ICPC 2018 - G. Panda Preserve
State the problem in your own words. Focus on the mathematical or algorithmic core rather than repeating the full statement.
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competitive_programming/icpc/2018/G-panda-preserve/solution.tex to update the written solution and
competitive_programming/icpc/2018/G-panda-preserve/solution.cpp to update the implementation.
The website does not replace those files with hand-maintained HTML. It reads the copied source tree during the build and exposes the exact files below.
Problem Statement
Copied statement text kept beside the solution archive for direct reference.
Problem G
Panda Preserve
Time limit: 10 seconds
Last month, Sichuan province secured funding to establish the Great Panda National Park, a natural
preserve for a population of more than 1 800 giant pandas. The park will be surrounded by a polygonal
fence. In order for researchers to track the pandas, wireless receivers will be placed at each vertex of the
enclosing polygon and each animal will be outfitted with a wireless transmitter. Each wireless receiver
will cover a circular area centered at the location of the receiver, and all receivers will have the same
range. Naturally, receivers with smaller range are cheaper, so your goal is to determine the smallest
possible range that suffices to cover the entire park.
As an example, Figure G.1 shows the park described by the first sample input. Notice that a wireless
range of 35 does not suffice (a), while the optimal range of 50 covers the entire park (b).
(a) An insufficient range for covering the park. (b) The minimal range for covering the park.
Figure G.1: Illustration of Sample Input 1.
Input
The first line of the input contains an integer n (3 ≤ n ≤ 2 000) specifying the number of vertices
of the polygon bounding the park. This is followed by n lines, each containing two integers x and y
(|x|, |y| ≤ 104 ) that give the coordinates (x, y) of the vertices of the polygon in counter-clockwise order.
The polygon is simple; that is, its vertices are distinct and no two edges of the polygon intersect or touch,
except that consecutive edges touch at their common vertex.
Output
Display the minimum wireless range that suffices to cover the park, with an absolute or relative error of
at most 10−6 .
Sample Input 1 Sample Output 1
5 50
0 0
170 0
140 30
60 30
0 70
Sample Input 2 Sample Output 2
5 51.538820320
0 0
170 0
140 30
60 30
0 100
Sample Input 3 Sample Output 3
5 1.581138830
0 0
1 2
1 5
0 2
0 1
Editorial
Rendered from the copied solution.tex file. The original TeX source remains
available below.
Key Observations
Write the structural observations that make the problem tractable.
State any useful invariant, monotonicity property, graph interpretation, or combinatorial reformulation.
If the constraints matter, explain exactly which part of the solution they enable.
Algorithm
Describe the data structures and the state maintained by the algorithm.
Explain the processing order and why it is sufficient.
Mention corner cases explicitly if they affect the implementation.
Correctness Proof
We prove that the algorithm returns the correct answer.
Lemma 1.
State the first key claim.
Proof.
Provide a concise proof.
Lemma 2.
State the next claim if needed.
Proof.
Provide a concise proof.
Theorem.
The algorithm outputs the correct answer for every valid input.
Proof.
Combine the lemmas and finish the argument.
Complexity Analysis
State the running time and memory usage in terms of the input size.
Implementation Notes
Mention any non-obvious implementation detail that is easy to get wrong.
Mention numeric limits, indexing conventions, or tie-breaking rules if relevant.
Code
Exact copied C++ implementation from solution.cpp.
#include <bits/stdc++.h>
using namespace std;
namespace {
void solve() {
// Fill in the full solution logic for the problem here.
}
} // namespace
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}
Source Files
Exact copied source-of-truth files. Edit solution.tex for the write-up and solution.cpp for the implementation.
\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{enumitem}
\title{ICPC World Finals 2018\\G. Panda Preserve}
\author{}
\date{}
\begin{document}
\maketitle
\section*{Problem Summary}
State the problem in your own words. Focus on the mathematical or algorithmic core rather than repeating the full statement.
\section*{Key Observations}
\begin{itemize}[leftmargin=*]
\item Write the structural observations that make the problem tractable.
\item State any useful invariant, monotonicity property, graph interpretation, or combinatorial reformulation.
\item If the constraints matter, explain exactly which part of the solution they enable.
\end{itemize}
\section*{Algorithm}
\begin{enumerate}[leftmargin=*]
\item Describe the data structures and the state maintained by the algorithm.
\item Explain the processing order and why it is sufficient.
\item Mention corner cases explicitly if they affect the implementation.
\end{enumerate}
\section*{Correctness Proof}
We prove that the algorithm returns the correct answer.
\paragraph{Lemma 1.}
State the first key claim.
\paragraph{Proof.}
Provide a concise proof.
\paragraph{Lemma 2.}
State the next claim if needed.
\paragraph{Proof.}
Provide a concise proof.
\paragraph{Theorem.}
The algorithm outputs the correct answer for every valid input.
\paragraph{Proof.}
Combine the lemmas and finish the argument.
\section*{Complexity Analysis}
State the running time and memory usage in terms of the input size.
\section*{Implementation Notes}
\begin{itemize}[leftmargin=*]
\item Mention any non-obvious implementation detail that is easy to get wrong.
\item Mention numeric limits, indexing conventions, or tie-breaking rules if relevant.
\end{itemize}
\end{document}
#include <bits/stdc++.h>
using namespace std;
namespace {
void solve() {
// Fill in the full solution logic for the problem here.
}
} // namespace
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}