prithivMLmods/Coder-Stat

1 2<H1><font color="#000">Problem I:</font> Crossing Prisms</H1>3 4<p>5Prof. Bocchan is a mathematician and a sculptor. He likes to create sculptures with mathematics.6</p>7<p>8His style to make sculptures is very unique. He uses two identical prisms. Crossing them at right9angles, he makes a polyhedron that is their intersection as a new work. Since he finishes it up10with painting, he needs to know the surface area of the polyhedron for estimating the amount11of pigment needed.12</p>13<p>14For example, let us consider the two identical prisms in Figure 1. The definition of their cross15section is given in Figure 2. The prisms are put at right angles with each other and their16intersection is the polyhedron depicted in Figure 3. An approximate value of its surface area17is 194.8255.18</p>19 20<center>21<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_crossingPrisms1">22<p>Figure 1: Two identical prisms at right angles</p>23</center>24 25<p>26Given the shape of the cross section of the two identical prisms, your job is to calculate the27surface area of his sculpture.28 29</p>30 31 32 33 34<H2>Input</H2>35 36<p>37The input consists of multiple datasets, followed by a single line containing only a zero. The38first line of each dataset contains an integer <i>n</i> indicating the number of the following lines, each39of which contains two integers <i>a<sub>i</sub></i> and <i>b<sub>i</sub></i> (<i>i</i> = 1, ... , <i>n</i>).40</p>41 42<center>43<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_crossingPrisms2">44<p>Figure 2: Outline of the cross section</p>45</center>46 47<center>48<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_crossingPrisms3">49<p>Figure 3: The intersection</p>50</center>51 52 53<p>54A closed path formed by the given points (<i>a</i><sub>1</sub>, <i>b</i><sub>1</sub>), (<i>a</i><sub>2</sub>, <i>b</i><sub>2</sub> ), ... , (<i>a<sub>n</sub></i>, <i>b<sub>n</sub></i>), (<i>a</i><sub><i>n</i>+1</sub>, <i>b</i><sub><i>n</i>+1</sub>)(= (<i>a</i><sub>1</sub>, <i>b</i><sub>1</sub>))55indicates the outline of the cross section of the prisms. The closed path is simple, that is, it does56not cross nor touch itself. The right-hand side of the line segment from (<i>a<sub>i</sub></i>, <i>b<sub>i</sub></i>) to (<i>a<sub>i</sub></i>+1 , <i>b<sub>i</sub></i>+1 ) is the inside of the section.57</p>58<p>59You may assume that 3 &le; <i>n</i> &le; 4, 0 &le; <i>a<sub>i</sub></i> &le; 10 and 0 &le; <i>b<sub>i</sub></i> &le; 10 (<i>i</i> = 1, ... , <i>n</i>).60</p>61<p>62One of the prisms is put along the <i>x</i>-axis so that the outline of its cross section at <i>x</i> = <i>&zeta;</i> is63indicated by points (<i>x<sub>i</sub></i>, <i>y<sub>i</sub></i>, <i>z<sub>i</sub></i> ) = (<i>&zeta;</i>, <i>a<sub>i</sub></i>, <i>b<sub>i</sub></i>) (0 &le; <i>&zeta;</i> &le; 10, <i>i</i> = 1, ... , <i>n</i>). The other prism is put64along the <i>y</i>-axis so that its cross section at <i>y</i> = <i>&eta;</i> is indicated by points (<i>x<sub>i</sub></i>, <i>y<sub>i</sub></i>, <i>z<sub>i</sub></i>) = (<i>a<sub>i</sub></i>, <i>&eta;</i>, <i>b<sub>i</sub></i>)65(0 &le; <i>&eta;</i> &le; 10, <i>i</i> = 1, ... , <i>n</i>).66 67</p>68 69 70<H2>Output</H2>71 72<p>73The output should consist of a series of lines each containing a single decimal fraction. Each74number should indicate an approximate value of the surface area of the polyhedron defined by the corresponding dataset. The value may contain an error less than or equal to 0.0001. You75may print any number of digits below the decimal point.76 77 78</p>79 80<H2>Sample Input</H2>81<pre>824835 0840 10857 58610 5874887 58910 5905 0910 10924930 109410 109510 0960 0973980 0990 1010010 010141020 1010310 51040 01059 510641075 01080 101095 511010 1011141120 51135 1011410 51155 011641177 11184 11190 11209 51210122</pre>123 124<H2>Output for the Sample Input</H2>125<pre>126194.8255127194.8255128600.0000129341.421413042.9519131182.5141132282.8427133149.2470134</pre>135 136