ICPC 2014 - A. Baggage
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/A-baggage. Edit
competitive_programming/icpc/2014/A-baggage/solution.tex to update the written solution and
competitive_programming/icpc/2014/A-baggage/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 A
Baggage
Time Limit: 1 second
An airline has two flights leaving at about the same time from ICPCity, one to city B and one to city A.
The airline also has n counters where passengers check their baggage. At each counter there is a pair of
identical baggage bins, one for city B and one for city A.
Just before the flights depart, each pair of baggage bins is moved by a motorized cart to a sorting area.
The cart always moves two bins at a time, one for city B and one for city A. After all the bins have been
moved, they line up in the sorting area like this:
B A B A B A ... B A
That is, there are 2n baggage bins in a row, starting with a bin for city B, then one for city A, and so
forth. The task now is to reorder them so all the baggage bins for city A precede the baggage bins for
city B. Then the bins can be loaded on the appropriate aircraft.
The reordering is done by moving pairs of adjacent baggage bins (not necessarily B then A), again via
the motorized cart. For proper balance, the cart must always carry two bins, never just one. A pair of
bins must always be moved to an empty space that is at least two bins wide. On the left of the first bin
are some empty spaces that can be used as needed during the reordering.
When the reordering process begins, the bin locations are numbered from 1 (initially containing the
leftmost B baggage bin) to 2n (initially containing the rightmost A baggage bin). There are 2n initially
empty spaces to the left of the bins, numbered from 0 to −2n + 1, as shown in Figure A.1 for the case
n = 4.
B A B A B A B A
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8
Figure A.1: Initial configuration of bins and empty spaces for n = 4
Given n, find a shortest sequence of moves that will reorder the bins so that all the A bins are to the left
of all the B bins. At the end of the process, it is possible that the leftmost A bin is at some location other
than 1, but the bins must be adjacent in a sequence of 2n locations.
Input
The input consists of a single test case, which consists of the integer n (3 ≤ n ≤ 100).
Output
Display a shortest sequence of moves that will correctly reorder the bins. Each move is of the form
“f to t”, where f and t are integers representing the movement of the bins in locations f and f + 1
to locations t and t + 1. If multiple solutions are possible, display any one of them.
Sample Input 1 Sample Output 1
5 8 to -1
3 to 8
6 to 3
0 to 6
9 to 0
Sample Input 2 Sample Output 2
8 10 to -1
3 to 10
14 to 3
7 to 14
0 to 7
11 to 0
4 to 11
15 to 4
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\\A. Baggage Time Limit: 1 second}
\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;
}