結果
| 問題 |
No.1905 PURE PHRASE
|
| コンテスト | |
| ユーザー |
 kakel-san
|
| 提出日時 | 2023-11-18 09:25:12 |
| 言語 | C# (.NET 8.0.404) |
| 結果 |
AC
|
| 実行時間 | 132 ms / 2,000 ms |
| コード長 | 14,115 bytes |
| コンパイル時間 | 13,710 ms |
| コンパイル使用メモリ | 167,576 KB |
| 実行使用メモリ | 208,356 KB |
| 最終ジャッジ日時 | 2024-09-26 05:41:14 |
| 合計ジャッジ時間 | 20,845 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 38 |
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 (86 ms)。 MSBuild のバージョン 17.9.6+a4ecab324 (.NET) main -> /home/judge/data/code/bin/Release/net8.0/main.dll main -> /home/judge/data/code/bin/Release/net8.0/publish/
ソースコード
using System;
using static System.Console;
using System.Linq;
using System.Collections.Generic;
class Program
{
static int NN => int.Parse(ReadLine());
static double[] NList => ReadLine().Split().Select(double.Parse).ToArray();
public static void Main()
{
Solve();
// Test();
// Test2();
}
static void Test()
{
var n = NN;
var a = NList;
for (var i = 0; i < a.Length; ++i) a[i] *= 0.54 - 0.46 * Math.Cos(2 * Math.PI * i / (n - 1));
var fft = FFT.Calc2(a);
WriteLine(string.Join("\n", fft));
// WriteLine(string.Join("\n", a));
}
static void Test2()
{
var f = 100;
var fs = 1000;
var n = 64;
var t = new double[n];
for (var i = 0; i < t.Length; ++i) t[i] = (double)i / fs;
var signal = new double[n];
for (var i = 0; i < signal.Length; ++i) signal[i] = Math.Sin(2 * Math.PI * f * t[i]);
var window = new double[n];
for (var i = 0; i < window.Length; ++i) window[i] = 0.54 - 0.46 * Math.Cos(2 * Math.PI * i / (n - 1));
var a = new double[n];
for (var i = 0; i < a.Length; ++i) a[i] = signal[i] * window[i];
var fft = FFT.Calc2(a);
WriteLine(string.Join("\n", fft));
// WriteLine(string.Join("\n", signal));
// WriteLine(string.Join("\n", window));
}
static void Solve()
{
var n = NN;
var a = NList;
for (var i = 0; i < a.Length; ++i) a[i] *= 0.54 - 0.46 * Math.Cos(2 * Math.PI * i / (n - 1));
var f = FFT.Calc2(a);
var w = new double[] { 261.6, 294.3, 327, 348.8, 392.4, 436, 490.5 };
var s = new string[] { "C4", "D4", "E4", "F4", "G4", "A4", "B4" };
var maxr = 0.0;
var ans = "";
for (var i = 0; i < w.Length; ++i)
{
// var pos = (int)(44100 / w[i]);
var pos = (int)w[i];
// WriteLine($"f[{pos}] = {f[pos]} ({f[pos].Magnitude})");
if (maxr < Math.Abs(f[pos].Magnitude))
{
maxr = Math.Abs(f[pos].Magnitude);
ans = s[i];
}
}
WriteLine(ans);
}
class FFT
{
public static System.Numerics.Complex[] DFT(int[] a)
{
var xi = new System.Numerics.Complex[a.Length];
for (var i = 0; i < xi.Length; ++i) xi[i] = new System.Numerics.Complex(Math.Cos(i * 2 * Math.PI / xi.Length), Math.Sin(i * 2 * Math.PI / xi.Length));
var ans = new System.Numerics.Complex[a.Length];
for (var i = 0; i < a.Length; ++i) for (var j = 0; j < a.Length; ++j)
{
ans[i] += a[j] * xi[i * j % xi.Length];
}
return ans;
}
public static System.Numerics.Complex[] Calc(int[] a)
{
if (a.Length == 0) return new System.Numerics.Complex[0];
var len = 1;
while (len < a.Length) len <<= 1;
var c = new int[len];
Array.Copy(a, c, a.Length);
var dp = new System.Numerics.Complex[len];
var xi = new System.Numerics.Complex[len];
for (var i = 0; i < xi.Length; ++i) xi[i] = new System.Numerics.Complex(Math.Cos(i * 2 * Math.PI / len), Math.Sin(i * 2 * Math.PI / len));
_Calc(dp, xi, c);
return dp;
}
static void _Calc(System.Numerics.Complex[] dp, System.Numerics.Complex[] xi, int[] c)
{
if (dp.Length == 1)
{
dp[0] = c[0];
return;
}
var len = dp.Length / 2;
var dp0 = new System.Numerics.Complex[len];
var dp1 = new System.Numerics.Complex[len];
var c0 = new int[len];
var c1 = new int[len];
var x0 = new System.Numerics.Complex[len];
for (var i = 0; i < len; ++i)
{
c0[i] = c[i * 2];
c1[i] = c[i * 2 + 1];
x0[i] = xi[i * 2];
}
_Calc(dp0, x0, c0);
_Calc(dp1, x0, c1);
for (var i = 0; i < dp.Length; ++i)
{
dp[i] = dp0[i % len] + xi[i] * dp1[i % len];
}
}
public static System.Numerics.Complex[] Calc2(double[] a)
{
if (a.Length == 0) return new System.Numerics.Complex[0];
var dp = new System.Numerics.Complex[a.Length];
for (var i = 0; i < a.Length; ++i) dp[i] = a[i];
_Calc2(dp);
return dp;
}
static void _Calc2(System.Numerics.Complex[] dp)
{
if (dp.Length == 1) return;
var len = dp.Length / 2;
var dp0 = new System.Numerics.Complex[len];
var dp1 = new System.Numerics.Complex[len];
for (var i = 0; i < len; ++i)
{
dp0[i] = dp[i * 2];
dp1[i] = dp[i * 2 + 1];
}
_Calc2(dp0);
_Calc2(dp1);
var now = new System.Numerics.Complex(1, 0);
var zeta = new System.Numerics.Complex(Math.Cos(2 * Math.PI / dp.Length), Math.Sin(2 * Math.PI / dp.Length));
for (var i = 0; i < dp.Length; ++i)
{
dp[i] = dp0[i % len] + now * dp1[i % len];
now *= zeta;
}
}
}
// 畳み込みを mod で計算する
class ConvolutionCalculator
{
int mod;
public ConvolutionCalculator(int mod)
{
this.mod = mod;
}
public int[] Calc(long[] a, long[] b)
{
var _a = new int[a.Length];
var _b = new int[b.Length];
for (var i = 0; i < a.Length; ++i) _a[i] = (int)(a[i] % mod);
for (var i = 0; i < b.Length; ++i) _b[i] = (int)(b[i] % mod);
return Calc(_a, _b);
}
public int[] Calc(int[] a, int[] b)
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0)
{
return new int[0];
}
if (Math.Min(n, m) <= 100)
{
return ShortComvolution(a, b);
}
var z = 1 << CeilPow(n + m - 1);
var za = new int[z];
var zb = new int[z];
Array.Copy(a, za, a.Length);
Array.Copy(b, zb, b.Length);
InitButterfly();
Butterfly(za);
Butterfly(zb);
for (var i = 0; i < z; ++i)
{
za[i] = (int)((long)za[i] * zb[i] % mod);
}
ButterflyInv(za);
var iz = PowMod(z, mod - 2, mod);
var ans = new int[n + m - 1];
for (var i = 0; i < ans.Length; ++i)
{
ans[i] = (int)((long)za[i] * iz % mod);
}
return ans;
}
int[] ShortComvolution(int[] a, int[] b)
{
var ans = new int[a.Length + b.Length - 1];
for (var i = 0; i < a.Length; ++i)
{
for (var j = 0; j < b.Length; ++j)
{
ans[i + j] = (int)((ans[i + j] + (long)a[i] * b[j] % mod) % mod);
}
}
return ans;
}
int[] sume = new int[30];
int[] sumie = new int[30];
void InitButterfly()
{
var g = PrimitiveRoot(mod);
var es = new int[30];
var ies = new int[30];
var cnt2 = BSF(mod - 1);
var e = PowMod(g, mod - 1 >> cnt2, mod);
var ie = PowMod(e, mod - 2, mod);
for (var i = cnt2; i >= 2; --i)
{
es[i - 2] = e;
ies[i - 2] = ie;
e = (int)((long)e * e % mod);
ie = (int)((long)ie * ie % mod);
}
var now = 1L;
var inow = 1L;
for (var i = 0; i < cnt2 - 2; ++i)
{
sume[i] = (int)(es[i] * now % mod);
now = now * ies[i] % mod;
sumie[i] = (int)(ies[i] * inow % mod);
inow = inow * es[i] % mod;
}
}
void Butterfly(int[] a)
{
var h = CeilPow(a.Length);
for (var ph = 1; ph <= h; ++ph)
{
var w = 1 << (ph - 1);
var p = 1 << (h - ph);
var now = 1L;
for (var s = 0; s < w; ++s)
{
var offset = s << (h - ph + 1);
for (var i = 0; i < p; ++i)
{
var l = a[i + offset];
var r = (int)(a[i + offset + p] * now % mod);
a[i + offset] = (l + r) % mod;
a[i + offset + p] = (int)((long)mod + l - r) % mod;
}
now = now * sume[BSF(~(uint)s)] % mod;
}
}
}
void ButterflyInv(int[] a)
{
var h = CeilPow(a.Length);
for (var ph = h; ph >= 1; --ph)
{
var w = 1 << (ph - 1);
var p = 1 << (h - ph);
var inow = 1L;
for (var s = 0; s < w; ++s)
{
var offset = s << (h - ph + 1);
for (var i = 0; i < p; ++i)
{
var l = a[i + offset];
var r = a[i + offset + p];
a[i + offset] = (l + r) % mod;
a[i + offset + p] = (int)(((long)mod + l - r) * inow % mod);
}
inow = inow * sumie[BSF(~(uint)s)] % mod;
}
}
}
static int PowMod(int n, int p, int mod)
{
long _n = n % mod;
var _p = p;
var result = 1L;
if ((_p & 1) == 1)
{
result *= _n;
}
while (_p > 0)
{
_n = _n * _n % mod;
_p >>= 1;
if ((_p & 1) == 1)
{
result = (result * _n) % mod;
}
}
return (int)result;
}
static int PrimitiveRoot(int m)
{
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
if (m == 1000000007) return 5;
var divs = new int[20];
divs[0] = 2;
var cnt = 1;
var x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (var i = 3; (long)i * i <= x; i += 2)
{
if (x % i == 0)
{
divs[cnt++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) divs[cnt++] = x;
for (var g = 2;; ++g)
{
var ok = true;
for (var i = 0; i < cnt; ++i)
{
if (PowMod(g, (m - 1) / divs[i], m) == 1)
{
ok = false;
break;
}
}
if (ok) return g;
}
}
static int CeilPow(int n)
{
var x = 0;
while ((1U << x) < (uint)n) x++;
return x;
}
static int BSF(int n)
{
if (n == 0) return 0;
var count = 0;
while ((n & 1) == 0)
{
++count;
n >>= 1;
}
return count;
}
static int BSF(uint n)
{
if (n == 0) return 0;
var count = 0;
while ((n & 1) == 0)
{
++count;
n >>= 1;
}
return count;
}
public long[] ConvolutionLL(long[] a, long[] b)
{
if (a.Length == 0 && b.Length == 0) return new long[0];
const ulong MOD1 = 754_974_721;
const ulong MOD2 = 167_772_161;
const ulong MOD3 = 469_762_049;
const ulong M2M3 = 78_812_994_116_517_889;
const ulong M1M3 = 354_658_471_880_163_329;
const ulong M1M2 = 126_663_740_442_542_081;
const ulong M1M2M3 = 560_135_205_046_714_369;
const ulong i1 = 190_329_765;
const ulong i2 = 58_587_104;
const ulong i3 = 187_290_749;
ulong[] offset = new ulong[] { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3 };
var c1 = new ConvolutionCalculator((int)MOD1).Calc(a, b);
var c2 = new ConvolutionCalculator((int)MOD2).Calc(a, b);
var c3 = new ConvolutionCalculator((int)MOD3).Calc(a, b);
var ans = new long[a.Length + b.Length - 1];
for (var i = 0; i < ans.Length; ++i)
{
ulong x = 0;
x += (ulong)c1[i] * i1 % MOD1 * M2M3;
x += (ulong)c2[i] * i2 % MOD2 * M1M3;
x += (ulong)c3[i] * i3 % MOD3 * M1M2;
var diff = c1[i] - SafeMod((long)x, (long)MOD1);
if (diff < 0) diff += (long)MOD1;
x -= offset[diff % 5];
ans[i] = (long)x;
}
return ans;
}
static long SafeMod(long a, long b)
{
a %= b;
if (a < 0) a += b;
return a;
}
}
}