prithivMLmods/Coder-Stat

1 2<H1><font color="#000">Problem I:</font> Most Distant Point from the Sea</H1>3 4<p>5The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it6is natural to ask a question: "Where is the most distant point from the sea?" The answer to7this question for Honshu was found in 1996. The most distant point is located in former Usuda8Town, Nagano Prefecture, whose distance from the sea is 114.86 km.9</p>10 11<p>12In this problem, you are asked to write a program which, given a map of an island, finds the13most distant point from the sea in the island, and reports its distance from the sea. In order to14simplify the problem, we only consider maps representable by convex polygons.15</p>16 17<H2>Input</H2>18 19<p>20The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.21</p>22<pre>23<i>n</i>24<i>x</i><sub>1</sub>    <i>y</i><sub>1</sub>25   .26   .27   .28<i>x</i><sub><i>n</i></sub>    <i>y</i><sub><i>n</i></sub>29</pre>30 31<p>32Every input item in a dataset is a non-negative integer. Two input items in a line are separated by a space.33</p>34<p>35<i>n</i> in the first line is the number of vertices of the polygon, satisfying 3 &le; <i>n</i> &le; 100. Subsequent36<i>n</i> lines are the <i>x</i>- and <i>y</i>-coordinates of the <i>n</i> vertices. Line segments (<i>x<sub>i</sub></i>, <i>y<sub>i</sub></i>) - (<i>x</i><sub><i>i</i>+1</sub>, <i>y</i><sub><i>i</i>+1</sub>) (1 &le; <i>i</i> &le; <i>n</i> - 1) and the line segment (<i>x<sub>n</sub></i>, <i>y<sub>n</sub></i>) - (<i>x</i><sub>1</sub>, <i>y</i><sub>1</sub>) form the border of the polygon in counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions. All coordinate values are between 0 and 10000, inclusive.37</p>38 39<p>40You can assume that the polygon is simple, that is, its border never crosses or touches itself. As stated above, the given polygon is always a convex one.41</p>42 43<p>44The last dataset is followed by a line containing a single zero.45</p>46 47<H2>Output</H2>48 49<p>50For each dataset in the input, one line containing the distance of the most distant point from51the sea should be output. An output line should not contain extra characters such as spaces.52</p>53 54<p>55The answer should not have an error greater than 0.00001 (10<sup>-5</sup> ). You may output any number56of digits after the decimal point, provided that the above accuracy condition is satisfied.57</p>58 59<H2>Sample Input</H2>60<pre>614620 06310000 06410000 10000650 10000663670 06810000 0697000 1000706710 4072100 2073250 4074250 7075100 90760 70773780 07910000 10000805000 500181082</pre>83 84<H2>Output for the Sample Input</H2>85<pre>865000.00000087494.2336418834.542948890.35355390</pre>91 92 93 94 95