prithivMLmods/Coder-Stat

1 2<h1><font color="#000000">Problem E:</font> Twirl Around</h1>3 4<!-- begin en only -->5<p>6Let's think about a bar rotating clockwise as if it were a7twirling baton moving on a planar surface surrounded by a8polygonal wall (see Figure 1).9</p>10<!-- end en only -->11 12<!-- <img src="https://judgeapi.u-aizu.ac.jp/resources/images/rot_triangle" /><br /> -->13<center>14<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_e2" />15<br />16<!-- begin en only -->17<p>Figure 1.  A bar rotating in a polygon</p>18<!-- end en only -->19</center>20 21 22<!-- begin en only -->23<p>24Initially, an end of the bar (called "end A") is at (0,0), and25the other end (called "end B") is at (0,<I>L</I>) where <I>L</I> is the26length of the bar.  Initially, the bar is touching the wall only27at the end A.28</p>29<!-- end en only -->30 31<!-- begin en only -->32<p>33The bar turns fixing a touching point as the center.34The center changes as a new point touches the wall.35</p>36<!-- end en only -->37 38<!-- begin en only -->39<p>40Your task is to calculate the coordinates of the end A when the41bar has fully turned by the given count <I>R</I>.42</p>43<!-- end en only -->44 45 46 47<center>48<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_e5" />49<br />50<!-- begin en only -->51<p>Figure 2.  Examples of turning bars</p>52<!-- end en only -->53</center>54 55<!-- begin en only -->56<p>In Figure 2, some examples are shown.  In cases (D) and57(E), the bar is stuck prematurely (cannot rotate clockwise anymore 58with any point touching the wall as the center)59before <i>R</i> rotations.  In such cases, you should answer the60coordinates of the end A in that (stuck) position.</p>61<!-- end en only -->62 63<!-- begin en only -->64<p>You can assume the following:</p>65<blockquote>66<p>67When the bar's length <i>L</i> changes by &epsilon; (|&epsilon;| &lt;680.00001), the final (<i>x</i>,<i>y</i>) coordinates69will not change more than 0.0005.70</p>71</blockquote>72<!-- end en only -->73 74 75 76<h3>Input</h3>77 78 79<!-- begin en only -->80 81<p>The input consists of multiple datasets.  The number of82datasets is no more than 100.  The end of the input is represented83by "0 0 0".</p>84<!-- end en only -->85 86 87<!-- begin en only -->88<p>89The format of each dataset is as follows:90</p>91<!-- end en only -->92 93<pre>94<i>L</i> <i>R</i> <i>N</i>95<i>X</i><sub>1</sub> <i>Y</i><sub>1</sub>96<i>X</i><sub>2</sub> <i>Y</i><sub>2</sub>97...98<i>X</i><sub>N</sub> <i>Y</i><sub>N</sub>99</pre>100 101<!-- begin en only -->102<p>103<i>L</i> is the length of the bar.104The bar rotates 2&pi;&times; <i>R</i> radians (if it is not105stuck prematurely).106<i>N</i> is the number of vertices which make the polygon.107</p>108 109<p>110The vertices of the polygon are arranged in a counter-clockwise order.111You may assume that the polygon is <em>simple</em>, that is,112its border never crosses or touches itself.113</p>114 115<p>116<i>N</i>, <i>X</i><sub>i</sub> and <i>Y</i><sub>i</sub> are117integer numbers; <i>R</i> and <i>L</i> are decimal fractions.118Ranges of those values are as follows:119</p>120<!-- end en only -->121 122<pre>1231.0 &le; <i>L</i> &le; 500.0,1241.0 &le; <i>R</i> &le; 10.0,1253 &le; <i>N</i> &le; 100,126-1000 &le; <i>X</i><sub>i</sub> &le; 1000,127-1000 &le; <i>Y</i><sub>i</sub> &le; 1000,128</pre>129 130<pre>131<i>X</i><sub>1</sub> &le; -1,  <i>Y</i><sub>1</sub> = 0,132<i>X</i><sub>2</sub> &ge; 1,  <i>Y</i><sub>2</sub> = 0.133</pre>134 135 136<h3>Output</h3>137 138<!-- begin en only -->139 140<p>141For each dataset, print one line containing <i>x-</i> and142<i>y-</i>coordinates of the final position of the end A,143separated by a space.144The value may contain an error less than or equal to 0.001.145You may print any number of digits after the decimal point.146</p>147<!-- end en only -->148 149 150<h3>Sample Input</h3>151 152<pre>1534.0 2.0 8154-1 01555 01565 -21577 -21587 015918 016018 6161-1 61624.0 2.0 4163-1 016410 016510 12166-1 121674.0 1.0 7168-1 01692 0170-1 -3171-1 -81726 -81736 6174-1 61754.0 2.0 6176-1 017710 017810 31797 31807 5181-1 51825.0 2.0 6183-1 01842 01852 -41866 -41876 6188-1 61896.0 1.0 8190-1 01918 01927 21939 21948 419511 419611 12197-1 121980 0 0199</pre>200 201 202<h3>Output for the Sample Input</h3>203<pre>20416.0 0.02059.999999999999998 7.46410161513775352060.585786437626906 -5.4142135623730952078.0 0.02086.0 0.02099.52786404500042 4.0210</pre>211 212 213<!-- begin en only -->214<p>215Note that the above sample input corresponds to the216cases in Figure 2.  For convenience, in Figure 3, we will show an217animation and corresponding photographic playback for the case (C).218</p>219<!-- end en only -->220 221<center>222<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_e6" />223<br />224 225<TABLE>226<TR><TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0000"></TD>227    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0045"></TD>228    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0090"></TD>229    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0135"></TD>230    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0180"></TD>231    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0225"></TD>232    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0270"></TD>233    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_Eframe0315"></TD>234    <TD><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_stopMotion_EframeLast"></TD></TR>235</TABLE>236 237<!-- begin en only -->238<p>Figure 3.  Animation and photographic playback for case (C)</p>239<!-- end en only -->240</center>241 242 243 244