ICPC 2012 - H. Room Service
State the problem in your own words. Focus on the mathematical or algorithmic core rather than repeating the full statement.
Source-first archive entry
This page is built from the copied files in competitive_programming/icpc/2012/H-room-service. Edit
competitive_programming/icpc/2012/H-room-service/solution.tex to update the written solution and
competitive_programming/icpc/2012/H-room-service/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 H
Room Service
Problem ID: room
You are working for a company designing cute, funny robot vacuum cleaners. At a high level, the robots’
behavior is divided into three modes:
1. Exploration
2. Vacuuming
3. Rampant Killing
Unfortunately, while consumer testing shows that the last two modes are working perfectly, the explo-
ration mode still has bugs. You’ve been put in charge of debugging.
At the beginning of the exploration mode, the robot is placed into a convex polygonal room. It has
sensors that should tell it where all the walls are. Your job is to write a program that verifies that these
readings are correct. To do this, the robot needs to physically touch every wall in the room.
Your problem is this: given the shape of a convex polygonal room with N walls and a starting point P
inside it, determine the shortest route that touches each wall and then returns to P . Touching a corner
counts as touching both incident walls.
Input
Each test case starts with a line containing the number of vertices N of the polygon (3 ≤ N ≤ 100) and
the integer coordinates Px and Py of the robot’s starting point (−10 000 ≤ Px , Py ≤ 10 000). This is
followed by N lines, each containing two integers x, y (−10 000 ≤ x, y ≤ 10 000) defining a vertex of
the polygon. Vertices are given in counterclockwise order, all interior angles are less than 180 degrees,
the polygon does not self-intersect, and the robot’s starting point is strictly inside the polygon.
Output
For each test case, display the case number and the length of the desired route, accurate to two decimal
places.
Sample Input Output for Sample Input
4 0 0 Case 1: 5.66
-1 -1 Case 2: 36.73
1 -1
1 1
-1 1
3 10 1
0 0
30 0
0 20
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16
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 2012\\H. Room Service}
\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;
}