EP Ethan Pham Project Euler, competitive programming, and notes on the things I keep studying.
ICPC 2015
ICPC 2015

A. Amalgamated Artichokes

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 pr...

Updated May 21, 2026
Track ICPC
Year 2015
Statement Text + PDF
TeXC++Statement textStatement PDF
Problem statement

Problem Statement

Formatted from the contest statement text, with sample tests broken out into copyable blocks.

Statement text Statement PDF
Time limit 5 seconds

(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 Tests

Sample 1
Sample Input 
 42 1 23 4 8 10
Sample Output 
104.855110477
Sample 2
Sample Input 
 100 7 615 998 801 3
Sample Output 
0.00
Sample 3
Sample Input 
 100 432 406 867 60 1000
Sample Output 
399.303813
Editorial

Editorial

The solution write-up is rendered from the LaTeX source, with equations kept live through MathJax.

Raw TeX

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.

Raw file 
#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;
}
Resources

Source Files and Assets

Raw files are still available here when you want the original TeX, C++, or statement assets.

Show raw files
TeX write-upcompetitive_programming/icpc/2015/A-amalgamated-artichokes/solution.texC++ implementationcompetitive_programming/icpc/2015/A-amalgamated-artichokes/solution.cppStatement textcompetitive_programming/icpc/2015/A-amalgamated-artichokes/statement.txtStatement PDFcompetitive_programming/icpc/2015/A-amalgamated-artichokes/statement.pdfMetadatacompetitive_programming/icpc/2015/A-amalgamated-artichokes/meta.jsonYear packetcompetitive_programming/icpc/2015/contest_problems.pdf