ICPC 2015 - A. Amalgamated Artichokes
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/2015/A-amalgamated-artichokes. Edit
competitive_programming/icpc/2015/A-amalgamated-artichokes/solution.tex to update the written solution and
competitive_programming/icpc/2015/A-amalgamated-artichokes/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 A
Amalgamated Artichokes
Time limit: 5 seconds
Fatima Cynara is an analyst at Amalgamated Artichokes
(AA). As with any company, AA has had some very good
times as well as some bad ones. Fatima does trending
analysis of the stock prices for AA, and she wants to deter-
mine the largest decline in stock prices over various time
spans. For example, if over a span of time the stock prices
were 19, 12, 13, 11, 20 and 14, then the largest decline
would be 8 between the first and fourth price. If the last
price had been 10 instead of 14, then the largest decline
would have been 10 between the last two prices.
Fatima has done some previous analyses and has found Picture by Hans Hillewaert via Wikimedia Commons
that the stock price over any period of time can be mod-
elled reasonably accurately with the following equation:
price(k) = p · (sin(a · k + b) + cos(c · k + d) + 2)
where p, a, b, c and d are constants. Fatima would like you to write a program to determine the largest
price decline over a given sequence of prices. Figure A.1 illustrates the price function for Sample Input 1.
You have to consider the prices only for integer values of k.
price(k)
1 2 3 4 5 6 7 8 9 10 k
Figure A.1: Sample Input 1. The largest decline occurs from the fourth to the seventh price.
Input
The input consists of a single line containing 6 integers p (1 ≤ p ≤ 1 000), a, b, c, d (0 ≤ a, b, c, d ≤
1 000) and n (1 ≤ n ≤ 106 ). The first 5 integers are described above. The sequence of stock prices to
consider is price(1), price(2), . . . , price(n).
Output
Display the maximum decline in the stock prices. If there is no decline, display the number 0. Your
output should have an absolute or relative error of at most 10−6 .
Sample Input 1 Sample Output 1
42 1 23 4 8 10 104.855110477
Sample Input 2 Sample Output 2
100 7 615 998 801 3 0.00
Sample Input 3 Sample Output 3
100 432 406 867 60 1000 399.303813
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\\A. Amalgamated Artichokes}
\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;
}