ICPC 2016 - K. String Theory
State the problem in your own words. Focus on the mathematical or algorithmic core rather than repeating the full statement.
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This page is built from the copied files in competitive_programming/icpc/2016/K-string-theory. Edit
competitive_programming/icpc/2016/K-string-theory/solution.tex to update the written solution and
competitive_programming/icpc/2016/K-string-theory/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 K
String Theory
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 Input 1 Sample Output 1
5 2
2 1 1 1 3
Sample Input 2 Sample Output 2
1 4
22
Sample Input 3 Sample Output 3
1 no quotation
1
This page is intentionally left 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 2016\\K. String Theory}
\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;
}