Started coding 3: Backtracking

Backtracking/README.md

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+# Coding 3: Backtracking
+
+## Rocket Sections
+
+In order to identify budding rocket science talent, SpaceX has designed a new
+modular build-your-own rocket kit for amateur rocketeers to use to construct
+model rockets. After careful user-studies, SpaceX has found that its customers
+want to be able to build rockets of widely varying height. Thus, they've arrived
+at the following idea. Instead of selling rocket fuselage tubing at every height
+desired by their customers, they'll offer an array of rocket "sections" at
+varying heights that can be fit together to form a full sized rocket. For
+example, for the Lil Falcons parts (their entry level kit for preschoolers, that
+comes complete with a mix your own rocket fuel kit and size 3T smocks) they
+offer rocket sections in the following sizes: 1 inch, 2 inch 5 inch, and 7 inch
+sections.
+
+In order to build a rocket of height 15, a kinderscientist could use two 5"
+sections, two 2" sections, and one 1" section for a total of five sections. Or
+three 5" sections for a total of three sections. Obviously, construction is made
+more complicated by the number of sections that need to be arc welded together
+(there's a companion Kids-Do-Welding TM starter kit made by Hasbro for the
+preschooler who hasn't gotten started welding yet). The goal of any good rocket
+designer is to minimize the number of sections used in the construction of their
+rocket.
+
+## Input
+
+The input to the program will be a line containing a space separated, sorted
+list of the n lengths of available rocket sections for a given kit. The second
+line will be a single integer representing the length of rocket the user wants
+to construct. The first line will always include a part of length 1, meaning
+that all requested lengths can be constructed.
+
+## Output
+
+For partial credit you can simply output a single line reporting the minimum
+total number of rocket sections needed to construct the rocket in the format "N
+rocket sections minimum\n".
+
+For full credit the output should have n+1 lines. The first n lines should
+detail how many of each rocket length the designer needs to buy. Each should be
+of the form "X of length Y" detailing how many (X) rocket sections of length
+value Y should be bought. The final line should report the total number of
+rocket sections in the format "N rocket sections minimum".
+
+### Sample Partial Credit Input/Output
+
+<table>
+    <tr>
+        <td>Sample Input</td>
+        <td>Sample Output</td>
+    </tr>
+    <tr>
+        <td><pre>1 2 5 7<br>15</pre></td>
+        <td><pre>3 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 2 3 5 7 14<br>15</pre></td>
+        <td><pre>2 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 9<br>17</pre></td>
+        <td><pre>9 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 9 10<br>18</pre></td>
+        <td><pre>2 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 9 10 90 100<br>198</pre></td>
+        <td><pre>4 rocket sections minimum</pre></td>
+    </tr>
+</table>
+
+### Sample Full Credit Input/Output
+
+<table>
+    <tr>
+        <td>Sample Input</td>
+        <td>Sample Output</td>
+    </tr>
+    <tr>
+        <td><pre>1 2 5 7<br>15</pre></td>
+        <td><pre>1 of length 1<br>0 of length 2<br>0 of length 5<br>2 of length 7<br>3 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 2 3 5 7 14<br>15</pre></td>
+        <td><pre>1 of length 1<br>0 of length 2<br>0 of length 3<br>0 of length 5<br>0 of length 7<br>1 of length 14<br>2 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 9<br>17</pre></td>
+        <td><pre>8 of length 1<br>1 of length 9<br>9 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 9 10<br>18</pre></td>
+        <td><pre>0 of length 1<br>2 of length 9<br>0 of length 10<br>2 rocket sections minimum</pre></td>
+    </tr>
+    <tr>
+        <td><pre>1 9 10 90 100<br>198</pre></td>
+        <td><pre>0 of length 1<br>2 of length 9<br>0 of length 10<br>2 of length 90<br>0 of length 100<br>4 rocket sections minimum</pre></td>
+    </tr>
+</table>
+
+## Your Task
+
+Develop a recursive backtracking solution to the problem. Turn your solution in
+as `cs412_hw3_a.py` to Gradescope.
+
+### Rubric:
+
+- (10 points) Does the code solve the samples in the write-up?
+- (7 point) Does the code solve the private testing samples?
+- (3 points) For solving the full credit option.