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ICPC 2016
ICPC 2016

G. Oil

A large part of the world economy depends on oil, which is why research into new methods for finding and extracting oil is still active. Profits of oil companies depend in part on how efficiently they can drill for oil. The International Crude Petroleum Con...

Updated May 21, 2026
Track ICPC
Year 2016
Statement Text + PDF
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Problem statement

Problem Statement

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Time limit 10 seconds

A large part of the world economy depends on oil, which is why research into new methods for finding and extracting oil is still active. Profits of oil companies depend in part on how efficiently they can drill for oil. The International Crude Petroleum Consortium (ICPC) hopes that extensive computer simulations will make it easier to determine how to drill oil wells in the best possible way. Drilling oil wells optimally is getting harder each day – the newly discovered oil deposits often do not form a single body, but are split into many parts. The ICPC is currently concerned with stratified deposits, as illustrated in Figure G.1.

Surface                                            x
(100, 20)                          (180, 20)
(30, 30)       (60, 30)
(70, 40)          (110, 40)
(10, 50)    (40, 50)
(0, 70)                                      (80, 70)
y
Figure G.1: Oil layers buried in the earth. This figure corresponds to Sample Input 1.

To simplify its analysis, the ICPC considers only the 2-dimensional case, where oil deposits are modeled as horizontal line segments parallel to the earth’s surface. The ICPC wants to know how to place a single oil well to extract the maximum amount of oil. The oil well is drilled from the surface along a straight line and can extract oil from all deposits that it intersects on its way down, even if the intersection is at an endpoint of a deposit. One such well is shown as a dashed line in Figure G.1, hitting three deposits. In this simple model the amount of oil contained in a deposit is equal to the width of the deposit. Can you help the ICPC determine the maximum amount of oil that can be extracted by a single well?

Input

The first line of input contains a single integer n (1 ≤ n ≤ 2 000), which is the number of oil deposits. This is followed by n lines, each describing a single deposit. These lines contain three integers x0 , x1 , and y giving the deposit’s position as the line segment with endpoints (x0 , y) and (x1 , y). These numbers satisfy |x0 |, |x1 | ≤ 106 and 1 ≤ y ≤ 106 . No two deposits will intersect, not even at a point.

Output

Display the maximum amount of oil that can be extracted by a single oil well.

Sample Tests

Sample 1
Sample Input 
5
100 180 20
30 60 30
70 110 40
10 40 50
0 80 70
Sample Output 
200
Sample 2
Sample Input 
3
50 60 10
-42 -42 20
25 0 10
Sample Output 
25
Editorial

Editorial

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

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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.

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#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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TeX write-upcompetitive_programming/icpc/2016/G-oil/solution.texC++ implementationcompetitive_programming/icpc/2016/G-oil/solution.cppStatement textcompetitive_programming/icpc/2016/G-oil/statement.txtStatement PDFcompetitive_programming/icpc/2016/G-oil/statement.pdfMetadatacompetitive_programming/icpc/2016/G-oil/meta.jsonYear packetcompetitive_programming/icpc/2016/contest_problems.pdf