結果
| 問題 | No.1340 おーじ君をさがせ |
| コンテスト | |
| ユーザー |
 nauclhlt
|
| 提出日時 | 2026-05-14 20:41:43 |
| 言語 | C# (.NET 10.0.201) |
| 結果 |
AC
|
| 実行時間 | 486 ms / 2,000 ms |
| コード長 | 56,223 bytes |
| 記録 | |
| コンパイル時間 | 12,020 ms |
| コンパイル使用メモリ | 172,068 KB |
| 実行使用メモリ | 213,244 KB |
| 最終ジャッジ日時 | 2026-05-14 20:42:05 |
| 合計ジャッジ時間 | 22,209 ms |
|
ジャッジサーバーID （参考情報） |
judge2_1 / judge1_1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 59 |
コンパイルメッセージ
復元対象のプロジェクトを決定しています... /home/judge/data/code/main.csproj を復元しました (95 ミリ秒)。 main -> /home/judge/data/code/bin/Release/net10.0/main.dll main -> /home/judge/data/code/bin/Release/net10.0/publish/
ソースコード
using System.ComponentModel;
using System.Diagnostics.CodeAnalysis;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Collections;
using System.Text;
using System.Text.RegularExpressions;
using static Tmpl;
using static CPDebug;
using System.Collections.Specialized;
using System.Globalization;
using System.Diagnostics;
StreamWriter writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
//using StreamWriter writer = new StreamWriter(File.Open("turn.txt", FileMode.Create, FileAccess.ReadWrite));
Console.SetOut(writer);
//using StreamReader reader = new StreamReader(File.Open("in.txt", FileMode.Open));
//Console.SetIn(reader);
Solver.Solve();
Console.Out.Flush();
public static class Solver
{
private static readonly CPIO cin = new CPIO();
public static unsafe void Solve()
{
int N = cin.Int();
int M = cin.Int();
long T = cin.Long();
SquareMatrix<MP> mat = SquareMatrix<MP>.Zero(N);
for (int i = 0; i < M; i++)
{
int a = cin.Int();
int b = cin.Int();
mat[b, a] = new(1);
}
SquareMatrix<MP> power = mat.Power(T);
int ans = 0;
for (int i = 0; i < N; i++)
{
if (power[i, 0].Value == 1) ans++;
}
print(ans);
}
}
public struct MP : IAdditionOperators<MP, MP, MP>, IMultiplyOperators<MP, MP, MP>, IAdditiveIdentity<MP, MP>, IMultiplicativeIdentity<MP, MP>, IEqualityOperators<MP, MP, bool>
{
public static MP AdditiveIdentity => new(0);
public static MP MultiplicativeIdentity => new(1);
public long Value;
public MP(long v)
{
Value = v;
}
public static MP operator +(MP a, MP b)
{
return new(a.Value | b.Value);
}
public static MP operator *(MP a, MP b)
{
return new MP(a.Value & b.Value);
}
public static bool operator ==(MP a, MP b) => a.Value == b.Value;
public static bool operator !=(MP a, MP b) => a.Value != b.Value;
public override bool Equals([NotNullWhen(true)] object obj)
{
if (obj is MP m) return this == m;
else return false;
}
public override int GetHashCode()
{
return base.GetHashCode();
}
public override string ToString()
{
return Value.ToString();
}
}
public sealed class SquareMatrix<T> : IEquatable<SquareMatrix<T>>
where T :
IAdditionOperators<T, T, T>,
IMultiplyOperators<T, T, T>,
IAdditiveIdentity<T, T>,
IMultiplicativeIdentity<T, T>,
IEqualityOperators<T, T, bool>
{
private T[,] _m;
private int _size;
public T this[int r, int c]
{
get
{
return _m[r, c];
}
set
{
_m[r, c] = value;
}
}
public T[,] M => _m;
public int Size => _size;
private SquareMatrix(int size)
{
if (size <= 0)
{
throw new InvalidOperationException();
}
_size = size;
_m = new T[size, size];
}
public static SquareMatrix<T> operator +(SquareMatrix<T> left, SquareMatrix<T> right)
{
if (left.Size != right.Size)
{
throw new InvalidOperationException();
}
SquareMatrix<T> dest = Zero(left.Size);
for (int r = 0; r < left.Size; r++)
{
for (int c = 0; c < left.Size; c++)
{
dest[r, c] = left[r, c] + right[r, c];
}
}
return dest;
}
public static SquareMatrix<T> operator *(SquareMatrix<T> left, SquareMatrix<T> right)
{
if (left.Size != right.Size)
{
throw new InvalidOperationException();
}
SquareMatrix<T> result = Zero(left.Size);
for (int r = 0; r < result.Size; r++)
{
for (int c = 0; c < result.Size; c++)
{
for (int i = 0; i < result.Size; i++)
{
result[r, c] += right[i, c] * left[r, i];
}
}
}
return result;
}
public SquareMatrix<T> Power(long exp)
{
if (exp == 0) return Identity(_size);
if (exp == 1) return this;
SquareMatrix<T> half = Power(exp / 2);
SquareMatrix<T> res = half * half;
if (exp % 2 == 1) res *= this;
return res;
}
public SquareMatrix<T> Transpose()
{
SquareMatrix<T> result = new(_size);
for (int i = 0; i < _size; i++)
{
for (int j = 0; j < _size; j++)
{
result[j, i] = this[i, j];
}
}
return result;
}
public static SquareMatrix<T> Zero(int size)
{
SquareMatrix<T> result = new SquareMatrix<T>(size);
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
result[i, j] = T.AdditiveIdentity;
}
}
return result;
}
public static SquareMatrix<T> Identity(int size)
{
SquareMatrix<T> result = new SquareMatrix<T>(size);
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
if (i == j) result[i, j] = T.MultiplicativeIdentity;
else result[i, j] = T.AdditiveIdentity;
}
}
return result;
}
public bool Equals(SquareMatrix<T> other)
{
if (_size != other.Size) return false;
for (int i = 0; i < _size; i++)
{
for (int j = 0; j < _size; j++)
{
if (this[i, j] != other[i, j]) return false;
}
}
return true;
}
public override bool Equals(object obj)
{
if (obj is SquareMatrix<T> mat)
{
return Equals(mat);
}
else
return false;
}
public override int GetHashCode()
{
return base.GetHashCode();
}
public static bool operator ==(SquareMatrix<T> a, SquareMatrix<T> b) => a.Equals(b);
public static bool operator !=(SquareMatrix<T> a, SquareMatrix<T> b) => !a.Equals(b);
public override string ToString()
{
int[] maxwidths = new int[_size];
for (int i = 0; i < _size; i++)
{
for (int j = 0; j < _size; j++)
{
maxwidths[j] = int.Max(maxwidths[j], _m[i, j].ToString().Length);
}
}
StringBuilder sb = new();
for (int i = 0; i < _size; i++)
{
sb.Append('|');
sb.Append(' ');
for (int j = 0; j < _size; j++)
{
sb.Append(_m[i, j].ToString().PadRight(maxwidths[j], ' '));
if (j < _size - 1) sb.Append(' ');
}
sb.Append(' ');
sb.Append('|');
if (i < _size - 1)
sb.Append(Environment.NewLine);
}
return sb.ToString();
}
}
public readonly struct Point
{
public readonly int X;
public readonly int Y;
public Point(int x, int y)
{
X = x;
Y = y;
}
public override int GetHashCode() => (X, Y).GetHashCode();
public override string ToString()
{
return $"({X}, {Y})";
}
}
public sealed class ReverseComparer<T> : IComparer<T>
{
public static readonly ReverseComparer<T> Default = new ReverseComparer<T>(Comparer<T>.Default);
public static ReverseComparer<T> Reverse(IComparer<T> comparer)
{
return new ReverseComparer<T>(comparer);
}
private readonly IComparer<T> comparer = Default;
private ReverseComparer(IComparer<T> comparer)
{
this.comparer = comparer;
}
public int Compare(T x, T y)
{
return comparer.Compare(y, x);
}
}
/// <summary>
/// Standard input reader for competitive programming.
/// </summary>
public sealed class CPIO
{
Queue<string> _readQueue = new Queue<string>();
static CPIO()
{
// faster standard output
StreamWriter writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
Console.SetOut(writer);
}
private void LoadQueue()
{
if (_readQueue.Count > 0) return;
string line = Console.ReadLine();
string[] split = line.Split(' ', StringSplitOptions.RemoveEmptyEntries);
for (int i = 0; i < split.Length; i++) _readQueue.Enqueue(split[i]);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private void Guard()
{
if (_readQueue.Count == 0)
{
throw new Exception("Standard input queue was empty.");
}
}
public int Int()
{
LoadQueue();
Guard();
return int.Parse(_readQueue.Dequeue());
}
public long Long()
{
LoadQueue();
Guard();
return long.Parse(_readQueue.Dequeue());
}
public string String()
{
LoadQueue();
Guard();
return _readQueue.Dequeue();
}
public short Short()
{
LoadQueue();
Guard();
return short.Parse(_readQueue.Dequeue());
}
public byte Byte()
{
LoadQueue();
Guard();
return byte.Parse(_readQueue.Dequeue());
}
public char Char()
{
LoadQueue();
Guard();
return char.Parse(_readQueue.Dequeue());
}
public double Double()
{
LoadQueue();
Guard();
return double.Parse(_readQueue.Dequeue());
}
public float Float()
{
LoadQueue();
Guard();
return float.Parse(_readQueue.Dequeue());
}
public T Read<T>()
{
Type type = typeof(T);
if (type == typeof(int)) return (T)(object)Int();
else if (type == typeof(long)) return (T)(object)Long();
else if (type == typeof(float)) return (T)(object)Float();
else if (type == typeof(double)) return (T)(object)Double();
else if (type == typeof(short)) return (T)(object)Short();
else if (type == typeof(byte)) return (T)(object)Byte();
else if (type == typeof(char)) return (T)(object)Char();
else if (type == typeof(string)) return (T)(object)String();
else return default(T);
}
public int[] IntArray(int n)
{
if (n == 0) return Array.Empty<int>();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
{
arr[i] = Int();
}
return arr;
}
public int[] ZeroIndexedPermutation(int n)
{
if (n == 0) return Array.Empty<int>();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
{
arr[i] = Int() - 1;
}
return arr;
}
public long[] LongArray(int n)
{
if (n == 0) return Array.Empty<long>();
long[] arr = new long[n];
for (int i = 0; i < n; i++)
{
arr[i] = Long();
}
return arr;
}
public double[] DoubleArray(int n)
{
if (n == 0) return Array.Empty<double>();
double[] arr = new double[n];
for (int i = 0; i < n; i++)
{
arr[i] = Double();
}
return arr;
}
public string[] StringArray(int n)
{
if (n == 0) return Array.Empty<string>();
string[] arr = new string[n];
for (int i = 0; i < n; i++)
{
arr[i] = String();
}
return arr;
}
public T[] ReadArray<T>(int n)
{
if (n == 0) return Array.Empty<T>();
T[] arr = new T[n];
for (int i = 0; i < n; i++)
{
arr[i] = Read<T>();
}
return arr;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void YesNo(bool t)
{
Console.WriteLine(t ? "Yes" : "No");
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Print<T>(IEnumerable<T> array, char delimiter = ' ')
{
Console.WriteLine(string.Join(delimiter, array));
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Print(string value) => Console.WriteLine(value);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Print(int value) => Console.WriteLine(value);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Print(long value) => Console.WriteLine(value);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Print(double value, int digits = 10) => Console.WriteLine(Math.Round(value, digits).ToString());
}
public static class CPDebug
{
public static void check<T>(T value, [CallerArgumentExpression(nameof(value))] string name = "value") where T : struct
{
#if DEBUG
Console.Error.WriteLine($"[DEBUG] {name}={value.ToString()}");
#endif
}
public static void check<T>(IEnumerable<T> value, [CallerArgumentExpression(nameof(value))] string name = "value")
{
#if DEBUG
Console.Error.WriteLine($"[DEBUG] {name}=({string.Join(' ', value)})");
#endif
}
}
public static class Tmpl
{
public static long pow(long b, long exp)
{
if (exp == 0) return 1;
if (exp == 1) return b;
long m = pow(b, exp / 2L);
m *= m;
if (exp % 2L == 1) m *= b;
return m;
}
public static long modpow(long b, long exp, long mod)
{
if (exp == 0) return 1;
if (exp == 1) return b % mod;
long m = modpow(b, exp / 2L, mod);
m *= m;
m %= mod;
if (exp % 2L == 1) m *= b % mod;
m %= mod;
return m;
}
static long modinv( long a, long mod )
{
long b = mod, u = 1, v = 0;
while ( b > 0 )
{
long t = a / b;
a -= t * b; swap( ref a, ref b );
u -= t * v; swap( ref u, ref v );
}
u %= mod;
if (u < 0) u += mod;
return u;
}
public static long calcLcm(long a, long b)
{
return a * b / calcGcd(a, b);
}
public static long calcGcd(long a, long b)
{
if (a % b == 0) return b;
return calcGcd(b, a % b);
}
// ax ≡ b (mod m)なる最小のxを求める
public static bool solveModLinear(long a, long b, long m, out long minSolution)
{
long gcd = calcGcd(calcGcd(a, b), m);
a /= gcd;
b /= gcd;
m /= gcd;
if (calcGcd(a, m) == 1)
{
long inv = modinv(a, m);
minSolution = (b * inv) % m;
return true;
}
minSolution = 0;
return false;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void YesNo(bool t)
{
Console.WriteLine(t ? "Yes" : "No");
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void YESNO(bool t)
{
Console.WriteLine(t ? "YES" : "NO");
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void yesno(bool t)
{
Console.WriteLine(t ? "yes" : "no");
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool checkBit(int bit, int n)
{
return ((1 << n) & bit) != 0;
}
public static bool nextSubset(ref int set, int super)
{
set = (set - 1) & super;
return set != 0;
}
public static bool nextCombination(int n, int r, int[] array)
{
int i = array.Length - 1;
while (i >= 0 && array[i] == i + n - r)
{
i--;
}
if (i < 0) return false;
array[i]++;
for (int j = i + 1; j < r; j++)
{
array[j] = array[j - 1] + 1;
}
return true;
}
public static bool nextPermutation<T>(T[] array, int start, int length) where T : IComparable<T>
{
int end = start + length - 1;
if (end <= start) return false;
int last = end;
while (true)
{
int pos = last--;
if (array[last].CompareTo(array[pos]) < 0)
{
int i;
for (i = end + 1; array[last].CompareTo(array[--i]) >= 0; ) { }
T tmp = array[last]; array[last] = array[i]; array[i] = tmp;
Array.Reverse(array, pos, end - pos + 1);
return true;
}
if (last == start)
{
Array.Reverse(array, start, end - start);
return false;
}
}
throw new Exception("NextPermutation: Fatal error");
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool chmax<T> (ref T target, T value) where T : struct, IComparisonOperators<T, T, bool>
{
if (value > target)
{
target = value;
return true;
}
return false;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool chmin<T>(ref T target, T value) where T : struct, IComparisonOperators<T, T, bool>
{
if (value < target)
{
target = value;
return true;
}
return false;
}
public static ReadOnlySpan<T> spanOf<T>(List<T> list)
{
return CollectionsMarshal.AsSpan(list);
}
public static int lowerBound<T>(T[] array, int start, int end, T value) where T : struct, IComparisonOperators<T, T, bool>
{
int low = start;
int high = end;
int mid;
while (low < high)
{
mid = ((high - low) >> 1) + low;
if (array[mid] < value)
low = mid + 1;
else
high = mid;
}
if (low == array.Length - 1 && array[low] < value)
{
return array.Length;
}
return low;
}
public static int lowerBound<T>(List<T> array, int start, int end, T value) where T : struct, IComparisonOperators<T, T, bool>
{
int low = start;
int high = end;
int mid;
while (low < high)
{
mid = ((high - low) >> 1) + low;
if (array[mid] < value)
low = mid + 1;
else
high = mid;
}
if (low == array.Count - 1 && array[low] < value)
{
return array.Count;
}
return low;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void swap<T>(ref T a, ref T b) where T : struct
{
T temp = a;
a = b;
b = temp;
}
public static int[] compressCoords<T>(T[] a) where T : struct, IComparisonOperators<T, T, bool>
{
T[] b = a.OrderBy(x => x).Distinct().ToArray();
int[] result = new int[a.Length];
for (int i = 0; i < a.Length; i++)
{
result[i] = lowerBound(b, 0, b.Length - 1, a[i]);
}
return result;
}
public static List<RunLengthElement<T>> compressRunLength<T>(T[] array) where T : struct, IEquatable<T>
{
List<RunLengthElement<T>> list = new List<RunLengthElement<T>>();
int count = 1;
int start = 0;
T prev = array[0];
for (int i = 1; i < array.Length; i++)
{
if (prev.Equals(array[i]))
{
count++;
}
else
{
list.Add(new RunLengthElement<T>(start, count, prev));
start = i;
count = 1;
}
prev = array[i];
}
list.Add(new RunLengthElement<T>(start, count, prev));
return list;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void print<T>(IEnumerable<T> array, char delimiter = ' ')
{
Console.WriteLine(string.Join(delimiter, array));
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void fprint<T>(IEnumerable<T> array, char delimiter = ' ')
{
print(array);
Console.Out.Flush();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void print(string msg)
{
Console.WriteLine(msg);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void fprint(string msg)
{
Console.WriteLine(msg);
Console.Out.Flush();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void print(int val)
{
print(val.ToString());
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void print(long val)
{
print(val.ToString());
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void print<T>(ModInt<T> val) where T : struct, IMod
{
print(val.ToString());
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void fprint(int val)
{
print(val.ToString());
Console.Out.Flush();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void fprint(long val)
{
print(val.ToString());
Console.Out.Flush();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void fprint<T>(ModInt<T> val) where T : struct, IMod
{
fprint(val.ToString());
Console.Out.Flush();
}
public static void print<T>(T[,] grid)
{
for (int y = 0; y < grid.GetLength(0); y++)
{
for (int x = 0; x < grid.GetLength(1); x++)
{
Console.Write(grid[y, x] + "\t");
}
Console.WriteLine();
}
}
public static void print01(bool t)
{
Console.WriteLine(t ? "1" : "0");
}
public static TSrc lowerBoundKth<TSrc, TCnt>(TSrc min, TSrc max, Func<TSrc, TCnt> f, TCnt bound)
where TSrc: struct, INumber<TSrc> where TCnt: struct, INumber<TCnt>
{
TSrc left = min;
TSrc right = max;
TSrc two = TSrc.CreateChecked(2);
TSrc one = TSrc.CreateChecked(1);
while (right > left)
{
TSrc mid = left + (right - left) / two;
TCnt c = f(mid);
if (c < bound)
{
left = mid + one;
}
else
{
right = mid;
}
}
return left;
}
public static bool isSquareNumber(long n)
{
long q = (long)Math.Floor(Math.Sqrt(n));
return q * q == n;
}
public static T[][] makeDPTable2D<T>(int length1, int length2, T value)
{
bool fill = !default(T).Equals(value);
T[][] table = new T[length1][];
for (int i = 0; i < length1; i++)
{
table[i] = new T[length2];
if (fill)
{
Array.Fill(table[i], value);
}
}
return table;
}
public static T[][][] makeDPTable3D<T>(int length1, int length2, int length3, T value)
{
bool fill = !default(T).Equals(value);
T[][][] table = new T[length1][][];
for (int i = 0; i < length1; i++)
{
table[i] = new T[length2][];
for (int j = 0; j < length2; j++)
{
table[i][j] = new T[length3];
if (fill)
{
Array.Fill(table[i][j], value);
}
}
}
return table;
}
}
public readonly struct RunLengthElement<T> where T : struct
{
public readonly int Count;
public readonly int StartIndex;
public readonly T Value;
public RunLengthElement(int startIndex, int count, T value)
{
this.StartIndex = startIndex;
this.Count = count;
this.Value = value;
}
}
public readonly struct Edge<T> : IEquatable<Edge<T>>, IComparable<Edge<T>> where T : struct, INumber<T>
{
public readonly int To;
public readonly int From;
public readonly T Weight;
public Edge(int to, T weight)
{
this.To = to;
this.Weight = weight;
}
public Edge(int from, int to, T weight)
{
this.To = to;
this.From = from;
this.Weight = weight;
}
public override bool Equals(object obj)
{
if (obj is Edge<T> edge)
{
return this.Equals(edge);
}
else
{
return false;
}
}
public int CompareTo(Edge<T> other)
{
return Weight.CompareTo(other.Weight);
}
public bool Equals(Edge<T> edge)
{
return To == edge.To && From == edge.From && Weight == edge.Weight;
}
public override int GetHashCode()
{
return (To, From, Weight).GetHashCode();
}
public static bool operator ==(Edge<T> left, Edge<T> right)
{
return left.Equals(right);
}
public static bool operator !=(Edge<T> left, Edge<T> right)
{
return !left.Equals(right);
}
}
/// <summary>
/// Integer on F_p. (p: prime)
/// </summary>
/// <typeparam name="T">Modulus.</typeparam>
public readonly struct ModInt<T> : INumber<ModInt<T>>, IMinMaxValue<ModInt<T>>
where T : struct, IMod
{
public static long Mod => default(T).Mod;
public readonly uint Value;
public long ValueLong => Value;
/// <summary>
/// Returns 1. Time complexity is O(1).
/// </summary>
public static ModInt<T> One { get; } = CreateFast(1);
/// <summary>
/// Returns 0. Time complexity is O(1).
/// </summary>
public static ModInt<T> Zero { get; } = CreateFast(0);
public static int Radix => 10;
public static ModInt<T> MinValue => CreateFast(0);
public static ModInt<T> MaxValue => CreateFast(default(T).Mod - 1);
/// <summary>
/// Returns the additive identity, 0. Time complexity is O(1).
/// </summary>
public static ModInt<T> AdditiveIdentity { get; } = CreateFast(0);
/// <summary>
/// Returns the multiplicative identity, 1. Time complexity is O(1).
/// </summary>
public static ModInt<T> MultiplicativeIdentity { get; } = CreateFast(1);
public ModInt(long value)
{
value %= default(T).Mod;
if (value < 0) value += default(T).Mod;
Value = (uint)value;
}
public ModInt(uint value)
{
value %= default(T).Mod;
Value = value;
}
private ModInt(uint value, bool dummy)
{
Value = value;
}
/// <summary>
/// Constructs the modint with the value. Can only be used when 0 <= value < MOD. Maybe slightly faster than implicit cast. Time complexity is O(1).
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ModInt<T> CreateFast(uint value)
{
return new ModInt<T>(value, false);
}
/// <summary>
/// Calculates the power to e. Time complexity is O(loge)
/// </summary>
public readonly ModInt<T> Power(long e)
{
if (e < 0)
{
return Power(-e).Inv();
}
else
{
ulong res = 1;
ulong b = Value;
while (e > 0)
{
if ((e & 1) == 1) res = res * b % default(T).Mod;
b = b * b % default(T).Mod;
e >>= 1;
}
return CreateFast((uint)res);
}
}
/// <summary>
/// Returns the inverse. Do not call this function when 0. Time complexity is O(logp).
/// Reference: https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a
/// </summary>
public readonly ModInt<T> Inv()
{
long x = 1, y = 0;
long x1 = 0, y1 = 1;
long b = default(T).Mod;
long a = Value;
while (b != 0)
{
long q = a / b;
long t = a % b;
a = b;
b = t;
long tx = x - q * x1;
long ty = y - q * y1;
x = x1;
y = y1;
x1 = tx;
y1 = ty;
}
return new(x);
}
[MethodImpl(256)]
public static ModInt<T> operator +(ModInt<T> left, ModInt<T> right) => CreateFast((left.Value + right.Value) % default(T).Mod);
[MethodImpl(256)]
public static ModInt<T> operator +(ModInt<T> self) => self;
[MethodImpl(256)]
public static ModInt<T> operator -(ModInt<T> left, ModInt<T> right) => CreateFast(left.Value >= right.Value ? left.Value - right.Value : (left.Value + default(T).Mod) - right.Value);
[MethodImpl(256)]
public static ModInt<T> operator -(ModInt<T> self) => CreateFast(default(T).Mod - self.Value);
[MethodImpl(256)]
public static ModInt<T> operator *(ModInt<T> left, ModInt<T> right) => CreateFast((uint)((ulong)left.Value * right.Value % default(T).Mod));
[MethodImpl(256)]
public static ModInt<T> operator /(ModInt<T> left, ModInt<T> right)
{
if (right.Value == 0)
{
throw new DivideByZeroException();
}
ModInt<T> inv = right.Inv();
return left * inv;
}
public static ModInt<T> operator %(ModInt<T> left, ModInt<T> right)
{
throw new NotImplementedException();
}
public static bool operator <(ModInt<T> left, ModInt<T> right) => left.Value < right.Value;
public static bool operator >(ModInt<T> left, ModInt<T> right) => left.Value > right.Value;
public static bool operator <=(ModInt<T> left, ModInt<T> right) => left.Value <= right.Value;
public static bool operator >=(ModInt<T> left, ModInt<T> right) => left.Value >= right.Value;
[MethodImpl(256)]
public static bool operator ==(ModInt<T> left, ModInt<T> right) => left.Value == right.Value;
[MethodImpl(256)]
public static bool operator !=(ModInt<T> left, ModInt<T> right) => !(left == right);
[MethodImpl(256)]
public static ModInt<T> operator ++(ModInt<T> self) => CreateFast((self.Value + 1) % default(T).Mod);
[MethodImpl(256)]
public static ModInt<T> operator --(ModInt<T> self) => CreateFast((self.Value + default(T).Mod - 1) % default(T).Mod);
[MethodImpl(256)]
public bool Equals(ModInt<T> other) => Value == other.Value;
[MethodImpl(256)]
public override bool Equals(object other)
{
if (other is ModInt<T> m)
{
return this == m;
}
else return false;
}
[MethodImpl(256)]
public override int GetHashCode() => Value.GetHashCode();
[MethodImpl(256)]
public static implicit operator ModInt<T>(long v) => new(v);
[MethodImpl(256)]
public static implicit operator ModInt<T>(int v) => new(v);
public override string ToString() => Value.ToString();
public string ToString(string format, IFormatProvider provider) => Value.ToString(format, provider);
#region INumberBase<TSelf> Implementation
public static ModInt<T> Abs(ModInt<T> value) => value;
public static bool IsCanonical(ModInt<T> value) => true;
public static bool IsComplexNumber(ModInt<T> value) => false;
public static bool IsFinite(ModInt<T> value) => true;
public static bool IsImaginaryNumber(ModInt<T> value) => false;
public static bool IsInfinity(ModInt<T> value) => false;
public static bool IsInteger(ModInt<T> value) => true;
public static bool IsNaN(ModInt<T> value) => false;
public static bool IsNegative(ModInt<T> value) => false;
public static bool IsPositive(ModInt<T> value) => value.Value != 0;
public static bool IsRealNumber(ModInt<T> value) => true;
public static bool IsZero(ModInt<T> value) => value.Value == 0;
public static bool IsEvenInteger(ModInt<T> value) => (value.Value & 1) == 0;
public static bool IsOddInteger(ModInt<T> value) => (value.Value & 1) == 1;
public static bool IsPositiveInfinity(ModInt<T> value) => false;
public static bool IsNegativeInfinity(ModInt<T> value) => false;
public static bool IsNormal(ModInt<T> value) => false;
public static bool IsSubnormal(ModInt<T> value) => false;
public static ModInt<T> MaxMagnitude(ModInt<T> x, ModInt<T> y)
{
if (x.Value > y.Value) return x;
else return y;
}
public static ModInt<T> MaxMagnitudeNumber(ModInt<T> x, ModInt<T> y) => MaxMagnitude(x, y);
public static ModInt<T> MinMagnitude(ModInt<T> x, ModInt<T> y)
{
if (x.Value < y.Value) return x;
else return y;
}
public static ModInt<T> MinMagnitudeNumber(ModInt<T> x, ModInt<T> y) => MinMagnitude(x, y);
public static ModInt<T> CreateChecked<TOther>(TOther value) where TOther : INumberBase<TOther>
=> new(long.CreateChecked(value));
public static ModInt<T> CreateSaturating<TOther>(TOther value) where TOther : INumberBase<TOther>
=> new(long.CreateSaturating(value));
public static ModInt<T> CreateTruncating<TOther>(TOther value) where TOther : INumberBase<TOther>
=> new(long.CreateTruncating(value));
public static ModInt<T> Parse(string s, NumberStyles style, IFormatProvider provider) => Parse(s.AsSpan(), style, provider);
public static ModInt<T> Parse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider provider) => new(long.Parse(s, style, provider));
#if NET10_0_OR_GREATER
public static ModInt<T> Parse(ReadOnlySpan<byte> s, NumberStyles style, IFormatProvider provider) => new(long.Parse(s, style, provider));
#endif
public static ModInt<T> Parse(string s, IFormatProvider provider) => new(long.Parse(s, provider));
public static ModInt<T> Parse(ReadOnlySpan<char> s, IFormatProvider provider) => new(long.Parse(s, provider));
#if NET10_0_OR_GREATER
public bool TryFormat(Span<byte> dest, out int bytesWritten, ReadOnlySpan<char> format, IFormatProvider provider)
{
return Value.TryFormat(dest, out bytesWritten, format, provider);
}
#endif
public bool TryFormat(Span<char> destination, out int charsWritten, ReadOnlySpan<char> format, IFormatProvider provider)
{
return Value.TryFormat(destination, out charsWritten, format, provider);
}
public static bool TryParse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider provider, out ModInt<T> result)
{
if (long.TryParse(s, style, provider, out long inner))
{
result = new(inner);
return true;
}
else
{
result = Zero;
return false;
}
}
public static bool TryParse(string s, NumberStyles style, IFormatProvider provider, out ModInt<T> result)
{
if (long.TryParse(s, style, provider, out long inner))
{
result = new(inner);
return true;
}
else
{
result = Zero;
return false;
}
}
public static bool TryParse(ReadOnlySpan<char> s, IFormatProvider provider, out ModInt<T> result)
{
if (long.TryParse(s, provider, out long inner))
{
result = new(inner);
return true;
}
else
{
result = Zero;
return false;
}
}
public static bool TryParse(string s, IFormatProvider provider, out ModInt<T> result)
{
if (long.TryParse(s, provider, out long inner))
{
result = new(inner);
return true;
}
else
{
result = Zero;
return false;
}
}
public static bool TryConvertFromChecked<TOther>(TOther value, out ModInt<T> result) where TOther : INumberBase<TOther>
{
throw new NotImplementedException();
}
public static bool TryConvertFromSaturating<TOther>(TOther value, out ModInt<T> result) where TOther : INumberBase<TOther>
{
throw new NotImplementedException();
}
public static bool TryConvertFromTruncating<TOther>(TOther value, [MaybeNullWhen(false)] out ModInt<T> result) where TOther : INumberBase<TOther>
{
throw new NotImplementedException();
}
public static bool TryConvertToChecked<TOther>(ModInt<T> value, [MaybeNullWhen(false)] out TOther result) where TOther : INumberBase<TOther>
{
throw new NotImplementedException();
}
public static bool TryConvertToSaturating<TOther>(ModInt<T> value, [MaybeNullWhen(false)] out TOther result) where TOther : INumberBase<TOther>
{
throw new NotImplementedException();
}
public static bool TryConvertToTruncating<TOther>(ModInt<T> value, [MaybeNullWhen(false)] out TOther result) where TOther : INumberBase<TOther>
{
throw new NotImplementedException();
}
#endregion
#region INumber<TSelf> Implementation
public int CompareTo(ModInt<T> other) => Value.CompareTo(other.Value);
public int CompareTo(object other) => Value.CompareTo(other);
#endregion
}
/// <summary>
/// Used to specify modulus.
/// </summary>
public interface IMod
{
public uint Mod { get; }
}
public readonly struct Mod998244353 : IMod { public uint Mod => 998244353; }
public readonly struct Mod1000000007 : IMod { public uint Mod => 1000000007; }
public readonly struct Mod897581057 : IMod { public uint Mod => 897581057; }
public readonly struct Mod880803841 : IMod { public uint Mod => 880803841; }
/// <summary>
/// Segment tree. (Non-recursive, can be used with non-commutative monoid)
/// </summary>
/// <typeparam name="T">Type of values.</typeparam>
public sealed class SegmentTree<T> where T : struct
{
public delegate T Monoid(T x, T y);
private int _treeSize;
private int _dataSize;
private int _originalDataSize;
private T[] _data;
private Monoid _operator;
private Monoid _update;
private T _identity;
public int OriginalDataSize => _originalDataSize;
public int TreeSize => _treeSize;
public T Identity => _identity;
/// <summary>
/// Gets the value by index. Time complexity is O(1).
/// </summary>
public T this[int index]
{
get
{
return _data[_dataSize - 1 + index];
}
}
/// <summary>
/// Builds the segment tree. Time complexity is O(n).
/// </summary>
public SegmentTree(int n, Monoid op, Monoid update, T identity)
{
_originalDataSize = n;
int size = 1;
while (n > size)
{
size <<= 1;
}
_dataSize = size;
_treeSize = 2 * size - 1;
_data = new T[_treeSize];
Array.Fill(_data, identity);
_identity = identity;
_operator = op;
_update = update;
}
/// <summary>
/// Rebuild the segment tree from the array. Time complexity is O(n).
/// Since the time complexity of n Update() calls is O(nlogn), when initializing the segment tree with an array,
/// call this function to make it faster.
/// </summary>
public void Build(T[] array)
{
for (int i = 0; i < array.Length; i++)
{
_data[i + _dataSize - 1] = array[i];
}
for (int i = _dataSize - 2; i >= 0; i--)
{
_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);
}
}
public void UpdateByArray(T[] array)
{
for (int i = 0; i < array.Length; i++)
{
_data[i + _dataSize - 1] = _update(_data[i + _dataSize - 1], array[i]);
}
for (int i = _dataSize - 2; i >= 0; i--)
{
_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);
}
}
/// <summary>
/// Fill the array with the uniform value. Time complexity is O(n).
/// </summary>
public void Fill(T value)
{
for (int i = 0; i < _originalDataSize; i++)
{
_data[i + _dataSize - 1] = value;
}
for (int i = _dataSize - 2; i >= 0; i--)
{
_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);
}
}
/// <summary>
/// Update the value at the specified position. Time complexity is O(logn).
/// </summary>
public void Update(int index, T value)
{
index += _dataSize - 1;
_data[index] = _update(_data[index], value);
while (index > 0)
{
index = (index - 1) >> 1;
_data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]);
}
}
/// <summary>
/// Gets the product of the range [l, r). Time complexity is O(logn).
/// </summary>
public T Fold(int l, int r)
{
l += _dataSize - 1;
r += _dataSize - 1;
T leftFold = _identity;
T rightFold = _identity;
while (l < r)
{
if ((l & 1) == 0)
{
leftFold = _operator(leftFold, _data[l]);
l++;
}
if ((r & 1) == 0)
{
r--;
rightFold = _operator(_data[r], rightFold);
}
l = (l - 1) >> 1;
r = (r - 1) >> 1;
}
return _operator(leftFold, rightFold);
}
/// <summary>
/// Returns the span of the underlying data. Time complexity is O(1).
/// </summary>
public ReadOnlySpan<T> AsSpan()
{
return _data.AsSpan(_dataSize - 1, _originalDataSize);
}
}
/// <summary>
/// Segment Tree with lazy evaluation. (Recursive, can be used with non-commutative monoid)
/// </summary>
public sealed class LazySegmentTree<T, M> where T : struct, IEquatable<T> where M : struct, IEquatable<M>
{
public delegate T Monoid(T x, T y);
public delegate M Composition(M x, M y);
public delegate T Mapping(T x, M y, int l);
private int _treeSize;
private int _dataSize;
private int _originalDataSize;
private T[] _data;
private M?[] _lazy;
private Monoid _operator;
private Mapping _mapping;
private Composition _composition;
private T _identity;
/// <summary>
/// Gets the value by index. Time complexity is O(logn).
/// </summary>
public T this[int index]
{
get
{
return Access(index);
}
}
/// <summary>
/// Builds the segment tree. Time complexity is O(n).
/// </summary>
/// <param name="n">Size of the segment tree.</param>
/// <param name="op">Binary operation.</param>
/// <param name="mapping">Mapping function.</param>
/// <param name="composition">Composition function. composition(x, y) := yox</param>
/// <param name="identity">Identity.</param>
public LazySegmentTree(int n, Monoid op, Mapping mapping, Composition composition, T identity)
{
_originalDataSize = n;
int size = 1;
while (n > size)
{
size <<= 1;
}
_dataSize = size;
_treeSize = 2 * size - 1;
_data = new T[_treeSize];
_data.AsSpan().Fill(_identity);
_lazy = new M?[_treeSize];
_identity = identity;
_operator = op;
_mapping = mapping;
_composition = composition;
}
/// <summary>
/// Rebuild the segment tree from the array. Time complexity is O(n).
/// Since the time complexity of n Update() calls is O(nlogn), when initializing the segment tree with an array,
/// call this function to make it faster.
/// </summary>
public void Build(T[] array)
{
for (int i = 0; i < array.Length; i++)
{
_data[i + _dataSize - 1] = array[i];
}
for (int i = _dataSize - 2; i >= 0; i--)
{
_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);
}
}
/// <summary>
/// Fill the array with the uniform value. Time complexity is O(n).
/// </summary>
public void Fill(T value)
{
for (int i = 0; i < _originalDataSize; i++)
{
_data[i + _dataSize - 1] = value;
}
for (int i = _dataSize - 2; i >= 0; i--)
{
_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);
}
}
private void Evaluate(int index, int l, int r)
{
if (_lazy[index] is null)
{
return;
}
if (index < _dataSize - 1)
{
_lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]);
_lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]);
}
_data[index] = _mapping(_data[index], (M)_lazy[index], r - l);
_lazy[index] = null;
}
private M GuardComposition(M? a, M? b)
{
if (a is null)
{
return (M)b;
}
else
{
return _composition((M)a, (M)b);
}
}
/// <summary>
/// Update the range [l, r) by m. Time complexity is O(logn).
/// </summary>
public void Update(int l, int r, M m)
{
if (l == r) return;
if (0 <= l && l < r && r <= _originalDataSize)
ApplyRec(l, r, m, 0, 0, _dataSize);
}
private void ApplyRec(int a, int b, M m, int index, int l, int r)
{
Evaluate(index, l, r);
if (a >= r || b <= l)
{
return;
}
if (a <= l && r <= b)
{
_lazy[index] = GuardComposition(_lazy[index], m);
Evaluate(index, l, r);
}
else
{
ApplyRec(a, b, m, (index << 1) + 1, l, (l + r) / 2);
ApplyRec(a, b, m, (index << 1) + 2, (l + r) / 2, r);
_data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]);
}
}
/// <summary>
/// Gets the product of the range [l, r). Time complexity is O(logn).
/// </summary>
/// <param name="l"></param>
/// <param name="r"></param>
/// <returns></returns>
public T Fold(int l, int r)
{
if (l == r) return _identity;
if (0 <= l && l < r && r <= _originalDataSize)
return QueryRec(l, r, 0, 0, _dataSize);
else
return _identity;
}
private T QueryRec(int left, int right, int index, int nodeLeft, int nodeRight)
{
Evaluate(index, nodeLeft, nodeRight);
if (left >= nodeRight || right <= nodeLeft)
{
return _identity;
}
if (left <= nodeLeft && nodeRight <= right)
{
return _data[index];
}
T leftChild = QueryRec(left, right, (index << 1) + 1, nodeLeft, (nodeLeft + nodeRight) >> 1);
T rightChild = QueryRec(left, right, (index << 1) + 2, (nodeLeft + nodeRight) >> 1, nodeRight);
return _operator(leftChild, rightChild);
}
/// <summary>
/// Gets the value at the specified index. Time complexity is O(logn).
/// </summary>
public T Access(int index)
{
if (index < 0 || index >= _originalDataSize)
{
throw new Exception("Index is out of range.");
}
return AccessRec(index, 0, 0, _dataSize);
}
private T AccessRec(int target, int index, int l, int r)
{
Evaluate(index, l, r);
if (index >= _dataSize - 1)
{
return _data[index];
}
int mid = (l + r) / 2;
if (target < mid)
{
return AccessRec(target, (index << 1) + 1, l, mid);
}
else
{
return AccessRec(target, (index << 1) + 2, mid, r);
}
}
private void EvaluateAll(int index, int l, int r)
{
if (_lazy[index] is null)
{
if (index < _dataSize - 1)
{
EvaluateAll((index << 1) + 1, l, (l + r) / 2);
EvaluateAll((index << 1) + 2, (l + r) / 2, r);
}
return;
}
if (index < _dataSize - 1)
{
_lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]);
_lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]);
EvaluateAll((index << 1) + 1, l, (l + r) / 2);
EvaluateAll((index << 1) + 2, (l + r) / 2, r);
}
_data[index] = _mapping(_data[index], (M)_lazy[index], r - l);
_lazy[index] = null;
}
/// <summary>
/// Returns the span of the underlying data. Time complexity is O(n).
/// </summary>
/// <returns></returns>
public ReadOnlySpan<T> AsSpan()
{
EvaluateAll(0, 0, _dataSize);
return _data.AsSpan(_dataSize - 1, _originalDataSize);
}
}
public static class SegmentTreeBuilder
{
public static LazySegmentTree<T, T> RangeAddMax<T>(int n, T identity) where T : struct, INumber<T>
{
return new LazySegmentTree<T, T>(n, T.Max,
(x, m, l) =>
{
return x + m;
},
(a, b) => { return a + b; },
identity);
}
public static LazySegmentTree<T, T> RangeUpdateMax<T>(int n, T identity) where T : struct, INumber<T>
{
return new LazySegmentTree<T, T>(n, T.Max,
(x, m, l) =>
{
return m;
},
(x, y) => { return y; },
identity);
}
public static LazySegmentTree<T, T> RangeAddMin<T>(int n, T identity) where T : struct, INumber<T>
{
return new LazySegmentTree<T, T>(n, T.Min,
(x, m, l) =>
{
return x + m;
},
(a, b) => { return a + b; },
identity);
}
public static LazySegmentTree<T, T> RangeUpdateMin<T>(int n, T identity) where T : struct, INumber<T>
{
return new LazySegmentTree<T, T>(n, T.Min,
(x, m, l) =>
{
return m;
},
(x, y) => { return y; },
identity);
}
public static LazySegmentTree<T, T> RangeAddSum<T>(int n, T identity) where T : struct, INumber<T>
{
return new LazySegmentTree<T, T>(n, (x, y) => x + y,
(x, m, l) =>
{
return x + m * T.CreateChecked(l);
},
(a, b) => { return a + b; },
identity);
}
public static LazySegmentTree<T, T> RangeUpdateSum<T>(int n, T identity) where T : struct, INumber<T>
{
return new LazySegmentTree<T, T>(n, (x, y) => x + y,
(x, m, l) =>
{
return m * T.CreateChecked(l);
},
(a, b) => { return b; },
identity);
}
public static SegmentTree<T> PointUpdateMax<T>(int n, T identity) where T : struct, INumber<T>
{
return new SegmentTree<T>(n, T.Max, (a, b) => b, identity);
}
public static SegmentTree<T> PointAddMax<T>(int n, T identity) where T : struct, INumber<T>
{
return new SegmentTree<T>(n, T.Max, (a, b) => a + b, identity);
}
public static SegmentTree<T> PointUpdateMin<T>(int n, T identity) where T : struct, INumber<T>
{
return new SegmentTree<T>(n, T.Min, (a, b) => b, identity);
}
public static SegmentTree<T> PointAddMin<T>(int n, T identity) where T : struct, INumber<T>
{
return new SegmentTree<T>(n, T.Min, (a, b) => a + b, identity);
}
public static SegmentTree<T> PointUpdateSum<T>(int n, T identity) where T : struct, INumber<T>
{
return new SegmentTree<T>(n, (x, y) => x + y, (a, b) => b, identity);
}
public static SegmentTree<T> PointAddSum<T>(int n, T identity) where T : struct, INumber<T>
{
return new SegmentTree<T>(n, (x, y) => x + y, (a, b) => a + b, identity);
}
}
public sealed class PrefixSum2D<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>
{
private T[,] _sums;
public PrefixSum2D(T[,] sequence)
{
int height = sequence.GetLength(0);
int width = sequence.GetLength(1);
_sums = new T[height + 1, width + 1];
// build prefix sum
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
_sums[y + 1, x + 1] = _sums[y + 1, x] + _sums[y, x + 1] - _sums[y, x] + sequence[y, x];
}
}
}
public T Sum(int startInclX, int startInclY, int endExclX, int endExclY)
{
return _sums[endExclY, endExclX] + _sums[startInclY, startInclX] - _sums[startInclY, endExclX] - _sums[endExclY, startInclX];
}
public T AllSum()
{
return _sums[_sums.GetLength(0) - 1, _sums.GetLength(1) - 1];
}
}
public sealed class PrefixSum<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>, IAdditiveIdentity<T, T>
{
private T[] _sums;
public PrefixSum(T[] sequence)
{
_sums = new T[sequence.Length + 1];
_sums[0] = T.AdditiveIdentity;
for (int i = 0; i < sequence.Length; i++)
{
_sums[i + 1] = _sums[i] + sequence[i];
}
}
// [a, b)
public T Sum(int aIncl, int bExcl)
{
return _sums[bExcl] - _sums[aIncl];
}
public T AllSum()
{
return _sums[^1];
}
public T[] GetArray()
{
return _sums;
}
}
/// <summary>
/// Union-Find(disjoint set union).
/// </summary>
public sealed class UnionFind
{
private int[] _parents;
private int[] _size;
private int _vertexCount;
public int VertexCount => _vertexCount;
public UnionFind(int n)
{
_vertexCount = n;
_parents = new int[n];
_size = new int[n];
for (int i = 0; i < n; i++)
{
_parents[i] = i;
_size[i] = 1;
}
}
/// <summary>
/// Gets the leader(root) of the connected component x belongs to. Time complexity is O(α(n)).
/// </summary>
public int Leader(int x)
{
if (_parents[x] == x)
return x;
return _parents[x] = Leader(_parents[x]);
}
/// <summary>
/// Gets the size of the connected component x belongs to. Time complexity is O(α(n)).
/// </summary>
public int Size(int x)
{
return _size[Leader(x)];
}
/// <summary>
/// Merge the two connected components. Time complexity is O(α(n)).
/// </summary>
public void Unite(int x, int y)
{
int rootX = Leader(x);
int rootY = Leader(y);
if (rootX == rootY)
return;
int from = rootX;
int to = rootY;
// union by size.(small-to-large merging)
if (_size[from] > _size[to])
{
(from, to) = (to, from);
}
_size[to] += _size[from];
_parents[from] = to;
}
/// <summary>
/// Gets the list of vertices which belong to the connected component of x. Time complexity is O(n).
/// </summary>
public List<int> GetGroup(int x)
{
int rootX = Leader(x);
List<int> set = new List<int>();
for (int i = 0; i < _vertexCount; i++)
{
if (Leader(i) == rootX)
set.Add(i);
}
return set;
}
/// <summary>
/// Gets the vertex list of all connected components. Time complexity is O(n).
/// </summary>
public Dictionary<int, List<int>> FindAll()
{
Dictionary<int, List<int>> sets = new Dictionary<int, List<int>>();
for (int i = 0; i < _vertexCount; i++)
{
int root = Leader(i);
if (sets.ContainsKey(root))
sets[root].Add(i);
else
sets[root] = new List<int>() { i };
}
return sets;
}
/// <summary>
/// Determines if the x and y belong to the same connected component. Time complexity is O(α(n)).
/// </summary>
public bool Same(int x, int y)
{
int rootX = Leader(x);
int rootY = Leader(y);
return rootX == rootY;
}
/// <summary>
/// Clears the data. Time complexity is O(n).
/// </summary>
public void Clear()
{
for (int i = 0; i < _vertexCount; i++)
{
_parents[i] = i;
_size[i] = 1;
}
}
}