Submission #648637

#	TimeUTC-0	Username	Problem	Language	Result	Execution time	Memory
648637	2022-10-07 08:44:09	alvinpiter	Teleporters (IOI08_teleporters)	C++17	90 / 100	1087 ms	42012 KiB

teleporters

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/*
Model the system as a graph, where each node (except the first and the last) is an interval between two consecutive
teleport endpoints.
Observation:
The graph will consist of exactly 1 line graph and some (maybe 0) cycles.
The line graph is the the intervals that we will pass through, while the cycles are the intervals we won't pass through.
Observation:
The answer to the problem is K - 1, where K is the number of nodes in the final line graph. So our goal is to maximize
this value.
Observation:
Adding a teleport means that we will interfere at most 2 intervals, i.e nodes. There are 3 possible actions:
1. Add a teleport on an interval. This action adds 1 node to the affected subgraph, and also add 1 cycle with length 1.
2. Add a teleport that connects two different intervals:
   a. The intervals are in the same subgraph -> This is not beneficial.
   b. The intervals are in different subgraphs -> These subgraphs are merged into a larger subgraph, it has 2 more nodes.
   Picture the teleport "hooks" both subgraph.
Algorithm:
* Build the graph
* Identify the line graph and the cycles
* Connect the line graph to the longest cycles first, using action 2b above. Do this as many times as possible.
* If there is still teleports left to be built, alternate action 1 and 2b.
*/
#include<bits/stdc++.h>
using namespace std;
#define INF 2000000002
 
 
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Compilation message (stderr)

teleporters.cpp: In function 'int main()':
teleporters.cpp:52:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   52 |   for (int i = 0; i < points.size(); i++) {
      |                   ~~^~~~~~~~~~~~~~~
teleporters.cpp:90:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   90 |   for (int i = 0; i < cycleLengths.size() && m > 0; i++, m--) {
      |                   ~~^~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 5 / 5
• Subtask 3: 5 / 5
• Subtask 4: 5 / 5
• Subtask 5: 5 / 5
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• Subtask 19: 0 / 5
• Subtask 20: 0 / 5