/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static Int32[] Convolution <TMod>(ReadOnlySpan <Int32> a, ReadOnlySpan <Int32> b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0)
{
return(Array.Empty <Int32>());
}
var a2 = new StaticModInt <TMod> [n];
var b2 = new StaticModInt <TMod> [m];
for (int i = 0; i < a2.Length; i++)
{
a2[i] = new StaticModInt <TMod>(a[i]);
}
for (int i = 0; i < b2.Length; i++)
{
b2[i] = new StaticModInt <TMod>(b[i]);
}
var c2 = Convolution(a2, b2);
var c = new Int32[n + m - 1];
for (int i = 0; i < c.Length; i++)
{
c[i] = (Int32)c2[i].Value;
}
return(c);
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static Span <StaticModInt <TMod> > Convolution <TMod>(ReadOnlySpan <StaticModInt <TMod> > a, ReadOnlySpan <StaticModInt <TMod> > b)
where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0)
{
return(Array.Empty <StaticModInt <TMod> >());
}
if (System.Math.Min(n, m) <= 60)
{
return(ConvolutionNaive(a, b));
}
int z = 1 << Internal.InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt <TMod> [z];
a.CopyTo(aTemp);
var bTemp = new StaticModInt <TMod> [z];
b.CopyTo(bTemp);
return(Convolution(aTemp.AsSpan(), bTemp.AsSpan(), n, m, z));
}
static StaticModInt <T>[] ConvNative <T>(StaticModInt <T>[] a, StaticModInt <T>[] b) where T : struct, IStaticMod
{
int n = a.Length, m = b.Length;
var c = new StaticModInt <T> [n + m - 1];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
c[i + j] += a[i] * b[j];
}
}
return(c);
}
public void Mid()
{
var mt = MTRandom.Create();
int n = 1234, m = 2345;
var a = new StaticModInt <Mod998244353> [n];
var b = new StaticModInt <Mod998244353> [m];
for (int i = 0; i < n; i++)
{
a[i] = mt.NextUInt();
}
for (int i = 0; i < m; i++)
{
b[i] = mt.NextUInt();
}
MathLib.Convolution(a, b).Should().Equal(ConvNative(a, b));
}
public void MemoryStatic()
{
var mt = MTRandom.Create();
for (int n = 0; n < 100; n++)
{
var arr = new StaticModInt <MemoryID> [n];
var expected = new uint[n];
for (int i = 0; i < n; i++)
{
var v = mt.NextUInt();
arr[i] = v;
expected[i] = v % 101;
}
MemoryMarshal.Cast <StaticModInt <MemoryID>, uint>(arr).ToArray()
.Should().Equal(expected);
}
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static ulong[] Convolution <TMod>(ulong[] a, ulong[] b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0)
{
return(Array.Empty <ulong>());
}
if (System.Math.Min(n, m) <= 60)
{
var c = ConvolutionNaive <TMod>(a.Select(TakeMod).ToArray(),
b.Select(TakeMod).ToArray());
return(c.Select(ci => (ulong)ci.Value).ToArray());
}
else
{
int z = 1 << Internal.InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt <TMod> [z];
for (int i = 0; i < a.Length; i++)
{
aTemp[i] = TakeMod(a[i]);
}
var bTemp = new StaticModInt <TMod> [z];
for (int i = 0; i < b.Length; i++)
{
bTemp[i] = TakeMod(b[i]);
}
var c = Convolution <TMod>(aTemp, bTemp, n, m, z)[0..(n + m - 1)];
var result = new ulong[c.Length];
for (int i = 0; i < result.Length; i++)
{
result[i] = (ulong)c[i].Value;
}
return(result);
}
StaticModInt <TMod> TakeMod(ulong x) => StaticModInt <TMod> .Raw((int)(x % default(TMod).Mod));
}
public void SimpleSMod()
{
var mt = MTRandom.Create();
for (int n = 1; n < 20; n++)
{
for (int m = 1; m < 20; m++)
{
var a = new StaticModInt <Mod998244353> [n];
var b = new StaticModInt <Mod998244353> [m];
for (int i = 0; i < n; i++)
{
a[i] = mt.NextUInt();
}
for (int i = 0; i < m; i++)
{
b[i] = mt.NextUInt();
}
MathLib.Convolution(a, b).Should().Equal(ConvNative(a, b));
}
}
for (int n = 1; n < 20; n++)
{
for (int m = 1; m < 20; m++)
{
var a = new StaticModInt <Mod924844033> [n];
var b = new StaticModInt <Mod924844033> [m];
for (int i = 0; i < n; i++)
{
a[i] = mt.NextUInt();
}
for (int i = 0; i < m; i++)
{
b[i] = mt.NextUInt();
}
MathLib.Convolution(a, b).Should().Equal(ConvNative(a, b));
}
}
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static int[] Convolution <TMod>(int[] a, int[] b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0)
{
return(Array.Empty <int>());
}
if (System.Math.Min(n, m) <= 60)
{
var c = ConvolutionNaive <TMod>(a.Select(ai => new StaticModInt <TMod>(ai)).ToArray(),
b.Select(bi => new StaticModInt <TMod>(bi)).ToArray());
return(c.Select(ci => ci.Value).ToArray());
}
else
{
int z = 1 << Internal.InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt <TMod> [z];
for (int i = 0; i < a.Length; i++)
{
aTemp[i] = new StaticModInt <TMod>(a[i]);
}
var bTemp = new StaticModInt <TMod> [z];
for (int i = 0; i < b.Length; i++)
{
bTemp[i] = new StaticModInt <TMod>(b[i]);
}
var c = Convolution <TMod>(aTemp, bTemp, n, m, z)[0..(n + m - 1)];
var result = new int[c.Length];
for (int i = 0; i < result.Length; i++)
{
result[i] = c[i].Value;
}
return(result);
}
}
private static StaticModInt <TMod>[] ConvolutionNaive <TMod>(ReadOnlySpan <StaticModInt <TMod> > a, ReadOnlySpan <StaticModInt <TMod> > b)
where TMod : struct, IStaticMod
{
if (a.Length < b.Length)
{
#pragma warning disable IDE0180 // ref 構造体のため型引数として使えない
var temp = a;
a = b;
b = temp;
#pragma warning restore IDE0180
}
var ans = new StaticModInt <TMod> [a.Length + b.Length - 1];
for (int i = 0; i < a.Length; i++)
{
for (int j = 0; j < b.Length; j++)
{
ans[i + j] += a[i] * b[j];
}
}
return(ans);
}
private static StaticModInt <TMod>[] ConvolutionFFT <TMod>(ReadOnlySpan <StaticModInt <TMod> > a, ReadOnlySpan <StaticModInt <TMod> > b)
where TMod : struct, IStaticMod
{
int n = a.Length, m = b.Length;
int z = 1 << InternalBit.CeilPow2(n + m - 1);
var a2 = new StaticModInt <TMod> [z];
var b2 = new StaticModInt <TMod> [z];
a.CopyTo(a2);
b.CopyTo(b2);
var result = ConvolutionFFTInner(a2, b2);
Array.Resize(ref result, n + m - 1);
var iz = new StaticModInt <TMod>(z).Inv();
for (int i = 0; i < result.Length; i++)
{
result[i] *= iz;
}
return(result);
}
public StaticModInt <T> Divide(StaticModInt <T> x, StaticModInt <T> y) => x / y;
public void Inv()
{
for (int i = 1; i < 10; i++)
{
int x = new StaticModInt <InvID11>(i).Inv().Value;
((long)x * i % 11).Should().Be(1);
}
for (int i = 1; i < 12; i++)
{
if (Gcd(i, 12) != 1)
{
continue;
}
int x = new StaticModInt <InvID12>(i).Inv().Value;
((long)x * i % 12).Should().Be(1);
}
for (int i = 1; i < 100000; i++)
{
int x = new StaticModInt <InvID1000000007>(i).Inv().Value;
((long)x * i % 1000000007).Should().Be(1);
}
for (int i = 1; i < 100000; i++)
{
if (Gcd(i, 1000000008) != 1)
{
continue;
}
int x = new StaticModInt <InvID1000000008>(i).Inv().Value;
((long)x * i % 1000000008).Should().Be(1);
}
for (int i = 1; i < 100000; i++)
{
int x = new StaticModInt <InvID998244353>(i).Inv().Value;
((long)x * i % 998244353).Should().Be(1);
}
DynamicModInt <InvID998244353> .Mod = 998244353;
for (int i = 1; i < 100000; i++)
{
int x = new DynamicModInt <InvID998244353>(i).Inv().Value;
x.Should().BeGreaterOrEqualTo(0);
x.Should().BeLessOrEqualTo(998244353 - 1);
((long)x * i % 998244353).Should().Be(1);
}
DynamicModInt <InvID1000000008> .Mod = 1000000008;
for (int i = 1; i < 100000; i++)
{
if (Gcd(i, 1000000008) != 1)
{
continue;
}
int x = new DynamicModInt <InvID1000000008>(i).Inv().Value;
((long)x * i % 1000000008).Should().Be(1);
}
}
public StaticModInt <T> Subtract(StaticModInt <T> x, StaticModInt <T> y) => x - y;
public StaticModInt <T> Add(StaticModInt <T> x, StaticModInt <T> y) => x + y;
public StaticModInt <T> Decrement(StaticModInt <T> x) => -- x;
public StaticModInt <T> Increment(StaticModInt <T> x) => ++ x;
public StaticModInt <T> Minus(StaticModInt <T> x) => - x;
StaticModInt <T> IDivisionOperator <StaticModInt <T> > .Modulo(StaticModInt <T> x, StaticModInt <T> y) => throw new NotSupportedException();
public StaticModInt <T> Multiply(StaticModInt <T> x, StaticModInt <T> y) => x * y;