ICPC 2015 - C. Catering
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/2015/C-catering. Edit
competitive_programming/icpc/2015/C-catering/solution.tex to update the written solution and
competitive_programming/icpc/2015/C-catering/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 C
Catering
Time limit: 4 seconds
Paul owns a catering company and business is booming. The com-
pany has k catering teams, each in charge of one set of catering equip-
ment. Every week, the company accepts n catering requests for var-
ious events. For every request, they send a catering team with their
equipment to the event location. The team delivers the food, sets up
the equipment, and instructs the host on how to use the equipment and
serve the food. After the event, the host is responsible for returning the
equipment back to Paul’s company.
Unfortunately, in some weeks the number of catering teams is less than
the number of requests, so some teams may have to be used for more
than one event. In these cases, the company cannot wait for the host
Picture from Wikimedia Commons
to return the equipment and must keep the team on-site to move the
equipment to another location. The company has an accurate estimate of the cost to move a set of
equipment from any location to any other location. Given these costs, Paul wants to prepare an Advance
Catering Map to service the requests while minimizing the total moving cost of equipment (including
the cost of the first move), even if that means not using all the available teams. Paul needs your help to
write a program to accomplish this task. The requests are sorted in ascending order of their event times
and they are chosen in such a way that for any i < j, there is enough time to transport the equipment
used in the ith request to the location of the j th request.
Input
The first line of input contains two integers n (1 ≤ n ≤ 100) and k (1 ≤ k ≤ 100) which are the number
of requests and the number of catering teams, respectively. Following that are n lines, where the ith line
contains n − i + 1 integers between 0 and 1 000 000 inclusive. The j th number in the ith line is the cost
of moving a set of equipment from location i to location i + j. The company is at location 1 and the n
requests are at locations 2 to n + 1.
Output
Display the minimum moving cost to service all requests. (This amount does not include the cost of
moving the equipment back to the catering company.)
Sample Input 1 Sample Output 1
3 2 80
40 30 40
50 10
50
Sample Input 2 Sample Output 2
3 2 40
10 10 10
20 21
21
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 2015\\C. Catering}
\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;
}