ICPC 2009 - H. The Ministers’ Major Mess
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/2009/H-the-ministers-major-mess. Edit
competitive_programming/icpc/2009/H-the-ministers-major-mess/solution.tex to update the written solution and
competitive_programming/icpc/2009/H-the-ministers-major-mess/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 H
The Ministers’ Major Mess
Input file: major.in
The ministers of the remote country of Stanistan are having severe problems with their decision making. It all
started a few weeks ago when a new process for deciding which bills to pass was introduced. This process
works as follows. During each voting session, there are several bills to be voted on. Each minister expresses an
opinion by voting either “yes” or “no” for some of these bills. Because of limitations in the design of the
technical solution used to evaluate the actual voting, each minister may vote on only at most four distinct bills
(though this does not tend to be a problem, as most ministers only care about a handful of issues). Then, given
these votes, the bills that are accepted are chosen in such a way that each minister gets more than half of his or
her opinions satisfied.
As the astute reader has no doubt already realized, this process can lead to various problems. For instance, what
if there are several possible choices satisfying all the ministers, or even worse, what if it is impossible to satisfy
all the ministers? And even if the ministers’ opinions lead to a unique choice, how is that choice found?
Your job is to write a program to help the ministers with some of these issues. Given the ministers’ votes, the
program must find out whether all the ministers can be satisfied, and if so, determine the decision on those bills
for which, given the constraints, there is only one possible choice.
Input
Input consists of multiple test cases. Each test case starts with integers B (1 ≤ B ≤ 100), which is the number of
distinct bills to vote on, and M (1 ≤ M ≤ 500), which is the number of ministers. The next M lines give the votes
of the ministers. Each such line starts with an integer 1 ≤ k ≤ 4, indicating the number of bills that the minister
has voted on, followed by the k votes. Each vote is of the format <bill> <vote>, where <bill> is an integer
between 1 and B identifying the bill that is voted on, and <vote> is either y or n, indicating that the minister’s
opinion is “yes” or “no.” No minister votes on the same bill more than once. The last test case is followed by a
line containing two zeros.
Output
For each test case, print the test case number (starting with 1) followed by the result of the process. If it is
impossible to satisfy all ministers, the result should be impossible. Otherwise, the result should be a string
of length B, where the ith character is y, n, or ?, depending on whether the decision on the ith bill should be
“yes,” whether it should be “no,” or whether the given votes do not determine the decision on this bill.
Sample Input Output for the Sample Input
5 2 Case 1: ?y??n
4 2 y 5 n 3 n 4 n Case 2: impossible
4 4 y 3 y 5 n 2 y
4 2
4 1 y 2 y 3 y 4 y
3 1 n 2 n 3 n
0 0
This page 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 2009\\H. The Ministers’ Major Mess}
\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;
}