結果
| 問題 | No.5007 Steiner Space Travel |
| ユーザー |
 Risen
|
| 提出日時 | 2022-07-30 17:33:01 |
| 言語 | C# (.NET 8.0.203) |
| 結果 |
AC
|
| 実行時間 | 387 ms / 1,000 ms |
| コード長 | 42,209 bytes |
| コンパイル時間 | 7,189 ms |
| 実行使用メモリ | 194,472 KB |
| スコア | 8,510,610 |
| 最終ジャッジ日時 | 2022-07-30 17:33:28 |
| 合計ジャッジ時間 | 19,689 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge14 |
| 純コード判定しない問題か言語 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 351 ms
55,164 KB |
| testcase_01 | AC | 323 ms
55,100 KB |
| testcase_02 | AC | 335 ms
55,204 KB |
| testcase_03 | AC | 338 ms
55,112 KB |
| testcase_04 | AC | 353 ms
54,952 KB |
| testcase_05 | AC | 345 ms
54,988 KB |
| testcase_06 | AC | 351 ms
55,264 KB |
| testcase_07 | AC | 334 ms
55,080 KB |
| testcase_08 | AC | 354 ms
55,492 KB |
| testcase_09 | AC | 354 ms
55,128 KB |
| testcase_10 | AC | 353 ms
55,132 KB |
| testcase_11 | AC | 328 ms
54,824 KB |
| testcase_12 | AC | 329 ms
55,388 KB |
| testcase_13 | AC | 322 ms
55,360 KB |
| testcase_14 | AC | 338 ms
55,132 KB |
| testcase_15 | AC | 326 ms
55,204 KB |
| testcase_16 | AC | 350 ms
55,212 KB |
| testcase_17 | AC | 360 ms
54,972 KB |
| testcase_18 | AC | 347 ms
55,452 KB |
| testcase_19 | AC | 329 ms
55,436 KB |
| testcase_20 | AC | 336 ms
55,464 KB |
| testcase_21 | AC | 387 ms
55,084 KB |
| testcase_22 | AC | 345 ms
55,456 KB |
| testcase_23 | AC | 357 ms
57,000 KB |
| testcase_24 | AC | 335 ms
55,444 KB |
| testcase_25 | AC | 327 ms
55,432 KB |
| testcase_26 | AC | 352 ms
57,044 KB |
| testcase_27 | AC | 333 ms
54,972 KB |
| testcase_28 | AC | 338 ms
57,508 KB |
| testcase_29 | AC | 340 ms
194,472 KB |
コンパイルメッセージ
Determining projects to restore... Restored /home/judge/data/code/main.csproj (in 136 ms). .NET 向け Microsoft (R) Build Engine バージョン 17.0.0-preview-21470-01+cb055d28f Copyright (C) Microsoft Corporation.All rights reserved. プレビュー版の .NET を使用しています。https://aka.ms/dotnet-core-preview をご覧ください main -> /home/judge/data/code/bin/Release/net6.0/main.dll main -> /home/judge/data/code/bin/Release/net6.0/publish/
ソースコード
using System;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using static Constants;
using static Common;
public static class Common
{
public static void Swap<T>(ref T lhs, ref T rhs)
{
T temp = lhs;
lhs = rhs;
rhs = temp;
}
}
public static class Constants
{
public const int N = 100;
public const int M = 8;
public const int UniverseSize = 1000;
public const int Alpha = 5;
public const int TypePlanet = 1;
public const int TypeStation = 2;
}
public struct PointD
{
public double X;
public double Y;
public PointD(Point p)
{
X = p.X;
Y = p.Y;
}
public PointD(int x, int y)
{
X = x;
Y = y;
}
public PointD(double x, double y)
{
X = x;
Y = y;
}
public static bool operator ==(PointD a, PointD b)
{
if ((object)a == null || (object)b == null)
{
if ((object)a == null && (object)b == null)
{
return true;
}
return false;
}
return (a.X == b.X && a.Y == b.Y);
}
public static bool operator !=(PointD a, PointD b)
{
if ((object)a == null || (object)b == null)
{
if ((object)a == null && (object)b == null)
{
return false;
}
return true;
}
return (a.X != b.X || a.Y != b.Y);
}
public static PointD operator *(PointD a, double i)
{
return new PointD(a.X * i, a.Y * i);
}
public static PointD operator /(PointD a, double i)
{
return new PointD(a.X / i, a.Y / i);
}
//objと自分自身が等価のときはtrueを返す
public override bool Equals(object obj)
{
if (obj == null || GetType() != obj.GetType())
{
return false;
}
PointD p = (PointD)obj;
return (X == p.X && Y == p.Y);
}
//Equalsがtrueを返すときに同じ値を返す
public override int GetHashCode()
{
int prime = 31;
int result = 1;
long temp;
temp = BitConverter.DoubleToInt64Bits(X);
result = prime * result + (int)(temp ^ (temp >> 32));
temp = BitConverter.DoubleToInt64Bits(Y);
result = prime * result + (int)(temp ^ (temp >> 32));
return result;
}
public static PointD operator +(PointD a, PointD b)
{
return new PointD(a.X + b.X, a.Y + b.Y);
}
public static PointD operator -(PointD a, PointD b)
{
return new PointD(a.X - b.X, a.Y - b.Y);
}
public static PointD operator +(PointD a)
{
return new PointD(+a.X, +a.Y);
}
public static PointD operator -(PointD a)
{
return new PointD(-a.X, -a.Y);
}
public override string ToString()
{
return $"({X},{Y})";
}
public double Distance2(Point p)
{
return (p.X - X) * (p.X - X) + (p.Y - Y) * (p.Y - Y);
}
public Point Round()
{
return new Point((int)X, (int)Y);
}
}
public static class ExMethods
{
public static PointD Average2(this IEnumerable<Point> points)
{
var n = points.Count();
if (n == 0)
{
return new PointD(-1, -1);
}
var sum2 = points.Select(p => new Point(p.X*p.X, p.Y*p.Y)).Aggregate((a, b) => a + b);
var p = new PointD(sum2) / points.Count();
return new PointD(Math.Sqrt(p.X), Math.Sqrt(p.Y));
}
}
namespace Edmonds
{
public enum TreeLevel
{
EVEN,
ODD,
DUMBBELL
}
public class Blossom
{
public Blossom()
{
charge = 0;
treeLevel = TreeLevel.EVEN;
treeParentBlossom = null;
treeParentEdge = null;
outwardBlossom = null;
}
public double Charge => charge;
public TreeLevel TreeLevel => treeLevel;
public void AddCharge(double delta)
{
charge += delta;
UpdateVertexTotal(delta);
}
public void UpdateCharge(double reserve)
{
if (TreeLevel == TreeLevel.EVEN)
{
AddCharge(reserve);
}
else
{
AddCharge(-reserve);
}
foreach (var child in treeChildren)
{
child.UpdateCharge(reserve);
}
}
public Blossom GetOutermostBlossom()
{
Blossom outermost = this;
while (outermost.outwardBlossom != null)
{
outermost = outermost.outwardBlossom;
}
return outermost;
}
public Blossom GetInnerBlossomContaining(Vertex v)
{
Blossom inner = v;
while (inner != null && inner.outwardBlossom != this)
{
inner = inner.outwardBlossom;
}
return inner;
}
public Blossom GetRootBlossom()
{
Blossom root = this;
while (root.treeParentBlossom != null)
{
root = root.treeParentBlossom;
}
return root;
}
public virtual Vertex GetStem()
{
return innerChildren[0].GetStem();
}
public void FlipPathAndDisassemble(Vertex v, Blossom pair = null, Edge pairEdge = null)
{
Vertex v2 = GetStem();
if (TreeLevel == TreeLevel.ODD)
{
v2 = treeParentEdge.V1;
if (v2.GetOutermostBlossom() != this)
{
v2 = treeParentEdge.V2;
}
}
FlipPathBetween(v, v2);
if (TreeLevel == TreeLevel.EVEN)
{
foreach (var child in treeChildren)
{
if (child != pair)
{
child.DisassembleTreeIntoDumbbells();
}
}
}
treeChildren.Clear();
Blossom parent = treeParentBlossom;
Edge parentEdge = treeParentEdge;
treeParentBlossom = null;
treeParentEdge = null;
TreeLevel oldTreeLevel = TreeLevel;
if (pair != null)
{
MakeDumbbellWith(pair, pairEdge);
}
if (parent == null)
{
return;
}
Vertex pv = parentEdge.V1;
if (pv.GetOutermostBlossom() == this)
{
pv = parentEdge.V2;
}
parentEdge.Flip();
if (oldTreeLevel == TreeLevel.EVEN)
{
parent.FlipPathAndDisassemble(pv);
}
else
{
parent.FlipPathAndDisassemble(pv, this, parentEdge);
}
}
public void DisassembleTreeIntoDumbbells()
{
if (TreeLevel == TreeLevel.EVEN)
{
foreach (var child in treeChildren)
{
child.DisassembleTreeIntoDumbbells();
}
treeChildren.Clear();
treeParentBlossom = null;
treeParentEdge = null;
}
else
{
Blossom pair = treeChildren.First.Value;
Edge pairEdge = treeChildren.First.Value.treeParentEdge;
pair.DisassembleTreeIntoDumbbells();
treeChildren.Clear();
treeParentBlossom = null;
treeParentEdge = null;
MakeDumbbellWith(pair, pairEdge);
}
}
public void FlipPathBetween(Vertex v1, Vertex v2)
{
if (GetStem() != v1)
{
Swap(ref v1, ref v2);
}
if (innerChildren.Count == 0)
{
return;
}
Blossom b2 = GetInnerBlossomContaining(v2);
Blossom first = innerChildren[0];
Blossom last = b2;
int pos = innerChildren.FindIndex(c => c == b2);
if (pos % 2 == 1)
{
Swap(ref v1, ref v2);
Swap(ref first, ref last);
}
Blossom current = first;
while (current != last)
{
Vertex b_v1 = current.nextBlossomEdge.V1;
Vertex b_v2 = current.nextBlossomEdge.V2;
if (GetInnerBlossomContaining(b_v1) != current)
{
Swap(ref b_v1, ref b_v2);
}
current.FlipPathBetween(v1, b_v1);
current.nextBlossomEdge.Flip();
current = GetInnerBlossomContaining(b_v2);
v1 = b_v2;
}
last.FlipPathBetween(v1, v2);
innerChildren = innerChildren.Skip(pos).Concat(innerChildren.Take(pos)).ToList();
}
public void MakeDumbbellWith(Blossom pair, Edge edge)
{
this.treeLevel = TreeLevel.DUMBBELL;
pair.treeLevel = TreeLevel.DUMBBELL;
this.treeParentBlossom = pair;
pair.treeParentBlossom = this;
this.treeParentEdge = edge;
pair.treeParentEdge = edge;
}
public void ConnectToTree(Blossom parent, Edge parentEdge)
{
treeLevel = TreeLevel.ODD;
treeChildren.AddLast(treeParentBlossom);
treeParentBlossom.treeLevel = TreeLevel.EVEN;
treeParentBlossom = parent;
treeParentEdge = parentEdge;
treeParentBlossom.treeChildren.AddLast(this);
}
public Blossom MakeBlossomWith(Blossom pair, Edge pairEdge)
{
LinkedList<Blossom> ourPath = new LinkedList<Blossom>();
LinkedList<Blossom> pairPath = new LinkedList<Blossom>();
ourPath.AddLast(this);
pairPath.AddLast(pair);
while (ourPath.Last.Value.treeParentBlossom != null)
{
ourPath.AddLast(ourPath.Last.Value.treeParentBlossom);
}
while (pairPath.Last.Value.treeParentBlossom != null)
{
pairPath.AddLast(pairPath.Last.Value.treeParentBlossom);
}
Blossom LCA = null;
while (ourPath.Count > 0 && pairPath.Count > 0 && ourPath.Last.Value == pairPath.Last.Value)
{
LCA = ourPath.Last.Value;
ourPath.RemoveLast();
pairPath.RemoveLast();
}
Blossom newBlossom = new Blossom
{
treeParentBlossom = LCA.treeParentBlossom,
treeParentEdge = LCA.treeParentEdge
};
if (newBlossom.treeParentBlossom != null)
{
newBlossom.treeParentBlossom.treeChildren.Remove(LCA);
newBlossom.treeParentBlossom.treeChildren.AddLast(newBlossom);
}
newBlossom.innerChildren.Add(LCA);
Blossom previous = LCA;
foreach (var p in ourPath.Reverse())
{
newBlossom.innerChildren.Add(p);
previous.nextBlossomEdge = p.treeParentEdge;
previous = p;
}
previous.nextBlossomEdge = pairEdge;
foreach (var p in pairPath)
{
newBlossom.innerChildren.Add(p);
p.nextBlossomEdge = p.treeParentEdge;
}
foreach (var inner in newBlossom.innerChildren)
{
inner.outwardBlossom = newBlossom;
}
foreach (var inner in newBlossom.innerChildren)
{
foreach (var child in inner.treeChildren)
{
if (child.outwardBlossom == null)
{
newBlossom.treeChildren.AddLast(child);
child.treeParentBlossom = newBlossom;
}
}
}
newBlossom.outwardBlossom = null;
if (LCA.treeParentEdge == null)
{
return newBlossom;
}
return null;
}
public void DisassembleBlossom()
{
Edge childEdge = treeChildren.First.Value.treeParentEdge;
Blossom parentInner;
if (treeParentEdge.V1.GetOutermostBlossom() == this)
{
parentInner = GetInnerBlossomContaining(treeParentEdge.V1);
}
else
{
parentInner = GetInnerBlossomContaining(treeParentEdge.V2);
}
int pos = innerChildren.FindIndex(c => c == parentInner);
int N = innerChildren.Count;
int start = 0;
int end = pos;
int diff = 1;
int ediff = 0;
int stem = 0;
if (pos % 2 == 1)
{
start = pos;
end = stem = N;
diff = ediff = -1;
}
for (int i = start; i <= end; i++)
{
innerChildren[i % N].treeLevel = (i % 2 == stem % 2) ? TreeLevel.ODD : TreeLevel.EVEN;
innerChildren[i % N].treeParentBlossom = (i == pos) ? treeParentBlossom : innerChildren[i + diff];
innerChildren[i % N].treeParentEdge = (i == pos) ? treeParentEdge : innerChildren[i + ediff].nextBlossomEdge;
innerChildren[i % N].treeChildren.Clear();
innerChildren[i % N].treeChildren.AddLast((i == stem) ? treeChildren.First.Value : innerChildren[(i - diff) % N]);
}
treeParentBlossom.treeChildren.Remove(this);
treeParentBlossom.treeChildren.AddLast(innerChildren[pos]);
treeChildren.First.Value.treeParentBlossom = innerChildren[0];
Blossom thiscopy = innerChildren[0].outwardBlossom;
foreach (var inner in innerChildren)
{
inner.outwardBlossom = null;
}
for (int i = (pos % 2 == 0) ? pos + 1 : 1; (pos % 2 == 0) ? i < N : i < pos; i += 2)
{
innerChildren[i].treeChildren.Clear();
innerChildren[i + 1].treeChildren.Clear();
innerChildren[i].treeParentBlossom = null;
innerChildren[i + 1].treeParentBlossom = null;
innerChildren[i].MakeDumbbellWith(innerChildren[i + 1], innerChildren[i].nextBlossomEdge);
}
}
public virtual double GetMaxNegativeCharge()
{
return Charge;
}
public bool UpdateTree()
{
foreach (var child in treeChildren)
{
if (child.UpdateTree())
{
return true;
}
}
if (GetMaxNegativeCharge() == 0 && TreeLevel == TreeLevel.ODD)
{
DisassembleBlossom();
return true;
}
return false;
}
public virtual void UpdateVertexTotal(double delta)
{
foreach (var inner in innerChildren)
{
inner.UpdateVertexTotal(delta);
}
}
private double charge;
private TreeLevel treeLevel;
private Blossom treeParentBlossom;
private Edge treeParentEdge;
private LinkedList<Blossom> treeChildren = new LinkedList<Blossom>();
private Blossom outwardBlossom;
private List<Blossom> innerChildren = new List<Blossom>();
private Edge nextBlossomEdge;
}
public class Vertex : Blossom
{
public Vertex(int _id) : base()
{
this.id = _id;
this.totalCharge = 0;
}
public double TotalCharge => totalCharge;
public override double GetMaxNegativeCharge()
{
return double.PositiveInfinity;
}
public override void UpdateVertexTotal(double delta)
{
totalCharge += delta;
}
public override Vertex GetStem()
{
return this;
}
public readonly int id;
private double totalCharge;
}
public class Edge
{
public Edge(EdmondsMatching edmondsMatching, Vertex v1, Vertex v2, double weight)
{
this.edmondsMatching = edmondsMatching;
this.v1 = v1;
this.v2 = v2;
this.weight = weight;
this.matched = false;
}
public Vertex V1 => v1;
public Vertex V2 => v2;
public double GetMaxCharge()
{
var outer1 = v1.GetOutermostBlossom();
var outer2 = v2.GetOutermostBlossom();
if (outer1 == outer2)
{
return double.PositiveInfinity;
}
double reserve = weight - v1.TotalCharge - v2.TotalCharge;
if (IsBetweenDumbbells(outer1, outer2))
{
return double.PositiveInfinity;
}
if (IsBetweenEvenAndDumbbell(outer1, outer2))
{
return reserve;
}
if (IsBetweenEvenBlossoms(outer1, outer2))
{
return reserve / 2;
}
reserve = double.PositiveInfinity;
if (outer1.TreeLevel == TreeLevel.ODD)
{
reserve = Math.Min(reserve, outer1.GetMaxNegativeCharge());
}
if (outer2.TreeLevel == TreeLevel.ODD)
{
reserve = Math.Min(reserve, outer2.GetMaxNegativeCharge());
}
return reserve;
}
public bool Update()
{
if (GetMaxCharge() > 0)
{
return false;
}
var outer1 = v1.GetOutermostBlossom();
var outer2 = v2.GetOutermostBlossom();
if (IsBetweenEvenAndDumbbell(outer1, outer2))
{
if (outer1.TreeLevel == TreeLevel.DUMBBELL)
{
outer1.ConnectToTree(outer2, this);
}
else
{
outer2.ConnectToTree(outer1, this);
}
return true;
}
if (IsBetweenEvenBlossoms(outer1, outer2))
{
var root1 = outer1.GetRootBlossom();
var root2 = outer2.GetRootBlossom();
if (root1 == root2)
{
Blossom newRoot = outer1.MakeBlossomWith(outer2, this);
if (newRoot != null)
{
edmondsMatching.RemoveRootFromForest(root1);
edmondsMatching.AddRootToForest(newRoot);
}
}
else
{
outer1.FlipPathAndDisassemble(v1);
outer2.FlipPathAndDisassemble(v2);
edmondsMatching.RemoveRootFromForest(root1);
edmondsMatching.RemoveRootFromForest(root2);
outer1.MakeDumbbellWith(outer2, this);
this.Flip();
edmondsMatching.IncreaseMatchingSize();
}
return true;
}
return true;
}
public void Flip()
{
matched = !matched;
}
public bool IsMatched()
{
return matched;
}
public double GetWeight()
{
return weight;
}
private EdmondsMatching edmondsMatching;
private Vertex v1;
private Vertex v2;
private double weight;
private bool matched;
private bool IsBetweenDumbbells(Blossom outer1, Blossom outer2)
{
return (outer1.TreeLevel == TreeLevel.DUMBBELL && outer2.TreeLevel == TreeLevel.DUMBBELL);
}
private bool IsBetweenEvenBlossoms(Blossom outer1, Blossom outer2)
{
return (outer1.TreeLevel == TreeLevel.EVEN && outer2.TreeLevel == TreeLevel.EVEN);
}
private bool IsBetweenEvenAndDumbbell(Blossom outer1, Blossom outer2)
{
return ((outer1.TreeLevel == TreeLevel.DUMBBELL && outer2.TreeLevel == TreeLevel.EVEN) || (outer1.TreeLevel == TreeLevel.EVEN && outer2.TreeLevel == TreeLevel.DUMBBELL));
}
}
public class EdmondsMatching
{
public EdmondsMatching(int numberOfVertices)
{
this.numberOfVertices = numberOfVertices;
this.matchingSize = 0;
vertices.Capacity = numberOfVertices;
for (int i = 0; i < numberOfVertices; i++)
{
vertices.Add(new Vertex(i));
roots.AddLast(vertices[vertices.Count - 1]);
}
}
public void AddEdge(int v1id, int v2id, double weight)
{
Vertex v1 = vertices[v1id];
Vertex v2 = vertices[v2id];
edges.Add(new Edge(this, v1, v2, weight));
}
public bool FindMinimumWeightMatching()
{
while (true)
{
double min_reserve = double.PositiveInfinity;
foreach (var edge in edges)
{
double edge_reserve = edge.GetMaxCharge();
min_reserve = Math.Min(min_reserve, edge_reserve);
}
foreach (var root in roots)
{
root.UpdateCharge(min_reserve);
}
bool change = false;
while (true)
{
bool round = false;
foreach (var root in roots)
{
if (root.UpdateTree())
{
round = change = true;
break;
}
}
if (round)
{
continue;
}
foreach (var edge in edges)
{
if (edge.Update())
{
round = change = true;
break;
}
}
if (round)
{
continue;
}
break;
}
if (!change && min_reserve == 0)
{
return false;
}
if (matchingSize * 2 == numberOfVertices)
{
return true;
}
if (min_reserve == double.PositiveInfinity)
{
return false;
}
}
}
public void RemoveRootFromForest(Blossom root)
{
roots.Remove(root);
}
public void AddRootToForest(Blossom root)
{
roots.AddLast(root);
}
public void IncreaseMatchingSize()
{
matchingSize += 1;
}
public double GetMatchingWeight()
{
double weight = 0;
foreach (var edge in edges)
{
if (edge.IsMatched())
{
weight += edge.GetWeight();
}
}
return weight;
}
public List<Tuple<int, int>> GetMatchedEdges()
{
return edges.Where(e => e.IsMatched()).Select(e => Tuple.Create(e.V1.id, e.V2.id)).ToList();
}
private int matchingSize;
private int numberOfVertices;
private List<Vertex> vertices = new List<Vertex>();
private List<Edge> edges = new List<Edge>();
private LinkedList<Blossom> roots = new LinkedList<Blossom>();
}
}
public class PriorityQueue<TKey, TValue>
{
SortedDictionary<TKey, Stack<TValue>> dict = new SortedDictionary<TKey, Stack<TValue>>();
int count;
public int Count
{
get
{
return count;
}
}
public void Enqueue(TKey key, TValue value)
{
Stack<TValue> set;
if (!dict.TryGetValue(key, out set))
{
set = new Stack<TValue>();
dict[key] = set;
}
set.Push(value);
count++;
}
public KeyValuePair<TKey, TValue> Dequeue()
{
var queue = dict.First();
if (queue.Value.Count <= 1)
{
dict.Remove(queue.Key);
}
var val = queue.Value.Pop();
count--;
return new KeyValuePair<TKey, TValue>(queue.Key, val);
}
public KeyValuePair<TKey, TValue> Peek()
{
var queue = dict.First();
var val = queue.Value.Peek();
return new KeyValuePair<TKey, TValue>(queue.Key, val);
}
}
public struct Point
{
public int X;
public int Y;
public Point(Point p)
{
X = p.X;
Y = p.Y;
}
public Point(int x, int y)
{
X = x;
Y = y;
}
public static bool operator ==(Point a, Point b)
{
return (a.X == b.X && a.Y == b.Y);
}
public static bool operator !=(Point a, Point b)
{
return !(a == b);
}
//objと自分自身が等価のときはtrueを返す
public override bool Equals(object obj)
{
if (!(obj is Point))
{
return false;
}
Point p = (Point)obj;
return (X == p.X && Y == p.Y);
}
//Equalsがtrueを返すときに同じ値を返す
public override int GetHashCode()
{
return (X << 16) ^ Y;
}
public Point Clone()
{
return new Point(X, Y);
}
public void Reverse()
{
X = -X;
Y = -Y;
}
public static Point operator +(Point a, Point b)
{
return new Point(a.X + b.X, a.Y + b.Y);
}
public static Point operator -(Point a, Point b)
{
return new Point(a.X - b.X, a.Y - b.Y);
}
public static Point operator *(Point a, int i)
{
return new Point(a.X * i, a.Y * i);
}
public static Point operator /(Point a, int i)
{
return new Point(a.X / i, a.Y / i);
}
public static Point operator +(Point a)
{
return new Point(+a.X, +a.Y);
}
public static Point operator -(Point a)
{
return new Point(-a.X, -a.Y);
}
public override string ToString()
{
return string.Format("({0},{1})", X, Y);
}
public string AsAnswer()
{
return string.Format("{0} {1}", X, Y);
}
public int Norm2()
{
return X * X + Y * Y;
}
public int Distance2(Point that)
{
return (that - this).Norm2();
}
}
public struct Edge
{
public readonly int Start;
public readonly int End;
public readonly double Weight;
public Edge(int v0, int v1, double w)
{
Start = v0;
End = v1;
Weight = w;
}
public override string ToString()
{
return $"{Start} {End} {Weight}";
}
}
public class Graph
{
// Prim法により最小全域木を求める
public static List<Edge>[] GetMinSpanningTree(Edge[][] edges, int startVertex = 0)
{
var treeEdges = Enumerable.Range(0, edges.Length).Select(_ => new List<Edge>()).ToArray();
var treeVertex = new HashSet<int>() { startVertex };
var nearEdges = new PriorityQueue<double, Edge>();
foreach (var e in edges[startVertex])
{
nearEdges.Enqueue(e.Weight, e);
}
while (nearEdges.Count > 0)
{
var edge = nearEdges.Dequeue().Value;
if (treeVertex.Contains(edge.End))
{
continue;
}
treeEdges[edge.Start].Add(edge);
treeEdges[edge.End].Add(new Edge(edge.End, edge.Start, edge.Weight));
treeVertex.Add(edge.End);
foreach (var e in edges[edge.End])
{
nearEdges.Enqueue(e.Weight, e);
}
}
return treeEdges;
}
// Edmondsの花分解により最小重み完全マッチングを求める
public static List<Edge> GetMinWeightMatching(Edge[][] edges, IList<int> vertexes)
{
var n = vertexes.Count;
var matching = new Edmonds.EdmondsMatching(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i == j)
{
continue;
}
matching.AddEdge(i, j, edges[vertexes[i]][vertexes[j]].Weight);
}
}
matching.FindMinimumWeightMatching();
var minEdges = matching.GetMatchedEdges();
return minEdges.Select(e => edges[vertexes[e.Item1]][vertexes[e.Item2]]).ToList();
}
// オイラー路を求める graphは消去される
public static List<int> EulerTour(List<Edge>[] graph, int current = 0)
{
var path = new List<int> { current };
if (graph[current].Count == 1)
{
while (graph[current].Count == 1)
{
var next = graph[current].First().End;
graph[current].RemoveAt(0);
graph[next].Remove(graph[next].First(e => e.End == current));
path.Add(next);
current = next;
}
}
if (graph[current].Count > 1)
{
var pathToEnd = new List<int>();
while (graph[current].Count > 0)
{
var next = graph[current].First().End;
graph[current].RemoveAt(0);
graph[next].Remove(graph[next].First(e => e.End == current));
var nextPath = EulerTour(graph, next);
if (nextPath.Last() != current)
{
pathToEnd = nextPath;
}
else
{
path.AddRange(nextPath);
}
}
path.AddRange(pathToEnd);
}
return path;
}
}
public class Solver
{
public Point[] Planets;
public Point[] Stations;
public List<int> Way;
public Stopwatch Sw;
Random Random = new Random();
public Solver(Point[] planets, Stopwatch sw)
{
Planets = planets;
Stations = new Point[M];
Sw = sw;
}
Point GetPoint(int id)
{
if (id < N)
{
return Planets[id];
}
return Stations[id - N];
}
long[,] Cost;
void InitCost()
{
Cost = new long[N + M, N + M];
for (int i = 0; i < N + M; i++)
{
for (int j = i + 1; j < N + M; j++)
{
var c = CalcCost(i, j);
Cost[i, j] = Cost[j, i] = c;
}
}
}
long CalcCost(int start, int goal)
{
var cost = GetPoint(start).Distance2(GetPoint(goal));
if (start < N)
{
cost *= Alpha;
}
if (goal < N)
{
cost *= Alpha;
}
return cost;
}
(long[] distance, int[] prev) Dijkstra(int start)
{
var d = new long[N + M];
Array.Fill(d, long.MaxValue);
var prev = new int[N + M];
d[start] = 0;
var q = new PriorityQueue<long, int>();
q.Enqueue(0, start);
while (q.Count > 0)
{
var t = q.Dequeue();
var u = t.Value;
if (t.Key > d[u])
{
continue;
}
for (int v = 0; v < N + M; v++)
{
if (u == v)
{
continue;
}
var len = Cost[u, v];
if (len == int.MaxValue)
{
continue;
}
if (d[v] > d[u] + len)
{
d[v] = d[u] + len;
q.Enqueue(d[v], v);
prev[v] = u;
}
}
}
return (d, prev);
}
(long[][] distance, int[][] prevs) CalcAllDistance()
{
var distance = new long[N + M][];
var prevs = new int[N + M][];
for (int i = 0; i < N + M; i++)
{
(distance[i], prevs[i]) = Dijkstra(i);
}
return (distance, prevs);
}
void InitStations()
{
var bestSocre = double.MaxValue;
for (int i = 0; i < 10; i++)
{
(var stations, var score) = GenerateStations();
if (score < bestSocre)
{
bestSocre = score;
Stations = stations;
}
}
}
(Point[], double) GenerateStations()
{
// k-means
var clusters = Enumerable.Range(0, M).Select(_ => new List<int>()).ToArray();
for (int i = 0; i < N; i++)
{
clusters[Random.Next(M)].Add(i);
}
var update = true;
PointD[] means = null;
double score = 0;
while (update && Sw.ElapsedMilliseconds < 100)
{
score = 0;
means = clusters.Select(c => c.Select(i => Planets[i]).Average2()).ToArray();
for (int i = 0; i < M; i++)
{
if (means[i].X < 0)
{
means[i] = new PointD(Planets[Random.Next(N)]);
}
}
var nextClusters = Enumerable.Range(0, M).Select(_ => new List<int>()).ToArray();
for (int i = 0; i < N; i++)
{
var p = Planets[i];
var nearest = Enumerable.Range(0, M).OrderBy(m => means[m].Distance2(p)).First();
score += means[nearest].Distance2(p);
nextClusters[nearest].Add(i);
}
update = false;
for (int i = 0; i < M; i++)
{
if (!clusters[i].SequenceEqual(nextClusters[i]))
{
update = true;
break;
}
}
if (!update)
{
break;
}
clusters = nextClusters;
}
return (means.Select(p => p.Round()).ToArray(), score);
}
public void SolveByNearestNeighbor()
{
InitStations();
InitCost();
var distance = new long[N + M][];
var prevs = new int[N + M][];
var remain = Enumerable.Range(1, N + M - 1).ToList();
var path = new List<int>() { 0 };
while (remain.Count > 0)
{
var last = path.Last();
(var d, var prev) = Dijkstra(last);
var min = remain.OrderBy(i => d[i]).First();
var way = new Stack<int>();
for (int i = min; i != last; i = prev[i])
{
way.Push(i);
}
foreach (var i in way)
{
path.Add(i);
}
remain.Remove(min);
}
{
var last = path.Last();
(var d, var prev) = Dijkstra(last);
var way = new Stack<int>();
for (int i = 0; i != last; i = prev[i])
{
way.Push(i);
}
foreach (var i in way)
{
path.Add(i);
}
}
Way = path;
}
public void Solve()
{
InitStations();
InitCost();
(var distance, var prevs) = CalcAllDistance();
var edges = Enumerable.Range(0, N).Select(_ => new Edge[N]).ToArray();
for (int i = 0; i < N; i++)
{
for (int j = i + 1; j < N; j++)
{
var d = distance[i][j];
edges[i][j] = new Edge(i, j, d);
edges[j][i] = new Edge(j, i, d);
}
}
var mst = Graph.GetMinSpanningTree(edges);
var oddVertexes = Enumerable.Range(0, edges.Length).Where(i => mst[i].Count % 2 == 1).ToList();
var minMatches = Graph.GetMinWeightMatching(edges, oddVertexes);
var graph = mst;
foreach (var e in minMatches)
{
graph[e.Start].Add(e);
graph[e.End].Add(new Edge(e.End, e.Start, e.Weight));
}
var eulerCycle = Graph.EulerTour(graph);
Optimize(edges, ref eulerCycle);
var path = new List<int>() { 0 };
for (int t = 0; t < eulerCycle.Count - 1; t++)
{
var u = eulerCycle[t];
var v = eulerCycle[t + 1];
var way = new Stack<int>();
for (int i = v; i != u; i = prevs[u][i])
{
way.Push(i);
}
foreach (var i in way)
{
path.Add(i);
}
}
Way = path;
}
public void Optimize(Edge[][] edges, ref List<int> path)
{
const int limit = 900;
long lap = 300;
var update = true;
while (update)
{
if (Sw.ElapsedMilliseconds + lap > limit)
{
break;
}
update = TwoOpt(edges, ref path);
//update |= ThreeOpt(edges, ref path);
}
}
public static bool TwoOpt(Edge[][] edges, ref List<int> path)
{
bool result = false;
var ps = path;
Func<int, int, double> distance = (s, e) =>
{
return edges[ps[s]][ps[e]].Weight;
};
var n = path.Count;
bool updated = true;
while (updated)
{
updated = false;
for (int i = 0; i < n - 2; i++)
{
for (int j = i + 2; j < n - 1; j++)
{
if (distance(i, i + 1) + distance(j, j + 1) > distance(i, j) + distance(i + 1, j + 1))
{
// i+1 <= x <= j を逆順にする
var a = ps.Take(i + 1);
var b = ps.Skip(i + 1).Take(j - i).Reverse();
var c = ps.Skip(j + 1);
ps = a.Concat(b).Concat(c).ToList();
updated = true;
result = true;
}
}
}
}
path = ps;
return result;
}
public static bool ThreeOpt(Edge[][] edges, ref List<int> path)
{
bool result = false;
var ps = path;
Func<int, int, double> distance = (s, e) =>
{
return edges[ps[s]][ps[e]].Weight;
};
var n = path.Count;
start:
for (int i = 0; i < n - 3; i++)
{
for (int j = i + 1; j < n - 2; j++)
{
for (int k = j + 1; k < n - 1; k++)
{
var d = new double[5];
d[0] = distance(i, i + 1) + distance(j, j + 1) + distance(k, k + 1); // original
d[1] = distance(i, j) + distance(i + 1, k) + distance(j + 1, k + 1);
d[2] = distance(i, j + 1) + distance(k, j) + distance(i + 1, k + 1);
d[3] = distance(i, j + 1) + distance(k, i + 1) + distance(j, k + 1);
d[4] = distance(i, k) + distance(j + 1, i + 1) + distance(j, k + 1);
var min = d.Min();
var minCase = Array.IndexOf(d, min);
if (minCase == 0)
{
continue;
}
switch (minCase)
{
case 1:
ps = ps.Take(i + 1).Concat(ps.Take(j + 1).Skip(i + 1).Reverse()).Concat(ps.Take(k + 1).Skip(j + 1).Reverse()).Concat(ps.Skip(k + 1)).ToList();
break;
case 2:
ps = ps.Take(i + 1).Concat(ps.Take(k + 1).Skip(j + 1)).Concat(ps.Take(j + 1).Skip(i + 1).Reverse()).Concat(ps.Skip(k + 1)).ToList();
break;
case 3:
ps = ps.Take(i + 1).Concat(ps.Take(k + 1).Skip(j + 1)).Concat(ps.Take(j + 1).Skip(i + 1)).Concat(ps.Skip(k + 1)).ToList();
break;
case 4:
ps = ps.Take(i + 1).Concat(ps.Take(k + 1).Skip(j + 1).Reverse()).Concat(ps.Take(j + 1).Skip(i + 1)).Concat(ps.Skip(k + 1)).ToList();
break;
}
result = true;
goto start;
}
}
}
path = ps;
return result;
}
public string GetAnswer()
{
var buff = new StringBuilder();
foreach (var p in Stations)
{
buff.AppendLine(p.AsAnswer());
}
buff.AppendLine(Way.Count.ToString());
foreach (var i in Way)
{
var type = i < N ? TypePlanet : TypeStation;
var index = (i < N ? i : i - N) + 1;
buff.AppendLine($"{type} {index}");
}
return buff.ToString();
}
}
public static class Solution
{
public static void Main()
{
var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
var points = new Point[N];
for (int i = 0; i < N; i++)
{
vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
points[i] = new Point(vals[0], vals[1]);
}
var sw = Stopwatch.StartNew();
var solver = new Solver(points, sw);
solver.Solve();
Console.Write(solver.GetAnswer());
}
}