117 lines
4.5 KiB
Markdown
117 lines
4.5 KiB
Markdown
# Coding 3: Backtracking
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## Rocket Sections
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In order to identify budding rocket science talent, SpaceX has designed a new
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modular build-your-own rocket kit for amateur rocketeers to use to construct
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model rockets. After careful user-studies, SpaceX has found that its customers
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want to be able to build rockets of widely varying height. Thus, they've arrived
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at the following idea. Instead of selling rocket fuselage tubing at every height
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desired by their customers, they'll offer an array of rocket "sections" at
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varying heights that can be fit together to form a full sized rocket. For
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example, for the Lil Falcons parts (their entry level kit for preschoolers, that
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comes complete with a mix your own rocket fuel kit and size 3T smocks) they
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offer rocket sections in the following sizes: 1 inch, 2 inch 5 inch, and 7 inch
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sections.
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In order to build a rocket of height 15, a kinderscientist could use two 5"
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sections, two 2" sections, and one 1" section for a total of five sections. Or
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three 5" sections for a total of three sections. Obviously, construction is made
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more complicated by the number of sections that need to be arc welded together
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(there's a companion Kids-Do-Welding TM starter kit made by Hasbro for the
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preschooler who hasn't gotten started welding yet). The goal of any good rocket
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designer is to minimize the number of sections used in the construction of their
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rocket.
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## Input
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The input to the program will be a line containing a space separated, sorted
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list of the n lengths of available rocket sections for a given kit. The second
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line will be a single integer representing the length of rocket the user wants
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to construct. The first line will always include a part of length 1, meaning
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that all requested lengths can be constructed.
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## Output
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For partial credit you can simply output a single line reporting the minimum
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total number of rocket sections needed to construct the rocket in the format "N
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rocket sections minimum\n".
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For full credit the output should have n+1 lines. The first n lines should
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detail how many of each rocket length the designer needs to buy. Each should be
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of the form "X of length Y" detailing how many (X) rocket sections of length
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value Y should be bought. The final line should report the total number of
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rocket sections in the format "N rocket sections minimum".
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### Sample Partial Credit Input/Output
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<table>
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<tr>
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<td>Sample Input</td>
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<td>Sample Output</td>
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</tr>
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<tr>
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<td><pre>1 2 5 7<br>15</pre></td>
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<td><pre>3 rocket sections minimum</pre></td>
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</tr>
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<tr>
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<td><pre>1 2 3 5 7 14<br>15</pre></td>
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<td><pre>2 rocket sections minimum</pre></td>
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</tr>
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<tr>
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<td><pre>1 9<br>17</pre></td>
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<td><pre>9 rocket sections minimum</pre></td>
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</tr>
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<tr>
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<td><pre>1 9 10<br>18</pre></td>
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<td><pre>2 rocket sections minimum</pre></td>
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</tr>
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<tr>
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<td><pre>1 9 10 90 100<br>198</pre></td>
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<td><pre>4 rocket sections minimum</pre></td>
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</tr>
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</table>
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### Sample Full Credit Input/Output
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<table>
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<tr>
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<td>Sample Input</td>
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<td>Sample Output</td>
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</tr>
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<tr>
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<td><pre>1 2 5 7<br>15</pre></td>
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<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>
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</tr>
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<tr>
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<td><pre>1 2 3 5 7 14<br>15</pre></td>
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<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>
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</tr>
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<tr>
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<td><pre>1 9<br>17</pre></td>
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<td><pre>8 of length 1<br>1 of length 9<br>9 rocket sections minimum</pre></td>
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</tr>
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<tr>
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<td><pre>1 9 10<br>18</pre></td>
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<td><pre>0 of length 1<br>2 of length 9<br>0 of length 10<br>2 rocket sections minimum</pre></td>
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</tr>
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<tr>
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<td><pre>1 9 10 90 100<br>198</pre></td>
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<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>
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</tr>
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</table>
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## Your Task
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Develop a recursive backtracking solution to the problem. Turn your solution in
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as `cs412_hw3_a.py` to Gradescope.
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> Eclypse's Note: The above is a lie, Gradescope actually wanted the file to be
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> named `cs412_rockets.py` as of 20:06 2025-09-13
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### Rubric:
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- (10 points) Does the code solve the samples in the write-up?
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- (7 point) Does the code solve the private testing samples?
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- (3 points) For solving the full credit option.
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