ICPC 2016 - D. Clock Breaking
State the problem in your own words. Focus on the mathematical or algorithmic core rather than repeating the full statement.
Source-first archive entry
This page is built from the copied files in competitive_programming/icpc/2016/D-clock-breaking. Edit
competitive_programming/icpc/2016/D-clock-breaking/solution.tex to update the written solution and
competitive_programming/icpc/2016/D-clock-breaking/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 D
Clock Breaking
Time limit: 5 seconds
After numerous unfortunate freak fatalities and the lawsuits, settlements, protests, and boycotts that
naturally followed, the beleaguered executives at ACME Clock Manufacturers have decided they need
to finally fix their disastrous quality control issues. It has been known for years that the digital clocks
they manufacture have an unacceptably high ratio of faulty liquid-crystal display (LCD) screens, and yet
these heartless souls have repeatedly failed to address the issue, or even warn their hapless consumers!
You have been called in as a quality consultant to finally put a stop to the madness. Your job is to write
an automated program that can test a clock and find faults in its display.
These clocks use a standard 7-segment LCD display for all digits (shown on the left in Figure D.1), plus
two small segments for the ‘:’, and show all times in a 24-hour format. The minute before midnight is
23:59, and midnight is 0:00. The ‘:’ segments of a working clock are on at all times. The representation
of each digit using the seven segments is shown on the right in Figure D.1.
Figure D.1: LCD display of each digit.
Your program will be given the display of a clock at several consecutive minutes, although you do not
know exactly what time these displays start. Some of the LCD segments are burnt out (permanently off)
and some are burnt in (permanently on). Your program must determine, where possible, which segments
are definitely malfunctioning and which are definitely in working order.
Input
The first input line contains a single integer n (1 ≤ n ≤ 100), which is the number of consecutive
minutes of a clock’s display. The next 8n − 1 lines contain n ASCII images of these clock displays of
size 7 × 21, with a single blank line separating the representations.
All digit segments are represented by two characters, and each colon segment is represented by one
character. The character ‘X’ indicates a segment that is on. The character ‘.’ indicates anything else
(segments that are off or non-segment portions of the display). See the sample input/output for details;
the first output shows every possible LCD segment along with the smaller segments used to represent
the ‘:’. No clock representation has an ‘X’ in a non-segment position or only half of a segment showing.
Output
Display a 7 × 21 ASCII image with a ‘0’ for every segment that is burnt out, a ‘1’ for every segment
that is burnt in, a ‘W’ for every segment that is definitely working, and a ‘?’ for every segment for which
the status cannot be determined. Use ‘.’ for non-segments. If the given displays cannot come from
consecutive minutes, display impossible.
Sample Input 1 Sample Output 1
3 .??...WW.....??...??.
......XX.....XX...XX. ?..?.W..?...?..1.0..?
.....X..X...X..X....X ?..?.W..?.?.?..1.0..?
.....X..X.X.X..X....X .??...??.....11...WW.
.............XX...XX. ?..?.W..?.0.W..?.1..?
.....X..X......X.X..X ?..?.W..?...W..?.1..?
.....X..X......X.X..X .??...11.....??...??.
......XX.....XX...XX.
......XX.....XX...XX.
.....X..X...X..X....X
.....X..X.X.X..X....X
.............XX...XX.
.....X..X......X.X..X
.....X..X......X.X..X
......XX.....XX...XX.
.............XX...XX.
........X...X..X....X
........X.X.X..X....X
.............XX......
........X...X..X.X..X
........X...X..X.X..X
......XX.....XX...XX.
Sample Input 2 Sample Output 2
2 impossible
......XX.....XX...XX.
...X....X...X..X.X..X
...X....X.X.X..X.X..X
......XX..........XX.
...X.X....X.X..X.X..X
...X.X......X..X.X..X
......XX.....XX...XX.
......XX.....XX......
...X....X...X..X.....
...X....X.X.X..X.....
......XX.............
...X.X....X.X..X.....
...X.X......X..X.....
......XX.....XX......
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\\D. Clock Breaking}
\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;
}