ICPC 2017 - E. Need for Speed
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/2017/E-need-for-speed/solution.tex to update the written solution and
competitive_programming/icpc/2017/E-need-for-speed/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.
Rapid City
event
sponsor
ICPC 2017
Problem E
Need for Speed
Time limit: 1 second
Sheila is a student and she drives a typical student car: it is old, slow,
rusty, and falling apart. Recently, the needle on the speedometer fell
off. She glued it back on, but she might have placed it at the wrong
angle. Thus, when the speedometer reads s, her true speed is s + c,
where c is an unknown constant (possibly negative).
Sheila made a careful record of a recent journey and wants to use
this to compute c. The journey consisted of n segments. In the ith
segment she traveled a distance of di and the speedometer read si for
the entire segment. This whole journey took time t. Help Sheila by
computing c.
Note that while Sheila’s speedometer might have negative readings,
her true speed was greater than zero for each segment of the journey.
Input
The first line of input contains two integers n (1 ≤ n ≤ 1 000), the number of sections in Sheila’s journey,
and t (1 ≤ t ≤ 106 ), the total time. This is followed by n lines, each describing one segment of Sheila’s
journey. The ith of these lines contains two integers di (1 ≤ di ≤ 1 000) and si (|si | ≤ 1 000), the distance
and speedometer reading for the ith segment of the journey. Time is specified in hours, distance in miles,
and speed in miles per hour.
Output
Display the constant c in miles per hour. Your answer should have an absolute or relative error of less than
10−6 .
Sample Input 1 Sample Output 1
3 5 3.000000000
4 -1
4 0
10 3
Sample Input 2 Sample Output 2
4 10 -0.508653377
5 3
2 2
3 6
3 1
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 2017\\E. Need for Speed}
\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;
}