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ICPC 2016
ICPC 2016

K. String Theory

Nested quotations are great not only for writing literature with a complex narrative structure, but also in programming languages. While it may seem necessary to use different quotation marks at different nesting levels for clarity, there is an alternative....

Updated May 21, 2026
Track ICPC
Year 2016
Statement Text + PDF
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Problem statement

Problem Statement

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Time limit 2 seconds

Nested quotations are great not only for writing literature with a complex narrative structure, but also in programming languages. While it may seem necessary to use different quotation marks at different nesting levels for clarity, there is an alternative. We can display various nesting levels using k-quotations, which are defined as follows. A 1-quotation is a string that begins with a quote character, ends with another quote character and contains no quote characters in-between. These are just the usual (unnested) quotations. For example, 'this is a string' is a 1-quotation. For k > 1, a k-quotation is a string that begins with k quote characters, ends with another k quote characters and contains a nested string in-between. The nested string is a non-empty sequence of (k − 1)-quotations, which may be preceded, separated, and/or succeeded by any number of non-quote characters. For example, ''All 'work' and no 'play''' is a 2-quotation. Given a description of a string, you must determine its maximum possible nesting level.

Input

The input consists of two lines. The first line contains an integer n (1 ≤ n ≤ 100). The second line contains n integers a1 , a2 , . . . , an (1 ≤ ai ≤ 100), which describe a string as follows. The string starts with a1 quote characters, which are followed by a positive number of non-quote characters, which are followed by a2 quote characters, which are followed by a positive number of non-quote characters, and so on, until the string ends with an quote characters.

Output

Display the largest number k such that a string described by the input is a k-quotation. If there is no such k, display no quotation instead.

Sample Tests

Sample 1
Sample Input 
 5
 2 1 1 1 3
Sample Output 
2
Sample 2
Sample Input 
 1
 22
Sample Output 
4
Sample 3
Sample Input 
 1
 1
Sample Output 
no quotation
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.

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#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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TeX write-upcompetitive_programming/icpc/2016/K-string-theory/solution.texC++ implementationcompetitive_programming/icpc/2016/K-string-theory/solution.cppStatement textcompetitive_programming/icpc/2016/K-string-theory/statement.txtStatement PDFcompetitive_programming/icpc/2016/K-string-theory/statement.pdfMetadatacompetitive_programming/icpc/2016/K-string-theory/meta.jsonYear packetcompetitive_programming/icpc/2016/contest_problems.pdf