,3,5,6,8},{1,2,3,5,6,8,9},{1,2,3,5,6,7},{1,2,3,5,6,7,9},{1,2,3,5,6,7,8},{1,2,3,5,6,7,8,9},{1,2,3,4},{1,2,3,4,9},{1,2,3,4,8},{1,2,3,4,8,9},{1,2,3,4,7},{1,2,3,4,7,9},{1,2,3,4,7,8},{1,2,3,4,7,8,9},{1,2,3,4,6},{1,2,3,4,6,9},{1,2,3,4,6,8},{1,2,3,4,6,8,9},{1,2,3,4,6,7},{1,2,3,4,6,7,9},{1,2,3,4,6,7,8},{1,2,3,4,6,7,8,9},{1,2,3,4,5},{1,2,3,4,5,9},{1,2,3,4,5,8},{1,2,3,4,5,8,9},{1,2,3,4,5,7},{1,2,3,4,5,7,9},{1,2,3,4,5,7,8},{1,2,3,4,5,7,8,9},{1,2,3,4,5,6},{1,2,3,4,5,6,9},{1,2,3,4,5,6,8},{1,2,3,4,5,6,8,9},{1,2,3,4,5,6,7},{1,2,3,4,5,6,7,9},{1,2,3,4,5,6,7,8},{1,2,3,4,5,6,7,8,9},{2},{2,9},{2,8},{2,8,9},{2,7},{2,7,9},{2,7,8},{2,7,8,9},{2,6},{2,6,9},{2,6,8},{2,6,8,9},{2,6,7},{2,6,7,9},{2,6,7,8},{2,6,7,8,9},{2,5},{2,5,9},{2,5,8},{2,5,8,9},{2,5,7},{2,5,7,9},{2,5,7,8},{2,5,7,8,9},{2,5,6},{2,5,6,9},{2,5,6,8},{2,5,6,8,9},{2,5,6,7},{2,5,6,7,9},{2,5,6,7,8},{2,5,6,7,8,9},{2,4},{2,4,9},{2,4,8},{2,4,8,9},{2,4,7},{2,4,7,9},{2,4,7,8},{2,4,7,8,9},{2,4,6},{2,4,6,9},{2,4,6,8},{2,4,6,8,9},{2,4,6,7},{2,4,6,7,9},{2,4,6,7,8},{2,4,6,7,8,9},{2,4,5},{2,4,5,9},{2,4,5,8},{2,4,5,8,9},{2,4,5,7},{2,4,5,7,9},{2,4,5,7,8},{2,4,5,7,8,9},{2,4,5,6},{2,4,5,6,9},{2,4,5,6,8},{2,4,5,6,8,9},{2,4,5,6,7},{2,4,5,6,7,9},{2,4,5,6,7,8},{2,4,5,6,7,8,9},{2,3},{2,3,9},{2,3,8},{2,3,8,9},{2,3,7},{2,3,7,9},{2,3,7,8},{2,3,7,8,9},{2,3,6},{2,3,6,9},{2,3,6,8},{2,3,6,8,9},{2,3,6,7},{2,3,6,7,9},{2,3,6,7,8},{2,3,6,7,8,9},{2,3,5},{2,3,5,9},{2,3,5,8},{2,3,5,8,9},{2,3,5,7},{2,3,5,7,9},{2,3,5,7,8},{2,3,5,7,8,9},{2,3,5,6},{2,3,5,6,9},{2,3,5,6,8},{2,3,5,6,8,9},{2,3,5,6,7},{2,3,5,6,7,9},{2,3,5,6,7,8},{2,3,5,6,7,8,9},{2,3,4},{2,3,4,9},{2,3,4,8},{2,3,4,8,9},{2,3,4,7},{2,3,4,7,9},{2,3,4,7,8},{2,3,4,7,8,9},{2,3,4,6},{2,3,4,6,9},{2,3,4,6,8},{2,3,4,6,8,9},{2,3,4,6,7},{2,3,4,6,7,9},{2,3,4,6,7,8},{2,3,4,6,7,8,9},{2,3,4,5},{2,3,4,5,9},{2,3,4,5,8},{2,3,4,5,8,9},{2,3,4,5,7},{2,3,4,5,7,9},{2,3,4,5,7,8},{2,3,4,5,7,8,9},{2,3,4,5,6},{2,3,4,5,6,9},{2,3,4,5,6,8},{2,3,4,5,6,8,9},{2,3,4,5,6,7},{2,3,4,5,6,7,9},{2,3,4,5,6,7,8},{2,3,4,5,6,7,8,9},{3},{3,9},{3,8},{3,8,9},{3,7},{3,7,9},{3,7,8},{3,7,8,9},{3,6},{3,6,9},{3,6,8},{3,6,8,9},{3,6,7},{3,6,7,9},{3,6,7,8},{3,6,7,8,9},{3,5},{3,5,9},{3,5,8},{3,5,8,9},{3,5,7},{3,5,7,9},{3,5,7,8},{3,5,7,8,9},{3,5,6},{3,5,6,9},{3,5,6,8},{3,5,6,8,9},{3,5,6,7},{3,5,6,7,9},{3,5,6,7,8},{3,5,6,7,8,9},{3,4},{3,4,9},{3,4,8},{3,4,8,9},{3,4,7},{3,4,7,9},{3,4,7,8},{3,4,7,8,9},{3,4,6},{3,4,6,9},{3,4,6,8},{3,4,6,8,9},{3,4,6,7},{3,4,6,7,9},{3,4,6,7,8},{3,4,6,7,8,9},{3,4,5},{3,4,5,9},{3,4,5,8},{3,4,5,8,9},{3,4,5,7},{3,4,5,7,9},{3,4,5,7,8},{3,4,5,7,8,9},{3,4,5,6},{3,4,5,6,9},{3,4,5,6,8},{3,4,5,6,8,9},{3,4,5,6,7},{3,4,5,6,7,9},{3,4,5,6,7,8},{3,4,5,6,7,8,9},{4},{4,9},{4,8},{4,8,9},{4,7},{4,7,9},{4,7,8},{4,7,8,9},{4,6},{4,6,9},{4,6,8},{4,6,8,9},{4,6,7},{4,6,7,9},{4,6,7,8},{4,6,7,8,9},{4,5},{4,5,9},{4,5,8},{4,5,8,9},{4,5,7},{4,5,7,9},{4,5,7,8},{4,5,7,8,9},{4,5,6},{4,5,6,9},{4,5,6,8},{4,5,6,8,9},{4,5,6,7},{4,5,6,7,9},{4,5,6,7,8},{4,5,6,7,8,9},{5},{5,9},{5,8},{5,8,9},{5,7},{5,7,9},{5,7,8},{5,7,8,9},{5,6},{5,6,9},{5,6,8},{5,6,8,9},{5,6,7},{5,6,7,9},{5,6,7,8},{5,6,7,8,9},{6},{6,9},{6,8},{6,8,9},{6,7},{6,7,9},{6,7,8},{6,7,8,9},{7},{7,9},{7,8},{7,8,9},{8},{8,9},{9}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
subset 들. set은 {1,2,3,4,5,6,7,8,9,10}이다.&lt;br /&gt;
갯수는 2^19 - 1로 1023개.&lt;br /&gt;
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/&gt;
&lt;/div&gt;</summary>
		<author><name>imported&gt;Unknown</name></author>
	</entry>
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