ICPC 2016 - B. Branch Assignment
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/2016/B-branch-assignment/solution.tex to update the written solution and
competitive_programming/icpc/2016/B-branch-assignment/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.
Problem B
Branch Assignment
Time limit: 3 seconds
The Innovative Consumer Products Company (ICPC) is planning to start a top-secret project. This
project consists of s subprojects. There will be b ≥ s branches of ICPC involved in this project and
ICPC wants to assign each branch to one of the subprojects. In other words, the branches will form s
disjoint groups, with each group in charge of a subproject.
At the end of each month, each branch will send a message to every other branch in its group (a different
message to each branch). ICPC has a particular protocol for its communications. Each branch i has
a secret key ki known only to the branch and the ICPC headquarters. Assume branch i wants to send
a message to branch j. Branch i encrypts its message with its key ki . A trusted courier picks up this
message from this branch and delivers it to the ICPC headquarters. Headquarters decrypts the message
with key ki and re-encrypts it with key kj . The courier then delivers this newly encrypted message to
branch j, which decrypts it with its own key kj . For security reasons, a courier can carry only one
message at a time.
Given a road network and the locations of branches and the headquarters in this network, your task is to
determine the minimum total distance that the couriers will need to travel to deliver all the end-of-month
messages, over all possible assignments of branches to subprojects.
Input
The first line of input contains four integers n, b, s, and r, where n (2 ≤ n ≤ 5 000) is the number of
intersections, b (1 ≤ b ≤ n − 1) is the number of branches, s (1 ≤ s ≤ b) is the number of subprojects,
and r (1 ≤ r ≤ 50 000) is the number of roads. The intersections are numbered from 1 through n. The
branches are at intersections 1 through b, and the headquarters is at intersection b + 1. Each of the next
r lines contains three integers u, v, and `, indicating a one-way road from intersection u to a different
intersection v (1 ≤ u, v ≤ n) of length ` (0 ≤ ` ≤ 10 000). No ordered pair (u, v) appears more than
once, and from any intersection it is possible to reach every other intersection.
Output
Display the minimum total distance that the couriers will need to travel.
Sample Input 1 Sample Output 1
5 4 2 10 13
5 2 1
2 5 1
3 5 5
4 5 0
1 5 1
2 3 1
3 2 5
2 4 5
2 1 1
3 4 2
Sample Input 2 Sample Output 2
5 4 2 10 24
5 2 1
2 5 1
3 5 5
4 5 10
1 5 1
2 3 1
3 2 5
2 4 5
2 1 1
3 4 2
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 2016\\B. Branch Assignment}
\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;
}