ICPC 2008 - I. Password Suspects
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/2008/I-password-suspects. Edit
competitive_programming/icpc/2008/I-password-suspects/solution.tex to update the written solution and
competitive_programming/icpc/2008/I-password-suspects/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 I
Password Suspects
Input file: password.in
You are the computer whiz for the secret organization known as the Sneaky Underground Smug Perpetrators of Evil
Crimes and Thefts. The target for SUSPECT’s latest evil crime is their greatest foe, the Indescribably Clever
Policemen’s Club, and everything is prepared. Everything, except for one small thing: the secret password for
ICPC’s main computer system.
The password is known to consist only of lowercase letters 'a'-'z'. Furthermore, through various sneaky observations,
you have been able to determine the length of the password, as well as a few (possibly overlapping) substrings of the
password, though you do not know exactly where in the password they occur.
For instance, say that you know that the password is 10 characters long, and that you have observed the substrings
"hello" and "world". Then the password must be either "helloworld" or "worldhello".
T T T T T T T T
The question is whether this information is enough to reduce the number of possible passwords to a reasonable
amount. To answer this, your task is to write a program that determines the number of possible passwords and, if
there are at most 42 of them, prints them all.
Input
The input file contains several test cases. Each test case begins with a line containing two integers N and M
(1 ≤ N ≤ 25, 0 ≤ M ≤ 10), giving the length of the password and the number of known substrings respectively. This is
followed by M lines, each containing a known substring. Each known substring consists of between 1 and 10
lowercase letters 'a'-'z'.
The last test case is followed by a line containing two zeroes.
Output
For each test case, print the case number (beginning with 1) followed by Y suspects, where Y is the number of
T T
possible passwords for this case. If the number of passwords is at most 42, then output all possible passwords in
alphabetical order, one per line.
The input will be such that the number of possible passwords at most 1015.
P P
Sample Input Output for the Sample Input
10 2 Case 1: 2 suspects
hello helloworld
world worldhello
10 0 Case 2: 141167095653376 suspects
4 1 Case 3: 1 suspects
icpc icpc
0 0
This page is intentionally 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 2008\\I. Password Suspects}
\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;
}