ICPC 2012 - E. Infiltration
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/2012/E-infiltration. Edit
competitive_programming/icpc/2012/E-infiltration/solution.tex to update the written solution and
competitive_programming/icpc/2012/E-infiltration/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 E
Infiltration
Problem ID: infiltration
Good morning, agent W-12. Your mission, should you choose to accept it, is as follows.
We are infiltrating the ever so insidious Association of Chaos and Mischief (ACM) in order to take
down their command structure. Unfortunately, they appear to be prepared for such an eventuality, and
have given their command structure an annoyingly complex design which makes our infiltration quite
difficult.
The ACM command structure is divided into several cells. For each pair of cells A and B, either A
controls B or B controls A. But this “control” relation can be cyclic, so it could happen that A controls
B and B controls C and C controls A.
We can send in agents to infiltrate any particular cell, which gives us control over that cell and the cells
that it controls, but not any other cells. So in the example above, infiltrating A would give us control
over A and B, but not C.
For a successful infiltration of the ACM, we must obtain control over all of its cells, otherwise the cells
that are out of our control will discover us and start causing some of their trademark chaos and mischief.
As you know, we’re on a tight spending leash from higher authority these days, so we need to execute
this mission as efficiently as possible. Your mission is to figure out the minimum number of cells we
need to infiltrate in order to succeed.
This mission briefing will self-destruct in five hours. Good luck!
Input
The first line of a test case contains the number n of cells the ACM has (1 ≤ n ≤ 75). Each of the next
n lines contains a binary string of length n where the ith character of the j th line is 1 if cell j controls
cell i, and 0 otherwise (1 ≤ i, j ≤ n).
The ith character of the ith line is 0 and for i 6= j, either the ith character of the j th line is 1 or the j th
character of the ith line is 1, but not both.
Output
For each test case, display its case number followed by the minimum number m of cells that must be
infiltrated to obtain complete control of the ACM. Then display m numbers c1 , . . . , cm in any order,
indicating the list of cells to infiltrate (cells are numbered from 1 to n). If more than one set of m cells
gives complete control, any one will be accepted.
Sample Input Output for Sample Input
2 Case 1: 1 2
00 Case 2: 2 1 2
10 Case 3: 2 2 3
3
010
001
100
5
01000
00011
11001
10100
10010
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 2012\\E. Infiltration}
\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;
}