prithivMLmods/Coder-Stat
Coder-Stat Dataset Overview The Coder-Stat dataset is a collection of programming-related data, including problem IDs, programming languages, original statuses, and source code snippets. This dataset is designed to assist in the analysis of coding patterns, error types, and performance metrics. Dataset Details Modalities Tabular: The dataset is structured in a tabular format. Text: Contains text data, including source code snippets.… See the full description on the dataset page: https://huggingface.co/datasets/prithivMLmods/Coder-Stat.
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1 2<H1><font color="#000">Problem F:</font> Power Calculus</H1>3 4<p>5Starting with <i>x</i> and repeatedly multiplying by <i>x</i>, we can compute <i>x</i><sup>31</sup> with thirty multiplications:6</p>7 8<center>9<p>10 <i>x</i><sup>2</sup> = <i>x</i> × <i>x</i>, <i>x</i><sup>3</sup> = <i>x</i><sup>2</sup> × <i>x</i>, <i>x</i><sup>4</sup> = <i>x</i><sup>3</sup> × <i>x</i>, ... , <i>x</i><sup>31</sup> = <i>x</i><sup>30</sup> × <i>x</i>.11</p>12</center>13<p>14The operation of squaring can appreciably shorten the sequence of multiplications. The following is a way to compute x<sup>31</sup> with eight multiplications:15</p>16 17<center>18<p>19 <i>x</i><sup>2</sup> = <i>x</i> × <i>x</i>, <i>x</i><sup>3</sup> = <i>x</i><sup>2</sup> × <i>x</i>, <i>x</i><sup>6</sup> = <i>x</i><sup>3</sup> × <i>x</i><sup>3</sup>, <i>x</i><sup>7</sup> = <i>x</i><sup>6</sup> × <i>x</i>, <i>x</i><sup>14</sup> = <i>x</i><sup>7</sup> × <i>x</i><sup>7</sup>,<br>20 <i>x</i><sup>15</sup> = <i>x</i><sup>14</sup> × <i>x</i>, <i>x</i><sup>30</sup> = <i>x</i><sup>15</sup> × <i>x</i><sup>15</sup>, <i>x</i><sup>31</sup> = <i>x</i><sup>30</sup> × <i>x</i>.21</p>22</center>23 24<p>25This is not the shortest sequence of multiplications to compute <i>x</i><sup>31</sup>. There are many ways with only seven multiplications. The following is one of them:26</p>27 28<center>29<p>30 <i>x</i><sup>2</sup> = <i>x</i> × <i>x</i>, <i>x</i><sup>4</sup> = <i>x</i><sup>2</sup> × <i>x</i><sup>2</sup>, <i>x</i><sup>8</sup> = <i>x</i><sup>4</sup> × <i>x</i><sup>4</sup>, <i>x</i><sup>10</sup> = <i>x</i><sup>8</sup> × <i>x</i><sup>2</sup>,<br>31 <i>x</i><sup>20</sup> = <i>x</i><sup>10</sup> × <i>x</i><sup>10</sup>, <i>x</i><sup>30</sup> = <i>x</i><sup>20</sup> × <i>x</i><sup>10</sup>, <i>x</i><sup>31</sup> = <i>x</i><sup>30</sup> × <i>x</i>.32</p>33</center>34 35<p>36There however is no way to compute <i>x</i><sup>31</sup> with fewer multiplications. Thus this is one of the37most eficient ways to compute <i>x</i><sup>31</sup> only by multiplications.38</p>39 40<p>41If division is also available, we can find a shorter sequence of operations. It is possible to42compute <i>x</i><sup>31</sup> with six operations (five multiplications and one division):43</p>44 45<center>46<p>47 <i>x</i><sup>2</sup> = <i>x</i> × <i>x</i>, <i>x</i><sup>4</sup> = <i>x</i><sup>2</sup> × <i>x</i><sup>2</sup>, <i>x</i><sup>8</sup> = <i>x</i><sup>4</sup> × <i>x</i><sup>4</sup>, <i>x</i><sup>16</sup> = <i>x</i><sup>8</sup> × <i>x</i><sup>8</sup>, <i>x</i><sup>32</sup> = <i>x</i><sup>16</sup> × <i>x</i><sup>16</sup>,<br>48 <i>x</i><sup>31</sup> = <i>x</i><sup>32</sup> ÷ <i>x</i>.49</p>50</center>51 52<p>53This is one of the most eficient ways to compute <i>x</i><sup>31</sup> if a division is as fast as a multiplication.54</p>55<p>56Your mission is to write a program to find the least number of operations to compute <i>x<sup>n</sup></i>57by multiplication and division starting with <i>x</i> for the given positive integer <i>n</i>. Products and58quotients appearing in the sequence of operations should be <i>x</i> to a positive integer's power. In59other words, <i>x</i><sup>-3</sup>, for example, should never appear.60 61</p>62 63<H2>Input</H2>64 65<p>66The input is a sequence of one or more lines each containing a single integer <i>n</i>. <i>n</i> is positive and67less than or equal to 1000. The end of the input is indicated by a zero.68 69</p>70 71<H2>Output</H2>72 73<p>74Your program should print the least total number of multiplications and divisions required to75compute <i>x<sup>n</sup></i> starting with <i>x</i> for the integer <i>n</i>. The numbers should be written each in a separate76line without any superfluous characters such as leading or trailing spaces.77</p>78 79<H2>Sample Input</H2>80<pre>8118231837084918547386512878118895389090</pre>91 92<H2>Output for the Sample Input</H2>93<pre>94095696897998119991001310112102</pre>103 104 105 106 107