ICPC 2014 - F. Messenger
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/F-messenger. Edit
competitive_programming/icpc/2014/F-messenger/solution.tex to update the written solution and
competitive_programming/icpc/2014/F-messenger/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 F
Messenger
Time Limit: 4 seconds
Misha needs to send packages to his friend Nadia. Both of them often travel across Russia, which is
very large. So they decide to hire a messenger. Since the cost of the messenger service depends on the
time it takes to deliver the package, they need your help to optimize a little bit.
Assume Misha and Nadia move on a two-dimensional plane, each visiting a sequence of places and
moving along straight line segments from place to place. Your task is to find the shortest possible
delivery time given their two paths.
Misha hands the package to the messenger at some point along his path. The messenger moves without
delay along a straight line from the pick-up to intercept Nadia, who is traveling along her path. Misha,
Nadia and the messenger move with a constant speed of 1 distance unit per time unit. The delivery time
is the time between Misha handing over the package and Nadia receiving it.
Input
The input consists of a single test case. The test case contains two path descriptions, the first for Misha
and the second for Nadia. Each path description starts with a line containing an integer n, the number of
places visited (2 ≤ n ≤ 50 000). This is followed by n lines, each with two integers xi and yi specifying
the coordinates of a place (0 ≤ xi , yi ≤ 30 000). Coordinates of the places are listed in the order in
which they are to be visited, and successive places do not have the same coordinates.
Misha and Nadia start their journeys at the same time, visiting the places along their paths without
stopping. The length of each path is at most 106 . The package must be picked up at the latest when
Misha reaches his final place and it must be delivered at the latest when Nadia reaches her final place.
Output
Display the minimal time needed for delivery. Give the answer with an absolute error of at most 10−3
or a relative error of at most 10−5 . If the package cannot be delivered, display impossible instead.
Sample Input 1 Sample Output 1
2 4.00000
0 0
0 10
2
4 10
4 0
Sample Input 2 Sample Output 2
2 5.00000
0 0
1 0
3
2 0
3 0
3 10
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\\F. Messenger 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;
}