ICPC 2013 - B. Hey, Better Bettor
State the problem in your own words. Focus on the mathematical or algorithmic core rather than repeating the full statement.
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competitive_programming/icpc/2013/B-hey-better-bettor/solution.tex to update the written solution and
competitive_programming/icpc/2013/B-hey-better-bettor/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.
ICPC 2013
2013 World Finals
St. Petersburg
HOSTED BY ITMO
Problem B
Hey, Better Bettor
Time Limit: 4 seconds
“In the casino, the cardinal rule is to keep them playing and to keep them coming back. The
longer they play, the more they lose, and in the end, we get it all.”
(from the 1995 film Casino)
Recent recessions have not been kind to entertainment venues, including the gambling industry. Com-
petition is fierce among casinos to attract players with lots of money, and some have begun to offer
especially sweet deals. One casino is offering the following: you can gamble as much as you want at the
casino. After you are finished, if you are down by any amount from when you started, the casino will
refund x% of your losses to you. Obviously, if you are ahead, you can keep all of your winnings. There
is no time limit or money limit on this offer, but you can redeem it only once.
For simplicity, assume all bets cost 1 dollar and pay out 2 dollars. Now suppose x is 20. If you make 10
bets in total before quitting and only 3 of them pay out, your total loss is 3.2 dollars. If 6 of them pay
out, you have gained 2 dollars.
Given x and the percentage probability p of winning any individual bet, write a program to determine
the maximum expected profit you can make from betting at this casino, using any gambling strategy.
Input
The input consists of a single test case. A test case consists of the refund percentage x (0 ≤ x < 100)
followed by the winning probability percentage p (0 ≤ p < 50). Both x and p have at most two digits
after the decimal point.
Output
Display the maximum expected profit with an absolute error of at most 10−3 .
Sample Input 1 Sample Output 1
0 49.9 0.0
Sample Input 2 Sample Output 2
50 49.85 7.10178453
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 2013\\B. Hey, Better Bettor Time Limit: 4 seconds}
\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;
}