ICPC 2010 - J. Sharing Chocolate
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/2010/J-sharing-chocolate/solution.tex to update the written solution and
competitive_programming/icpc/2010/J-sharing-chocolate/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.
blem J
Prob
S
Sharing Chocolate
olate
Problem ID: choco
d the world eveery day. It is a truly universall
Chocolate in its many forrms is enjoyed by millions off people around
candy, avaailable in virtuaally every counntry around thee world.
i with friends. Unfortunately
You find thhat the only thiing better than eating chocolaate is to share it y, your friends
d
are very piicky and have different appetites: some wouuld like more anda others less of the chocolate that you offe
fer
them. You have found it increasingly diifficult to deterrmine whetherr their demandss can be met. Itt is time to writte
a program that solves thee problem oncee and for all!
Your chocoolate comes ass a rectangular bar. The bar coonsists of samee-sized rectanggular pieces. Too share the
chocolate, you may breakk one bar into two b
t pieces alonng a division between t bar. You
rows oor columns of the
may then repeatedly
r g pieces in the ssame manner. Each of your ffriends insists on
breaak the resulting o a getting a
n of the chocollate that has a sspecified numbber of pieces. Y
single rectaangular portion You are a little bit insistent ass
w break up your
well: you will y bar only iff all of it can bee distributed too your friends, with none left over.
For exampple, Figure 9 shhows one way thatt a chocolatee bar consisting of 3 × 4 pieeces can be spliit into 4 parts
that containn 6, 3, 2, and 1 pieces respectively, by breaaking it 3 timess. (This correspponds to the firrst sample
input.)
Figure 9
F
Input
c
The input consists of mulltiple test casess, each describing a chocolatee bar to share. Each descriptiion starts with a
line containning a single innteger n (1 ≤ n ≤ 15), the nummber of parts innto which the bbar is supposedd to be split.
This is folllowed by a linee containing twwo integers x annd y (1 ≤ x, y ≤ 100), the dimmensions of the chocolate bar.
p
The next liine contains n positive integeers, giving the nnumber of piecces that are suppposed to be inn each of the n
parts.
i terminated by
The input is b a line containing the integeer zero.
Output
For each teest case, first display its case number. Then display whethher it is possiblee to break the chocolate
c in thhe
desired waay: display “Ye es” if it is posssible, and “No”” otherwise. Foollow the formaat of the samplle output.
Sample In
nput e Input
Output forr the Sample
4 Case 1: Yes
3 4 Case 2: No
6 3 2 1
2
2 3
1 5
0
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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 2010\\J. Sharing Chocolate}
\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;
}