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ICPC 2009
ICPC 2009

K. Suffix-Replacement Grammars

Input file: suffix.in As computer programmers, you have likely heard about regular expressions and context-free grammars. These are rich ways of generating sets of strings over a small alphabet (otherwise known as a formal language). There are other, more e...

Updated May 21, 2026
Track ICPC
Year 2009
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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Input file suffix.in

As computer programmers, you have likely heard about regular expressions and context-free grammars. These are rich ways of generating sets of strings over a small alphabet (otherwise known as a formal language). There are other, more esoteric ways of generating languages, such as tree-adjoining grammars, context-sensitive grammars, and unrestricted grammars. This problem uses a new method for generating a language: a suffix- replacement grammar.

A suffix-replacement grammar consists of a starting string S and a set of suffix-replacement rules. Each rule is of the form X Æ Y, where X and Y are equal-length strings of alphanumeric characters. This rule means that if the suffix (that is, the rightmost characters) of your current string is X, you can replace that suffix with Y. These rules may be applied arbitrarily many times.

For example, suppose there are 4 rules A Æ B, AB Æ BA, AA Æ CC, and CC Æ BB. You can then transform the string AA to BB using three rule applications: AA Æ AB (using the A Æ B rule), then AB Æ BA (using the AB Æ BA rule), and finally BA Æ BB (using the AÆ B rule again). But you can also do the transformation more quickly by applying only 2 rules: AA Æ CC and then CC Æ BB.

You must write a program that takes a suffix-replacement grammar and a string T and determines whether the grammar’s starting string S can be transformed into the string T. If this is possible, the program must also find the minimal number of rule applications required to do the transformation.

Input

The input consists of several test cases. Each case starts with a line containing two equal-length alphanumeric strings S and T (each between 1 and 20 characters long, and separated by whitespace), and an integer NR (0 ≤ NR ≤ 100), which is the number of rules. Each of the next NR lines contains two equal-length alphanumeric strings X and Y (each between 1 and 20 characters long, and separated by whitespace), indicating that X Æ Y is a rule of the grammar. All strings are case-sensitive. The last test case is followed by a line containing a period.

Output

For each test case, print the case number (beginning with 1) followed by the minimum number of rule applications required to transform S to T. If the transformation is not possible, print No solution. Follow the format of the sample output.

Sample Tests

Sample
Sample Input 
AA BB 4
A B
AB BA
AA CC
CC BB
A B 3
c B
.

This page intentionally left blank.
Sample Output 
Case 1: 2
Case 2: No solution
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;
}
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