ICPC 2014 - K. Surveillance
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/2014/K-surveillance. Edit
competitive_programming/icpc/2014/K-surveillance/solution.tex to update the written solution and
competitive_programming/icpc/2014/K-surveillance/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 K
Surveillance
Time Limit: 4 seconds
The International Corporation for Protection and Control (ICPC) develops efficient technology for, well,
protection and control. Naturally, they are keen to have their own headquarters protected and controlled.
Viewed from above, the headquarters building has the shape of a convex polygon. There are several
suitable places around it where cameras can be installed to monitor the building. Each camera covers a
certain range of the polygon sides (building walls), depending on its position. ICPC wants to minimize
the number of cameras needed to cover the whole building.
Input
The input consists of a single test case. Its first line contains two integers n and k (3 ≤ n ≤ 106 and
1 ≤ k ≤ 106 ), where n is the number of walls and k is the number of possible places for installing
cameras. Each of the remaining k lines contains two integers ai and bi (1 ≤ ai , bi ≤ n). These integers
specify which walls a camera at the ith place would cover. If ai ≤ bi then the camera covers each wall j
such that ai ≤ j ≤ bi . If ai > bi then the camera covers each wall j such that ai ≤ j ≤ n or 1 ≤ j ≤ bi .
Output
Display the minimal number of cameras that suffice to cover each wall of the building. The ranges
covered by two cameras may overlap. If the building cannot be covered, display impossible instead.
Sample Input 1 Sample Output 1
100 7 3
1 50
50 70
70 90
90 40
20 60
60 80
80 20
Sample Input 2 Sample Output 2
8 2 impossible
8 3
5 7
Sample Input 3 Sample Output 3
8 2 2
8 4
5 7
This page is intentionally left blank.
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 2014\\K. Surveillance Time Limit: 4 seconds}
\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;
}