SP_memo

何処にも披露する見込みの無いものを書き捨てる場所

油分け問題 (C#) 

		private static readonly int CAPACITY_MAX = 10;
		//private static readonly int CAPACITY_MAX = 30;
		//private static readonly int CAPACITY_MAX = 100;

		private class State_t
		{
			public int Contain1;
			public int Contain2;
			public int MovedCount;
			public string StrAction;
			public State_t Prev;
		}

		private CsvFileWriter Writer;
		private bool WroteHeader = false;

		public void Test01() // main
		{
			using (Writer = new CsvFileWriter(SCommon.NextOutputPath() + ".csv"))
			{
				for (int a = 1; a <= CAPACITY_MAX; a++)
				{
					for (int b = a; b <= CAPACITY_MAX; b++)
					{
						Test01_a(a, b);
					}
				}
			}
		}

		private void Test01_a(int capacity1, int capacity2)
		{
			List<State_t> states = new List<State_t>();

			states.Add(new State_t()
			{
				Contain1 = 0,
				Contain2 = 0,
				MovedCount = 0,
				StrAction = null,
				Prev = null,
			});

			for (int i = 0; i < states.Count; i++)
			{
				State_t curr = states[i];
				int nextMovedCount = curr.MovedCount + 1;

				int transfer1To2 = Math.Min(curr.Contain1, capacity2 - curr.Contain2);
				int transfer2To1 = Math.Min(capacity1 - curr.Contain1, curr.Contain2);

				State_t[] nexts = new State_t[]
				{
					new State_t()
					{
						Contain1 = 0,
						Contain2 = curr.Contain2,
						MovedCount = nextMovedCount,
						StrAction = "桶1を空にする",
						Prev = curr,
					},
					new State_t()
					{
						Contain1 = curr.Contain1,
						Contain2 = 0,
						MovedCount = nextMovedCount,
						StrAction = "桶2を空にする",
						Prev = curr,
					},
					new State_t()
					{
						Contain1 = capacity1,
						Contain2 = curr.Contain2,
						MovedCount = nextMovedCount,
						StrAction = "桶1を満杯にする",
						Prev = curr,
					},
					new State_t()
					{
						Contain1 = curr.Contain1,
						Contain2 = capacity2,
						MovedCount = nextMovedCount,
						StrAction = "桶2を満杯にする",
						Prev = curr,
					},
					new State_t()
					{
						Contain1 = curr.Contain1 - transfer1To2,
						Contain2 = curr.Contain2 + transfer1To2,
						MovedCount = nextMovedCount,
						StrAction = "桶1から桶2へ移せるだけ移す",
						Prev = curr,
					},
					new State_t()
					{
						Contain1 = curr.Contain1 + transfer2To1,
						Contain2 = curr.Contain2 - transfer2To1,
						MovedCount = nextMovedCount,
						StrAction = "桶2から桶1へ移せるだけ移す",
						Prev = curr,
					},
				};

				foreach (State_t next in nexts)
					if (!states.Any(known => known.Contain1 == next.Contain1 && known.Contain2 == next.Contain2))
						states.Add(next);
			}

			for (int targetContain = 1; targetContain <= CAPACITY_MAX; targetContain++)
			{
				State_t[] reacheds = states.Where(state => state.Contain1 == targetContain || state.Contain2 == targetContain).ToArray();

				if (reacheds.Length == 0)
					continue;

				int bestMovedCount = reacheds.Select(reached => reached.MovedCount).Min();
				State_t best = reacheds.Where(reached => reached.MovedCount == bestMovedCount).First();

				if (!WroteHeader)
				{
					Writer.WriteCell("桶1の容量");
					Writer.WriteCell("桶2の容量");
					Writer.WriteCell("目標量");
					Writer.WriteCell("最短手数");
					Writer.WriteCell("最短手順");
					Writer.EndRow();

					WroteHeader = true;
				}
				Writer.WriteCell(capacity1.ToString());
				Writer.WriteCell(capacity2.ToString());
				Writer.WriteCell(targetContain.ToString());
				Writer.WriteCell(bestMovedCount.ToString());
				Writer.WriteCell(string.Join("\r\n", GetRoute(best)));
				Writer.EndRow();
			}
		}

		private string[] GetRoute(State_t state)
		{
			List<string> dest = new List<string>();

			while (state.Prev != null)
			{
				dest.Add(string.Format("{0}　({1}, {2}) ⇒ ({3}, {4})"
					, state.StrAction
					, state.Prev.Contain1
					, state.Prev.Contain2
					, state.Contain1
					, state.Contain2
					));

				state = state.Prev;
			}
			dest.Reverse();
			return dest.ToArray();
		}
(桶のキャパ最大10で)最短手数が最長のやつ

なんか
・1手でできる操作は6通りあるけど、そのうち3通りだけ使えば攻略できる。
・{ 小さい桶を満杯にする ⇒ 小さい桶から大きい桶へ移せるだけ移す ⇒ 大きい桶が満杯なら_大きい桶を空にして小さい桶から大きい桶へ全て移す } を繰り返せばいずれ目的量に辿り着く。
・↑で辿り着けない量はそもそも量れない。
・桶1と桶2の容量の最大公約数の倍数は量れる。それ以外は量れない。
っぽい。
知らんけど。


↑の検証用(桶の容量100以下)
source:

		//private static readonly int CAPACITY_MAX = 10;
		//private static readonly int CAPACITY_MAX = 30;
		private static readonly int CAPACITY_MAX = 100;

		private class State_t
		{
			public int Contain1;
			public int Contain2;
		}

		private bool[, ,] Solvables = new bool[CAPACITY_MAX + 1, CAPACITY_MAX + 1, CAPACITY_MAX + 1];

		public void Test01() // main
		{
			for (int a = 1; a <= CAPACITY_MAX; a++)
			{
				for (int b = a; b <= CAPACITY_MAX; b++)
				{
					Test01_a(a, b);
				}
			}

			// 以下検証...

			for (int a = 1; a <= CAPACITY_MAX; a++)
			{
				for (int b = 1; b <= CAPACITY_MAX; b++)
				{
					for (int c = 0; c <= CAPACITY_MAX; c++)
					{
						Test01_b(a, b, c, Solvables[a, b, c]);
					}
				}
			}

			Console.WriteLine("OK!");
		}

		private void Test01_a(int capacity1, int capacity2)
		{
			List<State_t> states = new List<State_t>();

			states.Add(new State_t()
			{
				Contain1 = 0,
				Contain2 = 0,
			});

			for (int i = 0; i < states.Count; i++)
			{
				State_t curr = states[i];

				int transfer1To2 = Math.Min(curr.Contain1, capacity2 - curr.Contain2);
				int transfer2To1 = Math.Min(capacity1 - curr.Contain1, curr.Contain2);

				State_t[] nexts = new State_t[]
				{
					new State_t() // 桶1を空にする
					{
						Contain1 = 0,
						Contain2 = curr.Contain2,
					},
					new State_t() // 桶2を空にする
					{
						Contain1 = curr.Contain1,
						Contain2 = 0,
					},
					new State_t() // 桶1を満杯にする
					{
						Contain1 = capacity1,
						Contain2 = curr.Contain2,
					},
					new State_t() // 桶2を満杯にする
					{
						Contain1 = curr.Contain1,
						Contain2 = capacity2,
					},
					new State_t() // 桶1から桶2へ移せるだけ移す
					{
						Contain1 = curr.Contain1 - transfer1To2,
						Contain2 = curr.Contain2 + transfer1To2,
					},
					new State_t() // 桶2から桶1へ移せるだけ移す
					{
						Contain1 = curr.Contain1 + transfer2To1,
						Contain2 = curr.Contain2 - transfer2To1,
					},
				};

				foreach (State_t next in nexts)
					if (!states.Any(known => known.Contain1 == next.Contain1 && known.Contain2 == next.Contain2))
						states.Add(next);
			}

			// 量0は初期状態で完了
			Solvables[capacity1, capacity2, 0] = true;
			Solvables[capacity2, capacity1, 0] = true; // 桶1<=桶2なので逆の場合もセットしておく

			for (int targetContain = 1; targetContain <= CAPACITY_MAX; targetContain++)
			{
				bool solved = states.Any(state => state.Contain1 == targetContain || state.Contain2 == targetContain);

				if (solved)
				{
					Solvables[capacity1, capacity2, targetContain] = true;
					Solvables[capacity2, capacity1, targetContain] = true; // 桶1<=桶2なので逆の場合もセットしておく
				}
			}
		}

		private void Test01_b(int capacity1, int capacity2, int targetContain, bool solvable_KITAI)
		{
			// ・1手でできる操作は6通りあるけど、そのうち3通りだけ使えば攻略できる
			// ・{ 小さい桶を満杯にする ⇒ 小さい桶から大きい桶へ移せるだけ移す
			// 　⇒ 大きい桶が満杯なら_大きい桶を空にして小さい桶から大きい桶へ全て移す } を繰り返せばいずれ目的量に辿り着く
			// ・↑で辿り着けない量はそもそも量れない。
			//
			bool solvable = Test01_c(capacity1, capacity2, targetContain);

			if (solvable != solvable_KITAI)
				throw null; // souteigai !!!

			// ・桶1と桶2の容量の最大公約数の倍数は量れる。それ以外は量れない。
			//
			bool gcdMul = IsGCDMul(capacity1, capacity2, targetContain) && // 桶キャパの最大公約数の倍数か
				Math.Max(capacity1, capacity2) >= targetContain; // 目的量が桶のキャパ以下であること

			if (gcdMul != solvable_KITAI)
				throw null; // souteigai !!!
		}

		private bool Test01_c(int capacity1, int capacity2, int targetContain)
		{
			if (targetContain == 0)
				return true; // 量0は初期状態で完了

			if (Math.Max(capacity1, capacity2) < targetContain)
				return false; // 桶のキャパより多い量はそもそも量れないよ！

			if (capacity1 > capacity2)
				SCommon.Swap(ref capacity1, ref capacity2);　// capacity1 <= capacity2 となるようにする。

			int t1 = 0;
			int t2 = 0;

			Action[] actions = new Action[]
			{
				// 小さい桶を満杯にする
				() =>
				{
					t1 = capacity1;
				},
				// 小さい桶から大きい桶へ移せるだけ移す
				() =>
				{
					int transfer = Math.Min(t1, capacity2 - t2);

					t1 -= transfer;
					t2 += transfer;
				},
				// 大きい桶が満杯なら_大きい桶を空にして小さい桶から大きい桶へ全て移す
				() =>
				{
					if (t2 == capacity2)
					{
						t2 = t1;
						t1 = 0;
					}
				},
			};

			for (; ; )
			{
				foreach (Action a in actions)
				{
					a();

					// どちらかの桶が目的量になったので_成功
					if (
						t1 == targetContain ||
						t2 == targetContain
						)
						return true;

					// 初期状態に戻ってしまったので_失敗
					if (
						t1 == 0 &&
						t2 == 0
						)
						return false;
				}
			}
		}

		private static bool IsGCDMul(int a, int b, int c) // ret: ? c == Multiple of GCD(a, b)
		{
			return c % GetGCD(a, b) == 0;
		}

		private static int GetGCD(int a, int b)
		{
			while (b != 0)
			{
				int w = b;
				b = a % b;
				a = w;
			}
			return a;
		}

output:

OK!

分数の構造体とつべで見つけた数学の問題 (C#)

分数のクラスとかあったら便利じゃねと考えて、標準にあるだろうと思ったら無かった。
演算子をオーバーライドしたので構造体
分子・分母共に BigInteger を使う。

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;

namespace Charlotte.Tools
{
	public struct Fraction
	{
		public BigInteger Numer;
		public BigInteger Denom;

		public Fraction(BigInteger numer, BigInteger denom)
		{
			this.Numer = numer;
			this.Denom = denom;
		}

		public static implicit operator Fraction(long value)
		{
			return new Fraction(value, 1);
		}

		public static Fraction operator ++(Fraction instance)
		{
			return instance + new Fraction(1, 1);
		}

		public static Fraction operator --(Fraction instance)
		{
			return instance - new Fraction(1, 1);
		}

		public static Fraction operator +(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return new Fraction(a.Numer + b.Numer, b.Denom);
		}

		public static Fraction operator -(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return new Fraction(a.Numer - b.Numer, b.Denom);
		}

		public static Fraction operator *(Fraction a, Fraction b)
		{
			return new Fraction(a.Numer * b.Numer, a.Denom * b.Denom);
		}

		public static Fraction operator /(Fraction a, Fraction b)
		{
			return new Fraction(a.Numer * b.Denom, a.Denom * b.Numer);
		}

		public static bool operator ==(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return a.Numer == b.Numer;
		}

		public static bool operator !=(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return a.Numer != b.Numer;
		}

		public override bool Equals(object another)
		{
			return another is Fraction && this == (Fraction)another;
		}

		public override int GetHashCode()
		{
			//return this.Numer.GetHashCode() ^ this.Denom.GetHashCode();
			return (this.Numer.GetHashCode() + ":" + this.Denom.GetHashCode()).GetHashCode();
		}

		public static bool operator <(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return a.Numer < b.Numer;
		}

		public static bool operator >(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return a.Numer > b.Numer;
		}

		public static bool operator <=(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return a.Numer <= b.Numer;
		}

		public static bool operator >=(Fraction a, Fraction b)
		{
			Reduction(ref a, ref b);
			return a.Numer >= b.Numer;
		}

		public static void Reduction(ref Fraction a, ref Fraction b) // 通分
		{
			BigInteger d = a.Denom * b.Denom;

			a.Numer *= b.Denom;
			b.Numer *= a.Denom;
			a.Denom = d;
			b.Denom = d;
		}

		public void Simplify() // 約分とか
		{
			if (this.Denom == 0)
				throw new Exception("Bad fraction");

			if (this.Numer == 0)
			{
				this.Denom = 1;
				return;
			}
			if (this.Numer < 0)
			{
				this.Numer *= -1;
				this.Denom *= -1;
			}
			int sign = 1;

			if (this.Denom < 0)
			{
				sign = -1;
				this.Denom = BigInteger.Abs(this.Denom);
			}
			if (this.Numer == this.Denom)
			{
				this.Numer = sign;
				this.Denom = 1;
				return;
			}
			BigInteger d = GetGCD(this.Numer, this.Denom);

			this.Numer /= d;
			this.Denom /= d;

			this.Numer *= sign;
		}

		private static BigInteger GetGCD(BigInteger a, BigInteger b)
		{
			if (a < b)
			{
				BigInteger t = a;
				a = b;
				b = t;
			}
			while (b != 0)
			{
				BigInteger r = a % b;
				a = b;
				b = r;
			}
			return a;
		}
	}
}

　
で、これを使って...
　
www.youtube.com
...この問題を解いてみる。
　
source:

		public void Test01()
		{
			const int MURABITO_NUM = 100;

			List<Murabito_t> murabitoList = new List<Murabito_t>();
			Fraction rem = 1;

			for (int n = 1; n <= MURABITO_NUM; n++)
			{
				Fraction area = rem * new Fraction(n, MURABITO_NUM);
				rem -= area;

				area.Simplify();
				rem.Simplify();

				murabitoList.Add(new Murabito_t()
				{
					No = n,
					Area = area,
				});
			}
			murabitoList.Sort((a, b) => a.Area < b.Area ? 1 : (a.Area > b.Area ? -1 : 0)); // DESC

			Console.WriteLine("最も広い土地を貰ったのは " + murabitoList[0].No + " 番目の村人です。");
		}

		private class Murabito_t
		{
			public int No;
			public Fraction Area;
		}

　
output:

最も広い土地を貰ったのは 10 番目の村人です。


それぞれの村人が貰った土地の面積を出力してみる。
　
source:

		public void Test01()
		{
			const int MURABITO_NUM = 100;

			List<Murabito_t> murabitoList = new List<Murabito_t>();
			Fraction rem = 1;

			for (int n = 1; n <= MURABITO_NUM; n++)
			{
				Fraction area = rem * new Fraction(n, MURABITO_NUM);
				rem -= area;

				area.Simplify();
				rem.Simplify();

				murabitoList.Add(new Murabito_t()
				{
					No = n,
					Area = area,
				});
			}
			murabitoList.Sort((a, b) => a.Area < b.Area ? 1 : (a.Area > b.Area ? -1 : 0)); // DESC

			//Console.WriteLine("最も広い土地を貰ったのは " + murabitoList[0].No + " 番目の村人です。");
			foreach (Murabito_t x in murabitoList)
				Console.WriteLine(string.Join("\t", x.No, x.Area.Numer, x.Area.Denom));
		}

		private class Murabito_t
		{
			public int No;
			public Fraction Area;
		}

　
output:
面積の広い順
各行：村人番号 \t 面積の分子 \t 面積の分母

10	245373636545037	3906250000000000
11	24291990017958663	390625000000000000
9	24267722295663	390625000000000
12	589632848617723911	9765625000000000000
8	117235373409	1953125000000
13	28105832450778173091	488281250000000000000
7	8824167891	156250000000
14	1316650150963377493263	24414062500000000000000
6	80463537	1562500000
15	24263981353467956661561	488281250000000000000000
5	1411641	31250000
16	137495894336318421082179	3051757812500000000000000
17	49086034278065676326337903	1220703125000000000000000000
4	470547	12500000
18	2156898094453827071516141973	61035156250000000000000000000
19	186691512842170143190119399663	6103515625000000000000000000000
3	14553	500000
20	795895396853462189389456388037	30517578125000000000000000000000
21	16713803333922705977178584148777	762939453125000000000000000000000
2	99	5000
22	691633099865658642579437601204153	38146972656250000000000000000000000
23	56399535507226891126705048025465931	3814697265625000000000000000000000000
24	566447508789974428272559395386201307	47683715820312500000000000000000000000
1	1	100
25	3587500889003171379059542837445941611	381469726562500000000000000000000000000
26	139912534671123683783322170660391722829	19073486328125000000000000000000000000000
27	10751740164342504623041449883825487008167	1907348632812500000000000000000000000000000
28	203486637925148883791636329282771254117531	47683715820312500000000000000000000000000000
29	7587144642637694095659583134686185332096513	2384185791015625000000000000000000000000000000
30	55726269271787201461223834747867499163329561	23841857910156250000000000000000000000000000000
31	4030866810659274239028524046762415772814171579	2384185791015625000000000000000000000000000000000
32	8971929352757739435257037394406667365296059321	7450580596923828125000000000000000000000000000000
33	5033252366897091823179197978262140391931089279081	5960464477539062500000000000000000000000000000000000
34	173723468057448108684882015067896300194227596632523	298023223876953125000000000000000000000000000000000000
35	2360595360074736065071043851804943843815680871888989	5960464477539062500000000000000000000000000000000000000
36	39455665304106302801901732951596918532347808858715959	149011611938476562500000000000000000000000000000000000000
37	162206624027992578185596013245453998410763214196943387	931322574615478515625000000000000000000000000000000000000
38	5247603485446138272652930482562390164802258578209222547	46566128730773925781250000000000000000000000000000000000000
39	333913295468651640612494365969364721539259506371313161017	4656612873077392578125000000000000000000000000000000000000000
40	522274641630455130188773239080288410612687945862823149283	11641532182693481445312500000000000000000000000000000000000000
41	64239780920545981013219108406875474505360617341127247361809	2328306436538696289062500000000000000000000000000000000000000000
42	1941294842940401718911670129661432022247361094772113645884911	116415321826934814453125000000000000000000000000000000000000000000
43	115275936626032425880135840556562177702021870722896462686594477	11641532182693481445312500000000000000000000000000000000000000000000
44	1680884006151682116903376093696848498120179370773397258244063653	291038304567337036132812500000000000000000000000000000000000000000000
45	9626881126141452124082972172991041398324663668974911569943273649	2910383045673370361328125000000000000000000000000000000000000000000000
46	270622324990420820821443551085192608197348878694516958577294248133	145519152283668518066406250000000000000000000000000000000000000000000000
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グラフにしてみる。
しゃらくせえのでエクセルで、、、

貰った土地の面積(割合) / 村人番号

　
↑の source:

		public void Test01()
		{
			const int MURABITO_NUM = 100;

			List<Murabito_t> murabitoList = new List<Murabito_t>();
			Fraction rem = 1;

			for (int n = 1; n <= MURABITO_NUM; n++)
			{
				Fraction area = rem * new Fraction(n, MURABITO_NUM);
				rem -= area;

				area.Simplify();
				rem.Simplify();

				murabitoList.Add(new Murabito_t()
				{
					No = n,
					Area = area,
				});
			}
			//murabitoList.Sort((a, b) => a.Area < b.Area ? 1 : (a.Area > b.Area ? -1 : 0)); // DESC

			//Console.WriteLine("最も広い土地を貰ったのは " + murabitoList[0].No + " 番目の村人です。");
			//foreach (Murabito_t x in murabitoList)
			//Console.WriteLine(string.Join("\t", x.No, x.Area.Numer, x.Area.Denom));

			using (CsvFileWriter writer = new CsvFileWriter(SCommon.NextOutputPath() + ".csv"))
			{
				foreach (Murabito_t x in murabitoList)
				{
					const int GAISANCHI_SEIDO = 1000000000;
					double gaisanchi = (double)((x.Area.Numer * GAISANCHI_SEIDO) / x.Area.Denom) / GAISANCHI_SEIDO;

					writer.WriteCell(x.No.ToString()); // 村人番号
					writer.WriteCell(gaisanchi.ToString("F9")); // 面積の概算値
					writer.EndRow();
				}
			}
		}

		private class Murabito_t
		{
			public int No;
			public Fraction Area;
		}

ぼくのかんがえたプログラミングの問題 (C系)

前につぶやきSNSに上げたけど、ここにも置いておく。
環境としてはC言語系統を想定。

64ビットを整数型の最大のビット数とする処理系において、
2^64(2の64乗)を引数xで割った余りを返す関数
uint64_t Modulo2P64(uint64_t x) { ... }
を実装せよ。
補足：
・uint64_tは64ビット符号なし整数型である。
・標準関数をはじめ如何なる外部関数やマクロを使用してはならない。
・引数xに0を指定することはできないが、その引数チェックはしなくてよい。
・制御構文を使ったら70点、1つの式(1つのreturn文)で記述できたら100点

更に補足：(2^64)は2の64乗です。66じゃないです。
　
んで、答えは↓の方。クイズノックっぽく！
　

↓

↓

↓

↓

↓

　
模範解答：

uint64_t Modulo2P64(uint64_t x)
{
　　return (~x + 1) % x;
}


最初友人に出して返ってきた答え：

uint64_t Modulo2P64(uint64_t x)
{
　　const uint64_t UI2P63 = 1UI64 << 63;
　　return UI2P63 < x ? UI2P63 - (x - UI2P63) : ((UI2P63 % x) * 2) % x;
}

　
最初に僕が用意しておいた答え：

uint64_t Modulo2P64(uint64_t x)
{
　　return (0xffffffffffffffff % x + 1) % x;
}

　
それがいいなら、これでもいいじゃんみたいな答え：

uint64_t Modulo2P64(uint64_t x)
{
　　return (uint64_t)-(sint64_t)x % x;
}

　
ようわからんけど、これでもいいだろみたいな答え：

uint64_t Modulo2P64(uint64_t x)
{
　　return ((0xffffffffffffffff - x) + 1) % x;
}

　
その後ごにょごにょ友人と話した結果、上の模範解答になりましたとさ。。。

スライディングウィンドウアルゴリズム (C#)

数列 int[] arr が与えられるので、n 種類の値を含む最短の範囲を返せ
複数ある場合は arr の先頭に近い方を返すこと。
見つからない場合は null を返すこと。
制約：
1 ≦ arr.Length
1 ≦ n

という問題を愚直に実装するとこうなる……

		private Range_t Test01_e1(int[] arr, int n)
		{
			for (int w = n; w <= arr.Length; w++)
			{
				for (int s = 0; s + w <= arr.Length; s++)
				{
					HashSet<int> h = new HashSet<int>();

					for (int i = s; i < s + w; i++)
						h.Add(arr[i]);

					if (n <= h.Count)
						return new Range_t() { Start = s, End = s + w };
				}
			}
			return null;
		}

		// ----
		// ----
		// -- 以下共通 --

		private class Range_t
		{
			/// <summary>
			/// 開始位置(最初の要素のインデックス)
			/// </summary>
			public int Start;

			/// <summary>
			/// 終了位置(最後の要素のインデックス+1)
			/// </summary>
			public int End;

			/// <summary>
			/// 要素数
			/// </summary>
			public int Count
			{
				get
				{
					return this.End - this.Start;
				}
			}
		}

……のですが、arr の長さが 1,000,000 とかやたら長い場合はスライディングウィンドウで何とかする。
↓こんなん

		private Range_t Test01_e2(int[] arr, int n)
		{
			Dictionary<int, int> d = new Dictionary<int, int>();
			Range_t range = null;
			int l = 0;
			int r = 0;

			for (; ; )
			{
				for (; ; )
				{
					if (arr.Length <= r)
						return range;

					int k = arr[r++];

					if (d.ContainsKey(k))
						d[k]++;
					else
						d.Add(k, 1);

					if (n <= d.Count)
						break;
				}
				for (; ; )
				{
					int k = arr[l++];

					if (--d[k] == 0)
					{
						d.Remove(k);
						break;
					}
				}
				Range_t currRange = new Range_t() { Start = l - 1, End = r };

				if (range == null || range.Count > currRange.Count)
					range = currRange;
			}
		}

　
また似たようなやつで、

数列 int[] arr が与えられるので、値が重複しない最長の範囲を返せ
複数ある場合は arr の先頭に近い方を返すこと。
制約：
1 ≦ arr.Length

今度は最短じゃなくて最長。
これを愚直に実装すると、

		private Range_t Test02_e1(int[] arr)
		{
			for (int w = arr.Length; 2 <= w; w--)
			{
				for (int s = 0; s + w <= arr.Length; s++)
				{
					HashSet<int> h = new HashSet<int>();
					bool dupl = false;

					for (int i = s; i < s + w; i++)
					{
						int k = arr[i];

						if (h.Contains(k))
						{
							dupl = true;
							break;
						}
						h.Add(k);
					}
					if (!dupl)
						return new Range_t() { Start = s, End = s + w };
				}
			}
			return new Range_t() { Start = 0, End = 1 };
		}

これも長い arr の場合、同様にスライディングウィンドウで何とかする。
↓こんなん

		private Range_t Test02_e2(int[] arr)
		{
			Dictionary<int, int> d = new Dictionary<int, int>();
			Range_t range = null;
			int l = 0;
			int r = -1;

			for (; ; )
			{
				for (; ; )
				{
					if (arr.Length <= ++r)
						break;

					int k = arr[r];

					if (d.ContainsKey(k))
					{
						if (++d[k] == 2)
							break;
					}
					else
					{
						d.Add(k, 1);
					}
				}
				Range_t currRange = new Range_t() { Start = l, End = r };

				if (range == null || range.Count < currRange.Count)
					range = currRange;

				if (arr.Length <= r)
					return range;

				while (d[arr[l++]]-- != 2) ;
			}
		}


以下検証用

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Charlotte.Commons;

namespace Charlotte.Tests
{
	public class Test0009
	{
		private TimeSpan TotalTm1 = new TimeSpan(0L);
		private TimeSpan TotalTm2 = new TimeSpan(0L);

		public void Test01()
		{
			for (int c = 0; c < 10000; c++)
			{
				if (c % 100 == 0) ProcMain.WriteLog(string.Join(" / ", c, TotalTm1, TotalTm2)); // cout

				Test01_a();
			}
			ProcMain.WriteLog("OK! (TEST-0009-01)");
		}

		private void Test01_a()
		{
			Test01_b(10);
			Test01_b(30);
			Test01_b(100);
			Test01_b(300);
		}

		private void Test01_b(int arrScale)
		{
			Test01_c(arrScale, 10);
			Test01_c(arrScale, 20);
			Test01_c(arrScale, 100);
			Test01_c(arrScale, 300);
		}

		private void Test01_c(int arrScale, int elementKindScale)
		{
			Test01_d(arrScale, elementKindScale, 10);
			Test01_d(arrScale, elementKindScale, 30);
			Test01_d(arrScale, elementKindScale, 100);
			Test01_d(arrScale, elementKindScale, 300);
		}

		private void Test01_d(int arrScale, int elementKindScale, int requiredKindScale)
		{
			int arrLen = SCommon.CRandom.GetRange(1, arrScale);
			int elementKind = SCommon.CRandom.GetRange(1, elementKindScale);
			int requiredKind = SCommon.CRandom.GetRange(1, requiredKindScale);

			int elementMin = SCommon.CRandom.GetRange(-SCommon.IMAX / 2, SCommon.IMAX / 2); // rough range

			int[] arr = SCommon
				.Generate(arrLen, () => elementMin + SCommon.CRandom.GetInt(elementKind))
				.ToArray();

			DateTime stTm = DateTime.Now;
			Range_t ans1 = Test01_e1(arr, requiredKind);
			DateTime mdTm = DateTime.Now;
			Range_t ans2 = Test01_e2(arr, requiredKind);
			DateTime edTm = DateTime.Now;

			TimeSpan tm1 = mdTm - stTm;
			TimeSpan tm2 = edTm - mdTm;

			TotalTm1 += tm1;
			TotalTm2 += tm2;

			if (ans1 == null)
			{
				if (ans2 != null)
					throw null;
			}
			else
			{
				if (
					ans2 == null ||
					ans1.Start != ans2.Start ||
					ans1.End != ans2.End
					)
					throw null;
			}
		}

		private class Range_t
		{
			/// <summary>
			/// 開始位置(最初の要素のインデックス)
			/// </summary>
			public int Start;

			/// <summary>
			/// 終了位置(最後の要素のインデックス+1)
			/// </summary>
			public int End;

			/// <summary>
			/// 要素数
			/// </summary>
			public int Count
			{
				get
				{
					return this.End - this.Start;
				}
			}
		}

		// 乱数列が与えられるので、n種類の値を含む最短の範囲を返せ
		// 複数ある場合は乱数列の先頭に近い方を返すこと。
		// 見つからない場合は null を返すこと。
		// 制約：
		// 1 <= arr.Length
		// 1 <= n

		private Range_t Test01_e1(int[] arr, int n)
		{
			for (int w = n; w <= arr.Length; w++)
			{
				for (int s = 0; s + w <= arr.Length; s++)
				{
					HashSet<int> h = new HashSet<int>();

					for (int i = s; i < s + w; i++)
						h.Add(arr[i]);

					if (n <= h.Count)
						return new Range_t() { Start = s, End = s + w };
				}
			}
			return null;
		}

		private Range_t Test01_e2(int[] arr, int n)
		{
			Dictionary<int, int> d = new Dictionary<int, int>();
			Range_t range = null;
			int l = 0;
			int r = 0;

			for (; ; )
			{
				for (; ; )
				{
					if (arr.Length <= r)
						return range;

					int k = arr[r++];

					if (d.ContainsKey(k))
						d[k]++;
					else
						d.Add(k, 1);

					if (n <= d.Count)
						break;
				}
				for (; ; )
				{
					int k = arr[l++];

					if (--d[k] == 0)
					{
						d.Remove(k);
						break;
					}
				}
				Range_t currRange = new Range_t() { Start = l - 1, End = r };

				if (range == null || range.Count > currRange.Count)
					range = currRange;
			}
		}

		public void Test02()
		{
			for (int c = 0; c < 10000; c++)
			{
				if (c % 100 == 0) ProcMain.WriteLog(string.Join(" / ", c, TotalTm1, TotalTm2)); // cout

				Test02_a();
			}
			ProcMain.WriteLog("OK! (TEST-0009-02)");
		}

		private void Test02_a()
		{
			Test02_b(10);
			Test02_b(30);
			Test02_b(100);
			Test02_b(300);
		}

		private void Test02_b(int arrScale)
		{
			Test02_c(arrScale, 10);
			Test02_c(arrScale, 20);
			Test02_c(arrScale, 100);
			Test02_c(arrScale, 300);
		}

		private void Test02_c(int arrScale, int elementKindScale)
		{
			int arrLen = SCommon.CRandom.GetRange(1, arrScale);
			int elementKind = SCommon.CRandom.GetRange(1, elementKindScale);

			int elementMin = SCommon.CRandom.GetRange(-SCommon.IMAX / 2, SCommon.IMAX / 2); // rough range

			int[] arr = SCommon
				.Generate(arrLen, () => elementMin + SCommon.CRandom.GetInt(elementKind))
				.ToArray();

			DateTime stTm = DateTime.Now;
			Range_t ans1 = Test02_e1(arr);
			DateTime mdTm = DateTime.Now;
			Range_t ans2 = Test02_e2(arr);
			DateTime edTm = DateTime.Now;

			TimeSpan tm1 = mdTm - stTm;
			TimeSpan tm2 = edTm - mdTm;

			TotalTm1 += tm1;
			TotalTm2 += tm2;

			if (
				ans1 == null ||
				ans2 == null ||
				ans1.Start != ans2.Start ||
				ans1.End != ans2.End
				)
				throw null;
		}

		// 乱数列が与えられるので、値が重複しない最長の範囲を返せ
		// 複数ある場合は乱数列の先頭に近い方を返すこと。
		// 制約：
		// 1 <= arr.Length

		private Range_t Test02_e1(int[] arr)
		{
			for (int w = arr.Length; 2 <= w; w--)
			{
				for (int s = 0; s + w <= arr.Length; s++)
				{
					HashSet<int> h = new HashSet<int>();
					bool dupl = false;

					for (int i = s; i < s + w; i++)
					{
						int k = arr[i];

						if (h.Contains(k))
						{
							dupl = true;
							break;
						}
						h.Add(k);
					}
					if (!dupl)
						return new Range_t() { Start = s, End = s + w };
				}
			}
			return new Range_t() { Start = 0, End = 1 };
		}

		private Range_t Test02_e2(int[] arr)
		{
			Dictionary<int, int> d = new Dictionary<int, int>();
			Range_t range = null;
			int l = 0;
			int r = -1;

			for (; ; )
			{
				for (; ; )
				{
					if (arr.Length <= ++r)
						break;

					int k = arr[r];

					if (d.ContainsKey(k))
					{
						if (++d[k] == 2)
							break;
					}
					else
					{
						d.Add(k, 1);
					}
				}
				Range_t currRange = new Range_t() { Start = l, End = r };

				if (range == null || range.Count < currRange.Count)
					range = currRange;

				if (arr.Length <= r)
					return range;

				while (d[arr[l++]]-- != 2) ;
			}
		}
	}
}

2024.9.24　訂正：ウィンドウスライディング ⇒ スライディングウィンドウ

またまたお題が出た

ほにゃ

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Charlotte.Tests
{
	public class Test0011
	{
		public void Test01()
		{
			Test01_a(0.3);
			Test01_a(0.1);
			Test01_a(0.03);
			Test01_a(0.01);
			Test01_a(0.003);
			Test01_a(0.001);
			Test01_a(0.0003);
			Test01_a(0.0001);
			Test01_a(0.00003);
			Test01_a(0.00001);
			Test01_a(0.000003);
			Test01_a(0.000001);
			Test01_a(0.0000003);
			Test01_a(0.0000001);
		}

		private void Test01_a(double gravity)
		{
			double s1 = GetFallDownSpeed(gravity);
			double s2 = GetFreeFallSpeed(gravity);

			Console.WriteLine(string.Format("FD: {0:F9} , FF: {1:F9} , FD / FF: {2:F9} , FDT / FFT: {3:F9} , FDT: {4} , FFT {5}"
				, s1
				, s2
				, s1 / s2
				, FDTime * 1.0 / FFTime
				, FDTime
				, FFTime
				));
		}

		private const double BASE_HI = 100.0;
		//private const double BASE_HI = 150.0;
		//private const double BASE_HI = 200.0;
		//private const double BASE_HI = 250.0;
		//private const double BASE_HI = 300.0;

		private int FDTime;
		private int FFTime;

		private double GetFallDownSpeed(double gravity)
		{
			const double BAR_LENGTH = BASE_HI; // 質量ゼロの棒の先におもりを付けた。棒の長さ

			//const double INIT_ROT = 0.003;
			//const double INIT_ROT = 0.001;
			//const double INIT_ROT = 0.0003;
			//const double INIT_ROT = 0.0001;
			//const double INIT_ROT = 0.00003;
			//const double INIT_ROT = 0.000003;
			//const double INIT_ROT = 0.000001;
			//const double INIT_ROT = 0.0000003;
			const double INIT_ROT = 0.0000001;

			double rot = INIT_ROT;
			double speed = 0.0;

			const double 円周の長さ = BAR_LENGTH * 2.0 * Math.PI;
			const double 壱周の角度 = Math.PI * 2.0;

			for (int t = 0; ; t++)
			{
				double lastRot = rot;
				double lastSpeed = speed;

				double kasokudo = gravity * Math.Sin(rot);
				speed += kasokudo;

				double 移動した角度 = speed * 壱周の角度 / 円周の長さ;
				rot += 移動した角度;

				if (Math.PI / 2.0 <= rot)
				{
					FDTime = t;

					double secchiSpeed = GetSecchiSpeed(lastRot, rot, Math.PI / 2.0, lastSpeed, speed);
					return secchiSpeed;
				}
			}
		}

		private double GetFreeFallSpeed(double gravity)
		{
			const double INIT_HI = BASE_HI;

			double hi = INIT_HI;
			double speed = 0.0;

			for (int t = 0; ; t++)
			{
				double lastHi = hi;
				double lastSpeed = speed;

				speed += gravity;
				hi -= speed;

				if (hi <= 0.0)
				{
					FFTime = t;

					double secchiSpeed = GetSecchiSpeed(lastHi, hi, 0.0, lastSpeed, speed);
					return secchiSpeed;
				}
			}
		}

		private double GetSecchiSpeed(double lastPos, double currPos, double targetPos, double lastSpeed, double currSpeed)
		{
			double diffPos = currPos - lastPos;
			double diffSpeed = currSpeed - lastSpeed;
			double targetDiffPos = targetPos - lastPos;
			double targetDiffSpeed = diffSpeed * targetDiffPos / diffPos;
			double targetSpeed = lastSpeed + targetDiffSpeed;
			return targetSpeed;
		}
	}
}

出力

FD: 7.595323533 , FF: 7.596153846 , FD / FF: 0.999890693 , FDT / FFT: 12.600000000 , FDT: 315 , FFT 25
FD: 4.422122333 , FF: 4.422222222 , FD / FF: 0.999977412 , FDT / FFT: 12.431818182 , FDT: 547 , FFT 44
FD: 2.434470125 , FF: 2.434512195 , FD / FF: 0.999982719 , FDT / FFT: 12.333333333 , FDT: 999 , FFT 81
FD: 1.409212693 , FF: 1.409219858 , FD / FF: 0.999994916 , FDT / FFT: 12.364285714 , FDT: 1731 , FFT 140
FD: 0.773097090 , FF: 0.773096899 , FD / FF: 1.000000247 , FDT / FFT: 12.295719844 , FDT: 3160 , FFT 257
FD: 0.446713434 , FF: 0.446713647 , FD / FF: 0.999999524 , FDT / FFT: 12.275784753 , FDT: 5475 , FFT 446
FD: 0.244798988 , FF: 0.244799020 , FD / FF: 0.999999872 , FDT / FFT: 12.265030675 , FDT: 9996 , FFT 815
FD: 0.141371351 , FF: 0.141371358 , FD / FF: 0.999999954 , FDT / FFT: 12.254069356 , FDT: 17315 , FFT 1413
FD: 0.077444666 , FF: 0.077444667 , FD / FF: 0.999999989 , FDT / FFT: 12.248740798 , FDT: 31614 , FFT 2581
FD: 0.044716360 , FF: 0.044716360 , FD / FF: 1.000000001 , FDT / FFT: 12.247371953 , FDT: 54758 , FFT 4471
FD: 0.024493397 , FF: 0.024493397 , FD / FF: 0.999999999 , FDT / FFT: 12.245712886 , FDT: 99974 , FFT 8164
FD: 0.014141636 , FF: 0.014141636 , FD / FF: 1.000000000 , FDT / FFT: 12.245315041 , FDT: 173161 , FFT 14141
FD: 0.007745817 , FF: 0.007745817 , FD / FF: 1.000000000 , FDT / FFT: 12.244742244 , FDT: 316147 , FFT 25819
FD: 0.004472086 , FF: 0.004472086 , FD / FF: 1.000000000 , FDT / FFT: 12.244722719 , FDT: 547584 , FFT 44720


ふぬん

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Charlotte.Tests
{
	public class Test0012
	{
		public void Test01()
		{
			//Test01_a(0.001);
			//Test01_a(0.01);
			Test01_a(0.1);
			Test01_a(0.2);
			Test01_a(0.25);
			Test01_a(0.3);
			Test01_a(0.333333333);
			Test01_a(0.4);
			Test01_a(0.5);
			Test01_a(0.6);
			Test01_a(0.666666666);
			Test01_a(0.7);
			Test01_a(0.75);
			Test01_a(0.8);
			Test01_a(0.9);
			Test01_a(1.0);
		}

		private void Test01_a(double barGravCntr)
		{
			const double DEGREE_TO_RADIAN = Math.PI / 180.0;

			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 66.6666666);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 60.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 50.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 45.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 40.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 33.3333333);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 30.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 25.758);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 20.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 10.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 5.0);
			Test01_b(barGravCntr, DEGREE_TO_RADIAN * 1.0);
			Test01_b(barGravCntr, 0.0000001);
		}

		private void Test01_b(double barGravCntr, double barInitRot)
		{
			//Test01_c(barGravCntr, barInitRot, 0.3);
			//Test01_c(barGravCntr, barInitRot, 0.1);
			//Test01_c(barGravCntr, barInitRot, 0.03);
			//Test01_c(barGravCntr, barInitRot, 0.01);
			//Test01_c(barGravCntr, barInitRot, 0.003);
			//Test01_c(barGravCntr, barInitRot, 0.001);
			//Test01_c(barGravCntr, barInitRot, 0.0003);
			//Test01_c(barGravCntr, barInitRot, 0.0001);
			//Test01_c(barGravCntr, barInitRot, 0.00003);
			//Test01_c(barGravCntr, barInitRot, 0.00001);
			//Test01_c(barGravCntr, barInitRot, 0.000003);
			//Test01_c(barGravCntr, barInitRot, 0.000001);
			//Test01_c(barGravCntr, barInitRot, 0.0000003);
			Test01_c(barGravCntr, barInitRot, 0.0000001);
		}

		private void Test01_c(double barGravCntr, double barInitRot, double gravity)
		{
			double s1 = GetFallDownSpeed(gravity, barGravCntr, barInitRot);
			double s2 = GetFreeFallSpeed(gravity);

			Console.WriteLine(string.Format("FD: {0:F9} , FF: {1:F9} , FD / FF: {2:F9} , FDT / FFT: {3:F9} , FDT: {4} , FFT: {5} , BGC: {6:F3} , BIR: {7:F7} ({8:F3})"
				, s1
				, s2
				, s1 / s2
				, FDTime * 1.0 / FFTime
				, FDTime
				, FFTime
				, barGravCntr
				, barInitRot
				, barInitRot / Math.PI * 180.0
				));
		}

		//private const double BASE_HI = 100.0;
		//private const double BASE_HI = 150.0;
		//private const double BASE_HI = 200.0;
		//private const double BASE_HI = 250.0;
		private const double BASE_HI = 300.0;

		private int FDTime;
		private int FFTime;

		private double GetFallDownSpeed(double gravity, double barGravCntr, double barInitRot)
		{
			const double BAR_LENGTH = BASE_HI;

			// 質量ゼロの棒のどこかに重りを付けたという体。
			double 重りまでの長さ = BAR_LENGTH * barGravCntr;

			double rot = barInitRot;
			double speed = 0.0;

			double 円周の長さ = 重りまでの長さ * 2.0 * Math.PI;
			double 壱周の角度 = Math.PI * 2.0;

			for (int t = 0; ; t++)
			{
				double lastRot = rot;
				double lastSpeed = speed;

				double kasokudo = gravity * Math.Sin(rot);
				speed += kasokudo;

				double 移動した角度 = speed * 壱周の角度 / 円周の長さ;
				rot += 移動した角度;

				if (Math.PI / 2.0 <= rot)
				{
					FDTime = t;

					double secchiSpeed = GetSecchiSpeed(lastRot, rot, Math.PI / 2.0, lastSpeed, speed);

					secchiSpeed /= barGravCntr; // 重心の速度 ⇒ 先端の速度

					return secchiSpeed;
				}
			}
		}

		private double GetFreeFallSpeed(double gravity)
		{
			const double INIT_HI = BASE_HI;

			double hi = INIT_HI;
			double speed = 0.0;

			for (int t = 0; ; t++)
			{
				double lastHi = hi;
				double lastSpeed = speed;

				speed += gravity;
				hi -= speed;

				if (hi <= 0.0)
				{
					FFTime = t;

					double secchiSpeed = GetSecchiSpeed(lastHi, hi, 0.0, lastSpeed, speed);
					return secchiSpeed;
				}
			}
		}

		private double GetSecchiSpeed(double lastPos, double currPos, double targetPos, double lastSpeed, double currSpeed)
		{
			double diffPos = currPos - lastPos;
			double diffSpeed = currSpeed - lastSpeed;
			double targetDiffPos = targetPos - lastPos;
			double targetDiffSpeed = diffSpeed * targetDiffPos / diffPos;
			double targetSpeed = lastSpeed + targetDiffSpeed;
			return targetSpeed;
		}
	}
}

出力

FD: 0.015415331 , FF: 0.007745917 , FD / FF: 1.990123583 , FDT / FFT: 0.208174647 , FDT: 16125 , FFT: 77459 , BGC: 0.100 , BIR: 1.1635528 (66.667)
FD: 0.017320008 , FF: 0.007745917 , FD / FF: 2.236017861 , FDT / FFT: 0.241095289 , FDT: 18675 , FFT: 77459 , BGC: 0.100 , BIR: 1.0471976 (60.000)
FD: 0.019638048 , FF: 0.007745917 , FD / FF: 2.535277454 , FDT / FFT: 0.290876464 , FDT: 22531 , FFT: 77459 , BGC: 0.100 , BIR: 0.8726646 (50.000)
FD: 0.020597171 , FF: 0.007745917 , FD / FF: 2.659100563 , FDT / FFT: 0.317354988 , FDT: 24582 , FFT: 77459 , BGC: 0.100 , BIR: 0.7853982 (45.000)
FD: 0.021438405 , FF: 0.007745917 , FD / FF: 2.767704105 , FDT / FFT: 0.345834571 , FDT: 26788 , FFT: 77459 , BGC: 0.100 , BIR: 0.6981317 (40.000)
FD: 0.022389066 , FF: 0.007745917 , FD / FF: 2.890434711 , FDT / FFT: 0.388476484 , FDT: 30091 , FFT: 77459 , BGC: 0.100 , BIR: 0.5817764 (33.333)
FD: 0.022794571 , FF: 0.007745917 , FD / FF: 2.942785402 , FDT / FFT: 0.412631198 , FDT: 31962 , FFT: 77459 , BGC: 0.100 , BIR: 0.5235988 (30.000)
FD: 0.023245630 , FF: 0.007745917 , FD / FF: 3.001017251 , FDT / FFT: 0.447204327 , FDT: 34640 , FFT: 77459 , BGC: 0.100 , BIR: 0.4495619 (25.758)
FD: 0.023744301 , FF: 0.007745917 , FD / FF: 3.065395859 , FDT / FFT: 0.504034392 , FDT: 39042 , FFT: 77459 , BGC: 0.100 , BIR: 0.3490659 (20.000)
FD: 0.024307619 , FF: 0.007745917 , FD / FF: 3.138120382 , FDT / FFT: 0.658735589 , FDT: 51025 , FFT: 77459 , BGC: 0.100 , BIR: 0.1745329 (10.000)
FD: 0.024447748 , FF: 0.007745917 , FD / FF: 3.156211038 , FDT / FFT: 0.813423876 , FDT: 63007 , FFT: 77459 , BGC: 0.100 , BIR: 0.0872665 (5.000)
FD: 0.024492532 , FF: 0.007745917 , FD / FF: 3.161992697 , FDT / FFT: 1.173123846 , FDT: 90869 , FFT: 77459 , BGC: 0.100 , BIR: 0.0174533 (1.000)
FD: 0.024494397 , FF: 0.007745917 , FD / FF: 3.162233522 , FDT / FFT: 3.872035528 , FDT: 299924 , FFT: 77459 , BGC: 0.100 , BIR: 0.0000001 (0.000)
FD: 0.010900389 , FF: 0.007745917 , FD / FF: 1.407243250 , FDT / FFT: 0.294400909 , FDT: 22804 , FFT: 77459 , BGC: 0.200 , BIR: 1.1635528 (66.667)
FD: 0.012247199 , FF: 0.007745917 , FD / FF: 1.581116761 , FDT / FFT: 0.340967480 , FDT: 26411 , FFT: 77459 , BGC: 0.200 , BIR: 1.0471976 (60.000)
FD: 0.013886300 , FF: 0.007745917 , FD / FF: 1.792725249 , FDT / FFT: 0.411366013 , FDT: 31864 , FFT: 77459 , BGC: 0.200 , BIR: 0.8726646 (50.000)
FD: 0.014564503 , FF: 0.007745917 , FD / FF: 1.880281409 , FDT / FFT: 0.448818084 , FDT: 34765 , FFT: 77459 , BGC: 0.200 , BIR: 0.7853982 (45.000)
FD: 0.015159345 , FF: 0.007745917 , FD / FF: 1.957075710 , FDT / FFT: 0.489084548 , FDT: 37884 , FFT: 77459 , BGC: 0.200 , BIR: 0.6981317 (40.000)
FD: 0.015831564 , FF: 0.007745917 , FD / FF: 2.043859354 , FDT / FFT: 0.549387418 , FDT: 42555 , FFT: 77459 , BGC: 0.200 , BIR: 0.5817764 (33.333)
FD: 0.016118299 , FF: 0.007745917 , FD / FF: 2.080876882 , FDT / FFT: 0.583547425 , FDT: 45201 , FFT: 77459 , BGC: 0.200 , BIR: 0.5235988 (30.000)
FD: 0.016437246 , FF: 0.007745917 , FD / FF: 2.122053018 , FDT / FFT: 0.632450716 , FDT: 48989 , FFT: 77459 , BGC: 0.200 , BIR: 0.4495619 (25.758)
FD: 0.016789860 , FF: 0.007745917 , FD / FF: 2.167575568 , FDT / FFT: 0.712815812 , FDT: 55214 , FFT: 77459 , BGC: 0.200 , BIR: 0.3490659 (20.000)
FD: 0.017188186 , FF: 0.007745917 , FD / FF: 2.218999571 , FDT / FFT: 0.931589615 , FDT: 72160 , FFT: 77459 , BGC: 0.200 , BIR: 0.1745329 (10.000)
FD: 0.017287272 , FF: 0.007745917 , FD / FF: 2.231791597 , FDT / FFT: 1.150350508 , FDT: 89105 , FFT: 77459 , BGC: 0.200 , BIR: 0.0872665 (5.000)
FD: 0.017318939 , FF: 0.007745917 , FD / FF: 2.235879847 , FDT / FFT: 1.659045430 , FDT: 128508 , FFT: 77459 , BGC: 0.200 , BIR: 0.0174533 (1.000)
FD: 0.017320258 , FF: 0.007745917 , FD / FF: 2.236050136 , FDT / FFT: 5.475890471 , FDT: 424157 , FFT: 77459 , BGC: 0.200 , BIR: 0.0000001 (0.000)
FD: 0.009749628 , FF: 0.007745917 , FD / FF: 1.258679674 , FDT / FFT: 0.329154779 , FDT: 25496 , FFT: 77459 , BGC: 0.250 , BIR: 1.1635528 (66.667)
FD: 0.010954251 , FF: 0.007745917 , FD / FF: 1.414196871 , FDT / FFT: 0.381208123 , FDT: 29528 , FFT: 77459 , BGC: 0.250 , BIR: 1.0471976 (60.000)
FD: 0.012420308 , FF: 0.007745917 , FD / FF: 1.603465256 , FDT / FFT: 0.459920732 , FDT: 35625 , FFT: 77459 , BGC: 0.250 , BIR: 0.8726646 (50.000)
FD: 0.013026911 , FF: 0.007745917 , FD / FF: 1.681777866 , FDT / FFT: 0.501800953 , FDT: 38869 , FFT: 77459 , BGC: 0.250 , BIR: 0.7853982 (45.000)
FD: 0.013558954 , FF: 0.007745917 , FD / FF: 1.750464777 , FDT / FFT: 0.546818317 , FDT: 42356 , FFT: 77459 , BGC: 0.250 , BIR: 0.6981317 (40.000)
FD: 0.014160205 , FF: 0.007745917 , FD / FF: 1.828086428 , FDT / FFT: 0.614247537 , FDT: 47579 , FFT: 77459 , BGC: 0.250 , BIR: 0.5817764 (33.333)
FD: 0.014416668 , FF: 0.007745917 , FD / FF: 1.861195912 , FDT / FFT: 0.652435482 , FDT: 50537 , FFT: 77459 , BGC: 0.250 , BIR: 0.5235988 (30.000)
FD: 0.014701943 , FF: 0.007745917 , FD / FF: 1.898024967 , FDT / FFT: 0.707096658 , FDT: 54771 , FFT: 77459 , BGC: 0.250 , BIR: 0.4495619 (25.758)
FD: 0.015017331 , FF: 0.007745917 , FD / FF: 1.938741574 , FDT / FFT: 0.796950645 , FDT: 61731 , FFT: 77459 , BGC: 0.250 , BIR: 0.3490659 (20.000)
FD: 0.015373604 , FF: 0.007745917 , FD / FF: 1.984736601 , FDT / FFT: 1.041557469 , FDT: 80678 , FFT: 77459 , BGC: 0.250 , BIR: 0.1745329 (10.000)
FD: 0.015462230 , FF: 0.007745917 , FD / FF: 1.996178136 , FDT / FFT: 1.286138473 , FDT: 99623 , FFT: 77459 , BGC: 0.250 , BIR: 0.0872665 (5.000)
FD: 0.015490554 , FF: 0.007745917 , FD / FF: 1.999834778 , FDT / FFT: 1.854878065 , FDT: 143677 , FFT: 77459 , BGC: 0.250 , BIR: 0.0174533 (1.000)
FD: 0.015491733 , FF: 0.007745917 , FD / FF: 1.999987090 , FDT / FFT: 6.122232407 , FDT: 474222 , FFT: 77459 , BGC: 0.250 , BIR: 0.0000001 (0.000)
FD: 0.008900168 , FF: 0.007745917 , FD / FF: 1.149014138 , FDT / FFT: 0.360577854 , FDT: 27930 , FFT: 77459 , BGC: 0.300 , BIR: 1.1635528 (66.667)
FD: 0.009999833 , FF: 0.007745917 , FD / FF: 1.290981265 , FDT / FFT: 0.417601570 , FDT: 32347 , FFT: 77459 , BGC: 0.300 , BIR: 1.0471976 (60.000)
FD: 0.011338154 , FF: 0.007745917 , FD / FF: 1.463758872 , FDT / FFT: 0.503814921 , FDT: 39025 , FFT: 77459 , BGC: 0.300 , BIR: 0.8726646 (50.000)
FD: 0.011891904 , FF: 0.007745917 , FD / FF: 1.535248177 , FDT / FFT: 0.549697259 , FDT: 42579 , FFT: 77459 , BGC: 0.300 , BIR: 0.7853982 (45.000)
FD: 0.012377591 , FF: 0.007745917 , FD / FF: 1.597950461 , FDT / FFT: 0.599013672 , FDT: 46399 , FFT: 77459 , BGC: 0.300 , BIR: 0.6981317 (40.000)
FD: 0.012926456 , FF: 0.007745917 , FD / FF: 1.668809010 , FDT / FFT: 0.672872100 , FDT: 52120 , FFT: 77459 , BGC: 0.300 , BIR: 0.5817764 (33.333)
FD: 0.013160573 , FF: 0.007745917 , FD / FF: 1.699033695 , FDT / FFT: 0.714700680 , FDT: 55360 , FFT: 77459 , BGC: 0.300 , BIR: 0.5235988 (30.000)
FD: 0.013420993 , FF: 0.007745917 , FD / FF: 1.732653869 , FDT / FFT: 0.774590428 , FDT: 59999 , FFT: 77459 , BGC: 0.300 , BIR: 0.4495619 (25.758)
FD: 0.013708901 , FF: 0.007745917 , FD / FF: 1.769822876 , FDT / FFT: 0.873029603 , FDT: 67624 , FFT: 77459 , BGC: 0.300 , BIR: 0.3490659 (20.000)
FD: 0.014034132 , FF: 0.007745917 , FD / FF: 1.811810399 , FDT / FFT: 1.140964898 , FDT: 88378 , FFT: 77459 , BGC: 0.300 , BIR: 0.1745329 (10.000)
FD: 0.014115036 , FF: 0.007745917 , FD / FF: 1.822255044 , FDT / FFT: 1.408900192 , FDT: 109132 , FFT: 77459 , BGC: 0.300 , BIR: 0.0872665 (5.000)
FD: 0.014140892 , FF: 0.007745917 , FD / FF: 1.825593086 , FDT / FFT: 2.031913658 , FDT: 157390 , FFT: 77459 , BGC: 0.300 , BIR: 0.0174533 (1.000)
FD: 0.014141969 , FF: 0.007745917 , FD / FF: 1.825732127 , FDT / FFT: 6.706567345 , FDT: 519484 , FFT: 77459 , BGC: 0.300 , BIR: 0.0000001 (0.000)
FD: 0.008443449 , FF: 0.007745917 , FD / FF: 1.090051570 , FDT / FFT: 0.380084948 , FDT: 29441 , FFT: 77459 , BGC: 0.333 , BIR: 1.1635528 (66.667)
FD: 0.009486683 , FF: 0.007745917 , FD / FF: 1.224733413 , FDT / FFT: 0.440194167 , FDT: 34097 , FFT: 77459 , BGC: 0.333 , BIR: 1.0471976 (60.000)
FD: 0.010756326 , FF: 0.007745917 , FD / FF: 1.388644643 , FDT / FFT: 0.531080959 , FDT: 41137 , FFT: 77459 , BGC: 0.333 , BIR: 0.8726646 (50.000)
FD: 0.011281659 , FF: 0.007745917 , FD / FF: 1.456465352 , FDT / FFT: 0.579429117 , FDT: 44882 , FFT: 77459 , BGC: 0.333 , BIR: 0.7853982 (45.000)
FD: 0.011742422 , FF: 0.007745917 , FD / FF: 1.515949962 , FDT / FFT: 0.631417911 , FDT: 48909 , FFT: 77459 , BGC: 0.333 , BIR: 0.6981317 (40.000)
FD: 0.012263121 , FF: 0.007745917 , FD / FF: 1.583172284 , FDT / FFT: 0.709265547 , FDT: 54939 , FFT: 77459 , BGC: 0.333 , BIR: 0.5817764 (33.333)
FD: 0.012485224 , FF: 0.007745917 , FD / FF: 1.611845938 , FDT / FFT: 0.753366297 , FDT: 58355 , FFT: 77459 , BGC: 0.333 , BIR: 0.5235988 (30.000)
FD: 0.012732280 , FF: 0.007745917 , FD / FF: 1.643740835 , FDT / FFT: 0.816483559 , FDT: 63244 , FFT: 77459 , BGC: 0.333 , BIR: 0.4495619 (25.758)
FD: 0.013005413 , FF: 0.007745917 , FD / FF: 1.679002451 , FDT / FFT: 0.920254586 , FDT: 71282 , FFT: 77459 , BGC: 0.333 , BIR: 0.3490659 (20.000)
FD: 0.013313955 , FF: 0.007745917 , FD / FF: 1.718835313 , FDT / FFT: 1.202687874 , FDT: 93159 , FFT: 77459 , BGC: 0.333 , BIR: 0.1745329 (10.000)
FD: 0.013390707 , FF: 0.007745917 , FD / FF: 1.728743973 , FDT / FFT: 1.485108251 , FDT: 115035 , FFT: 77459 , BGC: 0.333 , BIR: 0.0872665 (5.000)
FD: 0.013415236 , FF: 0.007745917 , FD / FF: 1.731910718 , FDT / FFT: 2.141829871 , FDT: 165904 , FFT: 77459 , BGC: 0.333 , BIR: 0.0174533 (1.000)
FD: 0.013416258 , FF: 0.007745917 , FD / FF: 1.732042624 , FDT / FFT: 7.069339909 , FDT: 547584 , FFT: 77459 , BGC: 0.333 , BIR: 0.0000001 (0.000)
FD: 0.007707791 , FF: 0.007745917 , FD / FF: 0.995077929 , FDT / FFT: 0.416362205 , FDT: 32251 , FFT: 77459 , BGC: 0.400 , BIR: 1.1635528 (66.667)
FD: 0.008660129 , FF: 0.007745917 , FD / FF: 1.118025068 , FDT / FFT: 0.482203488 , FDT: 37351 , FFT: 77459 , BGC: 0.400 , BIR: 1.0471976 (60.000)
FD: 0.009819149 , FF: 0.007745917 , FD / FF: 1.267654865 , FDT / FFT: 0.581765837 , FDT: 45063 , FFT: 77459 , BGC: 0.400 , BIR: 0.8726646 (50.000)
FD: 0.010298711 , FF: 0.007745917 , FD / FF: 1.329566419 , FDT / FFT: 0.634735796 , FDT: 49166 , FFT: 77459 , BGC: 0.400 , BIR: 0.7853982 (45.000)
FD: 0.010719328 , FF: 0.007745917 , FD / FF: 1.383868190 , FDT / FFT: 0.691682051 , FDT: 53577 , FFT: 77459 , BGC: 0.400 , BIR: 0.6981317 (40.000)
FD: 0.011194658 , FF: 0.007745917 , FD / FF: 1.445233493 , FDT / FFT: 0.776965879 , FDT: 60183 , FFT: 77459 , BGC: 0.400 , BIR: 0.5817764 (33.333)
FD: 0.011397410 , FF: 0.007745917 , FD / FF: 1.471408839 , FDT / FFT: 0.825275307 , FDT: 63925 , FFT: 77459 , BGC: 0.400 , BIR: 0.5235988 (30.000)
FD: 0.011622940 , FF: 0.007745917 , FD / FF: 1.500524763 , FDT / FFT: 0.894421565 , FDT: 69281 , FFT: 77459 , BGC: 0.400 , BIR: 0.4495619 (25.758)
FD: 0.011872275 , FF: 0.007745917 , FD / FF: 1.532714067 , FDT / FFT: 1.008081695 , FDT: 78085 , FFT: 77459 , BGC: 0.400 , BIR: 0.3490659 (20.000)
FD: 0.012153935 , FF: 0.007745917 , FD / FF: 1.569076329 , FDT / FFT: 1.317484088 , FDT: 102051 , FFT: 77459 , BGC: 0.400 , BIR: 0.1745329 (10.000)
FD: 0.012223999 , FF: 0.007745917 , FD / FF: 1.578121657 , FDT / FFT: 1.626860662 , FDT: 126015 , FFT: 77459 , BGC: 0.400 , BIR: 0.0872665 (5.000)
FD: 0.012246391 , FF: 0.007745917 , FD / FF: 1.581012486 , FDT / FFT: 2.346247692 , FDT: 181738 , FFT: 77459 , BGC: 0.400 , BIR: 0.0174533 (1.000)
FD: 0.012247324 , FF: 0.007745917 , FD / FF: 1.581132899 , FDT / FFT: 7.744083967 , FDT: 599849 , FFT: 77459 , BGC: 0.400 , BIR: 0.0000001 (0.000)
FD: 0.006894069 , FF: 0.007745917 , FD / FF: 0.890026281 , FDT / FFT: 0.465497876 , FDT: 36057 , FFT: 77459 , BGC: 0.500 , BIR: 1.1635528 (66.667)
FD: 0.007745867 , FF: 0.007745917 , FD / FF: 0.999993545 , FDT / FFT: 0.539123924 , FDT: 41760 , FFT: 77459 , BGC: 0.500 , BIR: 1.0471976 (60.000)
FD: 0.008782526 , FF: 0.007745917 , FD / FF: 1.133826504 , FDT / FFT: 0.650434423 , FDT: 50382 , FFT: 77459 , BGC: 0.500 , BIR: 0.8726646 (50.000)
FD: 0.009211459 , FF: 0.007745917 , FD / FF: 1.189201881 , FDT / FFT: 0.709652849 , FDT: 54969 , FFT: 77459 , BGC: 0.500 , BIR: 0.7853982 (45.000)
FD: 0.009587670 , FF: 0.007745917 , FD / FF: 1.237770862 , FDT / FFT: 0.773325243 , FDT: 59901 , FFT: 77459 , BGC: 0.500 , BIR: 0.6981317 (40.000)
FD: 0.010012819 , FF: 0.007745917 , FD / FF: 1.292657657 , FDT / FFT: 0.868678914 , FDT: 67287 , FFT: 77459 , BGC: 0.500 , BIR: 0.5817764 (33.333)
FD: 0.010194165 , FF: 0.007745917 , FD / FF: 1.316069598 , FDT / FFT: 0.922681677 , FDT: 71470 , FFT: 77459 , BGC: 0.500 , BIR: 0.5235988 (30.000)
FD: 0.010395885 , FF: 0.007745917 , FD / FF: 1.342111673 , FDT / FFT: 0.999987090 , FDT: 77458 , FFT: 77459 , BGC: 0.500 , BIR: 0.4495619 (25.758)
FD: 0.010618898 , FF: 0.007745917 , FD / FF: 1.370902662 , FDT / FFT: 1.127073678 , FDT: 87302 , FFT: 77459 , BGC: 0.500 , BIR: 0.3490659 (20.000)
FD: 0.010870821 , FF: 0.007745917 , FD / FF: 1.403426057 , FDT / FFT: 1.472985709 , FDT: 114096 , FFT: 77459 , BGC: 0.500 , BIR: 0.1745329 (10.000)
FD: 0.010933489 , FF: 0.007745917 , FD / FF: 1.411516444 , FDT / FFT: 1.818884829 , FDT: 140889 , FFT: 77459 , BGC: 0.500 , BIR: 0.0872665 (5.000)
FD: 0.010953517 , FF: 0.007745917 , FD / FF: 1.414102080 , FDT / FFT: 2.623194206 , FDT: 203190 , FFT: 77459 , BGC: 0.500 , BIR: 0.0174533 (1.000)
FD: 0.010954351 , FF: 0.007745917 , FD / FF: 1.414209781 , FDT / FFT: 8.658141727 , FDT: 670651 , FFT: 77459 , BGC: 0.500 , BIR: 0.0000001 (0.000)
FD: 0.006293404 , FF: 0.007745917 , FD / FF: 0.812480145 , FDT / FFT: 0.509934288 , FDT: 39499 , FFT: 77459 , BGC: 0.600 , BIR: 1.1635528 (66.667)
FD: 0.007070984 , FF: 0.007745917 , FD / FF: 0.912866063 , FDT / FFT: 0.590583405 , FDT: 45746 , FFT: 77459 , BGC: 0.600 , BIR: 1.0471976 (60.000)
FD: 0.008017320 , FF: 0.007745917 , FD / FF: 1.035038281 , FDT / FFT: 0.712518881 , FDT: 55191 , FFT: 77459 , BGC: 0.600 , BIR: 0.8726646 (50.000)
FD: 0.008408881 , FF: 0.007745917 , FD / FF: 1.085588853 , FDT / FFT: 0.777391911 , FDT: 60216 , FFT: 77459 , BGC: 0.600 , BIR: 0.7853982 (45.000)
FD: 0.008752313 , FF: 0.007745917 , FD / FF: 1.129926063 , FDT / FFT: 0.847132031 , FDT: 65618 , FFT: 77459 , BGC: 0.600 , BIR: 0.6981317 (40.000)
FD: 0.009140419 , FF: 0.007745917 , FD / FF: 1.180030624 , FDT / FFT: 0.951587291 , FDT: 73709 , FFT: 77459 , BGC: 0.600 , BIR: 0.5817764 (33.333)
FD: 0.009305965 , FF: 0.007745917 , FD / FF: 1.201402704 , FDT / FFT: 1.010754076 , FDT: 78292 , FFT: 77459 , BGC: 0.600 , BIR: 0.5235988 (30.000)
FD: 0.009490109 , FF: 0.007745917 , FD / FF: 1.225175757 , FDT / FFT: 1.095431131 , FDT: 84851 , FFT: 77459 , BGC: 0.600 , BIR: 0.4495619 (25.758)
FD: 0.009693691 , FF: 0.007745917 , FD / FF: 1.251458213 , FDT / FFT: 1.234653171 , FDT: 95635 , FFT: 77459 , BGC: 0.600 , BIR: 0.3490659 (20.000)
FD: 0.009923665 , FF: 0.007745917 , FD / FF: 1.281147875 , FDT / FFT: 1.613576215 , FDT: 124986 , FFT: 77459 , BGC: 0.600 , BIR: 0.1745329 (10.000)
FD: 0.009980872 , FF: 0.007745917 , FD / FF: 1.288533355 , FDT / FFT: 1.992486348 , FDT: 154336 , FFT: 77459 , BGC: 0.600 , BIR: 0.0872665 (5.000)
FD: 0.009999155 , FF: 0.007745917 , FD / FF: 1.290893707 , FDT / FFT: 2.873558915 , FDT: 222583 , FFT: 77459 , BGC: 0.600 , BIR: 0.0174533 (1.000)
FD: 0.009999917 , FF: 0.007745917 , FD / FF: 1.290992024 , FDT / FFT: 9.484527298 , FDT: 734662 , FFT: 77459 , BGC: 0.600 , BIR: 0.0000001 (0.000)
FD: 0.005970451 , FF: 0.007745917 , FD / FF: 0.770786867 , FDT / FFT: 0.537523077 , FDT: 41636 , FFT: 77459 , BGC: 0.667 , BIR: 1.1635528 (66.667)
FD: 0.006708129 , FF: 0.007745917 , FD / FF: 0.866021312 , FDT / FFT: 0.622522883 , FDT: 48220 , FFT: 77459 , BGC: 0.667 , BIR: 1.0471976 (60.000)
FD: 0.007605902 , FF: 0.007745917 , FD / FF: 0.981924054 , FDT / FFT: 0.751055397 , FDT: 58176 , FFT: 77459 , BGC: 0.667 , BIR: 0.8726646 (50.000)
FD: 0.007977369 , FF: 0.007745917 , FD / FF: 1.029880538 , FDT / FFT: 0.819439962 , FDT: 63473 , FFT: 77459 , BGC: 0.667 , BIR: 0.7853982 (45.000)
FD: 0.008303177 , FF: 0.007745917 , FD / FF: 1.071942509 , FDT / FFT: 0.892962729 , FDT: 69168 , FFT: 77459 , BGC: 0.667 , BIR: 0.6981317 (40.000)
FD: 0.008671367 , FF: 0.007745917 , FD / FF: 1.119475868 , FDT / FFT: 1.003059683 , FDT: 77696 , FFT: 77459 , BGC: 0.667 , BIR: 0.5817764 (33.333)
FD: 0.008828418 , FF: 0.007745917 , FD / FF: 1.139751204 , FDT / FFT: 1.065428162 , FDT: 82527 , FFT: 77459 , BGC: 0.667 , BIR: 0.5235988 (30.000)
FD: 0.009003112 , FF: 0.007745917 , FD / FF: 1.162304302 , FDT / FFT: 1.154688287 , FDT: 89441 , FFT: 77459 , BGC: 0.667 , BIR: 0.4495619 (25.758)
FD: 0.009196247 , FF: 0.007745917 , FD / FF: 1.187238030 , FDT / FFT: 1.301436889 , FDT: 100808 , FFT: 77459 , BGC: 0.667 , BIR: 0.3490659 (20.000)
FD: 0.009414419 , FF: 0.007745917 , FD / FF: 1.215404116 , FDT / FFT: 1.700861101 , FDT: 131747 , FFT: 77459 , BGC: 0.667 , BIR: 0.1745329 (10.000)
FD: 0.009468691 , FF: 0.007745917 , FD / FF: 1.222410597 , FDT / FFT: 2.100259492 , FDT: 162684 , FFT: 77459 , BGC: 0.667 , BIR: 0.0872665 (5.000)
FD: 0.009486036 , FF: 0.007745917 , FD / FF: 1.224649824 , FDT / FFT: 3.028995985 , FDT: 234623 , FFT: 77459 , BGC: 0.667 , BIR: 0.0174533 (1.000)
FD: 0.009486758 , FF: 0.007745917 , FD / FF: 1.224743095 , FDT / FFT: 9.997559999 , FDT: 774401 , FFT: 77459 , BGC: 0.667 , BIR: 0.0000001 (0.000)
FD: 0.005826565 , FF: 0.007745917 , FD / FF: 0.752211187 , FDT / FFT: 0.550794614 , FDT: 42664 , FFT: 77459 , BGC: 0.700 , BIR: 1.1635528 (66.667)
FD: 0.006546465 , FF: 0.007745917 , FD / FF: 0.845150489 , FDT / FFT: 0.637898759 , FDT: 49411 , FFT: 77459 , BGC: 0.700 , BIR: 1.0471976 (60.000)
FD: 0.007422602 , FF: 0.007745917 , FD / FF: 0.958259983 , FDT / FFT: 0.769607147 , FDT: 59613 , FFT: 77459 , BGC: 0.700 , BIR: 0.8726646 (50.000)
FD: 0.007785117 , FF: 0.007745917 , FD / FF: 1.005060719 , FDT / FFT: 0.839670019 , FDT: 65040 , FFT: 77459 , BGC: 0.700 , BIR: 0.7853982 (45.000)
FD: 0.008103073 , FF: 0.007745917 , FD / FF: 1.046109000 , FDT / FFT: 0.915013104 , FDT: 70876 , FFT: 77459 , BGC: 0.700 , BIR: 0.6981317 (40.000)
FD: 0.008462389 , FF: 0.007745917 , FD / FF: 1.092496809 , FDT / FFT: 1.027834080 , FDT: 79615 , FFT: 77459 , BGC: 0.700 , BIR: 0.5817764 (33.333)
FD: 0.008615655 , FF: 0.007745917 , FD / FF: 1.112283510 , FDT / FFT: 1.091738855 , FDT: 84565 , FFT: 77459 , BGC: 0.700 , BIR: 0.5235988 (30.000)
FD: 0.008786140 , FF: 0.007745917 , FD / FF: 1.134293080 , FDT / FFT: 1.183206600 , FDT: 91650 , FFT: 77459 , BGC: 0.700 , BIR: 0.4495619 (25.758)
FD: 0.008974620 , FF: 0.007745917 , FD / FF: 1.158625907 , FDT / FFT: 1.333570018 , FDT: 103297 , FFT: 77459 , BGC: 0.700 , BIR: 0.3490659 (20.000)
FD: 0.009187534 , FF: 0.007745917 , FD / FF: 1.186113193 , FDT / FFT: 1.742870422 , FDT: 135001 , FFT: 77459 , BGC: 0.700 , BIR: 0.1745329 (10.000)
FD: 0.009240498 , FF: 0.007745917 , FD / FF: 1.192950818 , FDT / FFT: 2.152132096 , FDT: 166702 , FFT: 77459 , BGC: 0.700 , BIR: 0.0872665 (5.000)
FD: 0.009257425 , FF: 0.007745917 , FD / FF: 1.195136079 , FDT / FFT: 3.103796847 , FDT: 240417 , FFT: 77459 , BGC: 0.700 , BIR: 0.0174533 (1.000)
FD: 0.009258130 , FF: 0.007745917 , FD / FF: 1.195227103 , FDT / FFT: 10.244451904 , FDT: 793525 , FFT: 77459 , BGC: 0.700 , BIR: 0.0000001 (0.000)
FD: 0.005628999 , FF: 0.007745917 , FD / FF: 0.726705349 , FDT / FFT: 0.570120967 , FDT: 44161 , FFT: 77459 , BGC: 0.750 , BIR: 1.1635528 (66.667)
FD: 0.006324489 , FF: 0.007745917 , FD / FF: 0.816493245 , FDT / FFT: 0.660284796 , FDT: 51145 , FFT: 77459 , BGC: 0.750 , BIR: 1.0471976 (60.000)
FD: 0.007170917 , FF: 0.007745917 , FD / FF: 0.925767398 , FDT / FFT: 0.796614983 , FDT: 61705 , FFT: 77459 , BGC: 0.750 , BIR: 0.8726646 (50.000)
FD: 0.007521140 , FF: 0.007745917 , FD / FF: 0.970981204 , FDT / FFT: 0.869143676 , FDT: 67323 , FFT: 77459 , BGC: 0.750 , BIR: 0.7853982 (45.000)
FD: 0.007828315 , FF: 0.007745917 , FD / FF: 1.010637611 , FDT / FFT: 0.947133322 , FDT: 73364 , FFT: 77459 , BGC: 0.750 , BIR: 0.6981317 (40.000)
FD: 0.008175447 , FF: 0.007745917 , FD / FF: 1.055452492 , FDT / FFT: 1.063904775 , FDT: 82409 , FFT: 77459 , BGC: 0.750 , BIR: 0.5817764 (33.333)
FD: 0.008323516 , FF: 0.007745917 , FD / FF: 1.074568261 , FDT / FFT: 1.130055901 , FDT: 87533 , FFT: 77459 , BGC: 0.750 , BIR: 0.5235988 (30.000)
FD: 0.008488220 , FF: 0.007745917 , FD / FF: 1.095831526 , FDT / FFT: 1.224738249 , FDT: 94867 , FFT: 77459 , BGC: 0.750 , BIR: 0.4495619 (25.758)
FD: 0.008670309 , FF: 0.007745917 , FD / FF: 1.119339270 , FDT / FFT: 1.380381879 , FDT: 106923 , FFT: 77459 , BGC: 0.750 , BIR: 0.3490659 (20.000)
FD: 0.008876003 , FF: 0.007745917 , FD / FF: 1.145894511 , FDT / FFT: 1.804038265 , FDT: 139739 , FFT: 77459 , BGC: 0.750 , BIR: 0.1745329 (10.000)
FD: 0.008927171 , FF: 0.007745917 , FD / FF: 1.152500285 , FDT / FFT: 2.227668831 , FDT: 172553 , FFT: 77459 , BGC: 0.750 , BIR: 0.0872665 (5.000)
FD: 0.008943524 , FF: 0.007745917 , FD / FF: 1.154611448 , FDT / FFT: 3.212744807 , FDT: 248856 , FFT: 77459 , BGC: 0.750 , BIR: 0.0174533 (1.000)
FD: 0.008944205 , FF: 0.007745917 , FD / FF: 1.154699385 , FDT / FFT: 10.604022773 , FDT: 821377 , FFT: 77459 , BGC: 0.750 , BIR: 0.0000001 (0.000)
FD: 0.005450257 , FF: 0.007745917 , FD / FF: 0.703629694 , FDT / FFT: 0.588827638 , FDT: 45610 , FFT: 77459 , BGC: 0.800 , BIR: 1.1635528 (66.667)
FD: 0.006123662 , FF: 0.007745917 , FD / FF: 0.790566449 , FDT / FFT: 0.681947869 , FDT: 52823 , FFT: 77459 , BGC: 0.800 , BIR: 1.0471976 (60.000)
FD: 0.006943213 , FF: 0.007745917 , FD / FF: 0.896370693 , FDT / FFT: 0.822744936 , FDT: 63729 , FFT: 77459 , BGC: 0.800 , BIR: 0.8726646 (50.000)
FD: 0.007282314 , FF: 0.007745917 , FD / FF: 0.940148773 , FDT / FFT: 0.897649079 , FDT: 69531 , FFT: 77459 , BGC: 0.800 , BIR: 0.7853982 (45.000)
FD: 0.007579735 , FF: 0.007745917 , FD / FF: 0.978545924 , FDT / FFT: 0.978194916 , FDT: 75770 , FFT: 77459 , BGC: 0.800 , BIR: 0.6981317 (40.000)
FD: 0.007915845 , FF: 0.007745917 , FD / FF: 1.021937746 , FDT / FFT: 1.098800656 , FDT: 85112 , FFT: 77459 , BGC: 0.800 , BIR: 0.5817764 (33.333)
FD: 0.008059212 , FF: 0.007745917 , FD / FF: 1.040446510 , FDT / FFT: 1.167120670 , FDT: 90404 , FFT: 77459 , BGC: 0.800 , BIR: 0.5235988 (30.000)
FD: 0.008218685 , FF: 0.007745917 , FD / FF: 1.061034578 , FDT / FFT: 1.264901432 , FDT: 97978 , FFT: 77459 , BGC: 0.800 , BIR: 0.4495619 (25.758)
FD: 0.008394992 , FF: 0.007745917 , FD / FF: 1.083795853 , FDT / FFT: 1.425644535 , FDT: 110429 , FFT: 77459 , BGC: 0.800 , BIR: 0.3490659 (20.000)
FD: 0.008594155 , FF: 0.007745917 , FD / FF: 1.109507854 , FDT / FFT: 1.863205050 , FDT: 144322 , FFT: 77459 , BGC: 0.800 , BIR: 0.1745329 (10.000)
FD: 0.008643698 , FF: 0.007745917 , FD / FF: 1.115903867 , FDT / FFT: 2.300726836 , FDT: 178212 , FFT: 77459 , BGC: 0.800 , BIR: 0.0872665 (5.000)
FD: 0.008659532 , FF: 0.007745917 , FD / FF: 1.117947992 , FDT / FFT: 3.318103771 , FDT: 257017 , FFT: 77459 , BGC: 0.800 , BIR: 0.0174533 (1.000)
FD: 0.008660192 , FF: 0.007745917 , FD / FF: 1.118033137 , FDT / FFT: 10.951780942 , FDT: 848314 , FFT: 77459 , BGC: 0.800 , BIR: 0.0000001 (0.000)
FD: 0.005138555 , FF: 0.007745917 , FD / FF: 0.663388872 , FDT / FFT: 0.624536852 , FDT: 48376 , FFT: 77459 , BGC: 0.900 , BIR: 1.1635528 (66.667)
FD: 0.005773447 , FF: 0.007745917 , FD / FF: 0.745353632 , FDT / FFT: 0.723311687 , FDT: 56027 , FFT: 77459 , BGC: 0.900 , BIR: 1.0471976 (60.000)
FD: 0.006546127 , FF: 0.007745917 , FD / FF: 0.845106829 , FDT / FFT: 0.872655211 , FDT: 67595 , FFT: 77459 , BGC: 0.900 , BIR: 0.8726646 (50.000)
FD: 0.006865835 , FF: 0.007745917 , FD / FF: 0.886381199 , FDT / FFT: 0.952103694 , FDT: 73749 , FFT: 77459 , BGC: 0.900 , BIR: 0.7853982 (45.000)
FD: 0.007146246 , FF: 0.007745917 , FD / FF: 0.922582379 , FDT / FFT: 1.037529532 , FDT: 80366 , FFT: 77459 , BGC: 0.900 , BIR: 0.6981317 (40.000)
FD: 0.007463133 , FF: 0.007745917 , FD / FF: 0.963492581 , FDT / FFT: 1.165455273 , FDT: 90275 , FFT: 77459 , BGC: 0.900 , BIR: 0.5817764 (33.333)
FD: 0.007598301 , FF: 0.007745917 , FD / FF: 0.980942812 , FDT / FFT: 1.237919415 , FDT: 95888 , FFT: 77459 , BGC: 0.900 , BIR: 0.5235988 (30.000)
FD: 0.007748654 , FF: 0.007745917 , FD / FF: 1.000353428 , FDT / FFT: 1.341625892 , FDT: 103921 , FFT: 77459 , BGC: 0.900 , BIR: 0.4495619 (25.758)
FD: 0.007914878 , FF: 0.007745917 , FD / FF: 1.021812964 , FDT / FFT: 1.512128997 , FDT: 117128 , FFT: 77459 , BGC: 0.900 , BIR: 0.3490659 (20.000)
FD: 0.008102651 , FF: 0.007745917 , FD / FF: 1.046054472 , FDT / FFT: 1.976219678 , FDT: 153076 , FFT: 77459 , BGC: 0.900 , BIR: 0.1745329 (10.000)
FD: 0.008149360 , FF: 0.007745917 , FD / FF: 1.052084691 , FDT / FFT: 2.440284538 , FDT: 189022 , FFT: 77459 , BGC: 0.900 , BIR: 0.0872665 (5.000)
FD: 0.008164288 , FF: 0.007745917 , FD / FF: 1.054011910 , FDT / FFT: 3.519384449 , FDT: 272608 , FFT: 77459 , BGC: 0.900 , BIR: 0.0174533 (1.000)
FD: 0.008164910 , FF: 0.007745917 , FD / FF: 1.054092185 , FDT / FFT: 11.616119495 , FDT: 899773 , FFT: 77459 , BGC: 0.900 , BIR: 0.0000001 (0.000)
FD: 0.004874864 , FF: 0.007745917 , FD / FF: 0.629346292 , FDT / FFT: 0.658322467 , FDT: 50993 , FFT: 77459 , BGC: 1.000 , BIR: 1.1635528 (66.667)
FD: 0.005477176 , FF: 0.007745917 , FD / FF: 0.707104891 , FDT / FFT: 0.762442066 , FDT: 59058 , FFT: 77459 , BGC: 1.000 , BIR: 1.0471976 (60.000)
FD: 0.006210204 , FF: 0.007745917 , FD / FF: 0.801739083 , FDT / FFT: 0.919854375 , FDT: 71251 , FFT: 77459 , BGC: 1.000 , BIR: 0.8726646 (50.000)
FD: 0.006513506 , FF: 0.007745917 , FD / FF: 0.840895388 , FDT / FFT: 1.003601906 , FDT: 77738 , FFT: 77459 , BGC: 1.000 , BIR: 0.7853982 (45.000)
FD: 0.006779527 , FF: 0.007745917 , FD / FF: 0.875238844 , FDT / FFT: 1.093649544 , FDT: 84713 , FFT: 77459 , BGC: 1.000 , BIR: 0.6981317 (40.000)
FD: 0.007080153 , FF: 0.007745917 , FD / FF: 0.914049669 , FDT / FFT: 1.228495075 , FDT: 95158 , FFT: 77459 , BGC: 1.000 , BIR: 0.5817764 (33.333)
FD: 0.007208384 , FF: 0.007745917 , FD / FF: 0.930604411 , FDT / FFT: 1.304870964 , FDT: 101074 , FFT: 77459 , BGC: 1.000 , BIR: 0.5235988 (30.000)
FD: 0.007351022 , FF: 0.007745917 , FD / FF: 0.949018939 , FDT / FFT: 1.414206225 , FDT: 109543 , FFT: 77459 , BGC: 1.000 , BIR: 0.4495619 (25.758)
FD: 0.007508715 , FF: 0.007745917 , FD / FF: 0.969377242 , FDT / FFT: 1.593927110 , FDT: 123464 , FFT: 77459 , BGC: 1.000 , BIR: 0.3490659 (20.000)
FD: 0.007686852 , FF: 0.007745917 , FD / FF: 0.992374755 , FDT / FFT: 2.083127848 , FDT: 161357 , FFT: 77459 , BGC: 1.000 , BIR: 0.1745329 (10.000)
FD: 0.007731165 , FF: 0.007745917 , FD / FF: 0.998095523 , FDT / FFT: 2.572289857 , FDT: 199247 , FFT: 77459 , BGC: 1.000 , BIR: 0.0872665 (5.000)
FD: 0.007745327 , FF: 0.007745917 , FD / FF: 0.999923844 , FDT / FFT: 3.709756129 , FDT: 287354 , FFT: 77459 , BGC: 1.000 , BIR: 0.0174533 (1.000)
FD: 0.007745917 , FF: 0.007745917 , FD / FF: 1.000000000 , FDT / FFT: 12.244464814 , FDT: 948444 , FFT: 77459 , BGC: 1.000 , BIR: 0.0000001 (0.000)

　
2024.7.4　慣性モーメントを考慮していないので？意図した答えと違っている。しれっと「倒れる質量ゼロの棒の上にしがみつくか飛び降りるか」という話にしておく。コメント訂正。変数名も変更