D. Money for Nothing
event sponsor ICPC 2017 Problem D Money for Nothing Time limit: 5 seconds In this problem you will be solving one of the most profound challenges of humans across the world since the beginning of time – how to make lots of money. You are a middleman in the...
Problem Statement
Formatted from the contest statement text, with sample tests broken out into copyable blocks.
In this problem you will be solving one of the most profound challenges of humans across the world since the beginning of time – how to make lots of money. You are a middleman in the widget market. Your job is to buy widgets from widget producer companies and sell them to widget consumer companies. Each widget consumer company has an open request for one widget per day, until some end date, and a price at which it is willing to buy the widgets. On the other hand, each widget producer company has a start date at which it can start delivering widgets and a price at which it will deliver each widget. Due to fair competition laws, you can sign a contract with only one producer company and only one con- sumer company. You will buy widgets from the producer company, one per day, starting on the day it can start delivering, and ending on the date specified by the consumer company. On each of those days you earn the difference between the producer’s selling price and the consumer’s buying price. Your goal is to choose the consumer company and the producer company that will maximize your profits.
Input
The first line of input contains two integers m and n (1 ≤ m, n ≤ 500 000) denoting the number of producer and consumer companies in the market, respectively. It is followed by m lines, the ith of which contains two integers pi and di (1 ≤ pi , di ≤ 109 ), the price (in dollars) at which the ith producer sells one widget and the day on which the first widget will be available from this company. Then follow n lines, the j th of which contains two integers qj and ej (1 ≤ qj , ej ≤ 109 ), the price (in dollars) at which the j th consumer is willing to buy widgets and the day immediately after the day on which the last widget has to be delivered to this company.
Output
Display the maximum total number of dollars you can earn. If there is no way to sign contracts that gives you any profit, display 0.
Sample Tests
2 2
1 3
2 1
3 5
7 25
Rapid City
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ICPC 20171 2
10 10
9 11
11 90Editorial
The solution write-up is rendered from the LaTeX source, with equations kept live through MathJax.
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
C++ solution used for this page.
#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;
}
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