EP Ethan Pham Project Euler, competitive programming, and notes on the things I keep studying.
ICPC 2008
ICPC 2008

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...

Updated May 21, 2026
Track ICPC
Year 2008
Statement Text + PDF
TeXC++Statement textStatement PDF
Problem statement

Problem Statement

Formatted from the contest statement text, with sample tests broken out into copyable blocks.

Statement text Statement PDF
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".

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

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.

Sample Tests

Sample
Sample Input 
10 2
hello
world
10 0
4 1
icpc
0 0

This page is intentionally blank.
Sample Output 
Case 1: 2 suspects
helloworld
worldhello
Case 2: 141167095653376 suspects
Case 3: 1 suspects
icpc
Editorial

Editorial

The solution write-up is rendered from the LaTeX source, with equations kept live through MathJax.

Raw TeX

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

  1. Describe the data structures and the state maintained by the algorithm.

  2. Explain the processing order and why it is sufficient.

  3. 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.

Implementation

Code

C++ solution used for this page.

C++

Clean code view with a raw-file link when you want the original source.

Raw file 
#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;
}
Resources

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TeX write-upcompetitive_programming/icpc/2008/I-password-suspects/solution.texC++ implementationcompetitive_programming/icpc/2008/I-password-suspects/solution.cppStatement textcompetitive_programming/icpc/2008/I-password-suspects/statement.txtStatement PDFcompetitive_programming/icpc/2008/I-password-suspects/statement.pdfMetadatacompetitive_programming/icpc/2008/I-password-suspects/meta.jsonYear packetcompetitive_programming/icpc/2008/contest_problems.pdf