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ICPC 2009
ICPC 2009

D. Conduit Packing

Input File: conduit.in Allied Conduit Manufacturing (ACM) makes metal conduit tubes with round cross-sections that enclose many different types of wires. The circular cross-section of a wire can have a diameter up to 20 millimeters (20000 micrometers). ACM...

Updated May 21, 2026
Track ICPC
Year 2009
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
Input file conduit.in

Allied Conduit Manufacturing (ACM) makes metal conduit tubes with round cross-sections that enclose many different types of wires. The circular cross-section of a wire can have a diameter up to 20 millimeters (20000 micrometers). ACM needs a program to compute the minimum diameter of a conduit that can hold 4 wires with specified diameters.

Figure 4 shows examples of fitting four wires of different sizes into conduits of minimum diameters.

Figure 4: Fitting wires inside conduits

Your program must take the diameters of wires and determine the minimum inside diameter of the conduit that can hold the wires.

Input

The input file contains several test cases. Each test case consists of a line with four integers, d1, d2, d3, and d4, which are the diameters of the wires in micrometers. The integers satisfy 20000 ≥ d1 ≥ d2 ≥ d3 ≥ d4 > 0. The last test case is followed by a line containing a single integer zero.

Output

For each test case, print the number of the test case (starting with 1) followed by the minimum conduit diameter in micrometers, rounded to the nearest integer. Follow the format of the sample output.

Sample Tests

Sample
Sample Input 
10000 10000 10000 10000
10000 10000 10000 3000
12000 12000 3600 3600
0

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Sample Output 
Case 1: 24142
Case 2: 21547
Case 3: 24000
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

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TeX write-upcompetitive_programming/icpc/2009/D-conduit-packing/solution.texC++ implementationcompetitive_programming/icpc/2009/D-conduit-packing/solution.cppStatement textcompetitive_programming/icpc/2009/D-conduit-packing/statement.txtStatement PDFcompetitive_programming/icpc/2009/D-conduit-packing/statement.pdfMetadatacompetitive_programming/icpc/2009/D-conduit-packing/meta.jsonYear packetcompetitive_programming/icpc/2009/contest_problems.pdf