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ICPC 2013
ICPC 2013

A. Self-Assembly

2013 World Finals St. Petersburg HOSTED BY ITMO Problem A Self-Assembly Time Limit: 3 seconds Automatic Chemical Manufacturing is experimenting with a process called self-assembly. In this pro- cess, molecules with natural affinity for each other are mixe...

Updated May 21, 2026
Track ICPC
Year 2013
Statement Text + PDF
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Problem statement

Problem Statement

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

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Time limit 3 seconds

Automatic Chemical Manufacturing is experimenting with a process called self-assembly. In this pro- cess, molecules with natural affinity for each other are mixed together in a solution and allowed to spon- taneously assemble themselves into larger structures. But there is one problem: sometimes molecules assemble themselves into a structure of unbounded size, which gums up the machinery. You must write a program to decide whether a given collection of molecules can be assembled into a structure of unbounded size. You should make two simplifying assumptions: 1) the problem is restricted to two dimensions, and 2) each molecule in the collection is represented as a square. The four edges of the square represent the surfaces on which the molecule can connect to other compatible molecules. In each test case, you will be given a set of molecule descriptions. Each type of molecule is described by four two-character connector labels that indicate how its edges can connect to the edges of other molecules. There are two types of connector labels:

  • An uppercase letter (A, . . . , Z) followed by + or −. Two edges are compatible if their labels have the same letter but different signs. For example, A+ is compatible with A− but is not compatible with A+ or B−.
  • Two zero digits 00. An edge with this label is not compatible with any edge (not even with another edge labeled 00).

Assume there is an unlimited supply of molecules of each type, which may be rotated and reflected. As the molecules assemble themselves into larger structures, the edges of two molecules may be adjacent to each other only if they are compatible. It is permitted for an edge, regardless of its connector label, to be connected to nothing (no adjacent molecule on that edge). Figure A.1 shows an example of three molecule types and a structure of bounded size that can be assem- bled from them (other bounded structures are also possible with this set of molecules).

Figure A.1: Illustration of Sample Input 1.
                                                                ICPC 2013
2013 World Finals
                                                           St. Petersburg
                                                           HOSTED BY   ITMO

Input

The input consists of a single test case. A test case consists of two lines. The first contains an integer n (1 ≤ n ≤ 40 000) indicating the number of molecule types. The second line contains n eight-character strings, each describing a single type of molecule, separated by single spaces. Each string consists of four two-character connector labels representing the four edges of the molecule in clockwise order.

Output

Display the word unbounded if the set of molecule types can generate a structure of unbounded size. Otherwise, display the word bounded.

Sample Tests

Sample 1
Sample Input 
 3
 A+00A+A+ 00B+D+A- B-C+00C+
Sample Output 
bounded
Sample 2
Sample Input 
 1
 K+K-Q+Q-
Sample Output 
unbounded
Editorial

Editorial

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

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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;
}
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