{ Solutions to the Advent Of Code. Copyright (C) 2023-2024 Stefan Müller This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . } unit UNeverTellMeTheOdds; {$mode ObjFPC}{$H+} interface uses Classes, SysUtils, Generics.Collections, Math, USolver, UVector; type { THailstone } THailstone = class public Position, Velocity: TVector3Int64; constructor Create(const ALine: string); constructor Create(const APosition, AVelocity: TVector3Int64); function GetParameterMinimum(const AMin, AMax: Int64): Int64; function GetParameterMaximum(const AMin, AMax: Int64): Int64; end; THailstones = specialize TObjectList; //{ TFirstCollisionPolynomial } // //TFirstCollisionPolynomial = class //private // FA: array[0..10] of TBigInt; // FH: array[0..6] of TBigInt; // procedure NormalizeCoefficients; //public // procedure Init(constref AHailstone1, AHailstone2, AHailstone3: THailstone; const t_0, t_1, t_2: Int64); // function EvaluateAt(const AT0: Int64): TBigInt; // function CalcPositiveIntegerRoot: Int64; // function CalcT1(const AT0: Int64): Int64; //end; { TNeverTellMeTheOdds } TNeverTellMeTheOdds = class(TSolver) private FMin, FMax: Int64; FHailstones: THailstones; function AreIntersecting(constref AHailstone1, AHailstone2: THailstone): Boolean; procedure FindRockThrow(const AIndex1, AIndex2, AIndex3: Integer); public constructor Create(const AMin: Int64 = 200000000000000; const AMax: Int64 = 400000000000000); destructor Destroy; override; procedure ProcessDataLine(const ALine: string); override; procedure Finish; override; function GetDataFileName: string; override; function GetPuzzleName: string; override; end; const CIterationThreshold = 0.00001; CEpsilon = 0.0000000001; implementation { THailstone } constructor THailstone.Create(const ALine: string); var split: TStringArray; begin split := ALine.Split([',', '@']); Position.Init( StrToInt64(Trim(split[0])), StrToInt64(Trim(split[1])), StrToInt64(Trim(split[2]))); Velocity.Init( StrToInt64(Trim(split[3])), StrToInt64(Trim(split[4])), StrToInt64(Trim(split[5]))); //Position.init( // StrToFloat(Trim(split[0])), // StrToFloat(Trim(split[1])), // StrToFloat(Trim(split[2]))); //Velocity.init( // StrToFloat(Trim(split[3])), // StrToFloat(Trim(split[4])), // StrToFloat(Trim(split[5]))); end; constructor THailstone.Create(const APosition, AVelocity: TVector3Int64); begin Position := APosition; Velocity := AVelocity; end; function THailstone.GetParameterMinimum(const AMin, AMax: Int64): Int64; var i: TVector3DataRange; boundary: Int64; begin Result := 0; for i in TVector3DataRange do begin if Velocity.Data[i] > 0 then boundary := AMin else boundary := AMax; Result := Max(Result, Ceil64((boundary - Position.Data[i]) / Velocity.Data[i])); end; end; function THailstone.GetParameterMaximum(const AMin, AMax: Int64): Int64; var i: TVector3DataRange; boundary: Int64; begin Result := Int64.MaxValue; for i in TVector3DataRange do begin if Velocity.Data[i] > 0 then boundary := AMax else boundary := AMin; Result := Min(Result, Floor64((boundary - Position.Data[i]) / Velocity.Data[i])); end; end; //{ TFirstCollisionPolynomial } // //procedure TFirstCollisionPolynomial.NormalizeCoefficients; //var // shift: Integer; // i: Low(FA)..High(FA); // //gcd: TBigInt; //begin // // Eliminates zero constant term. // shift := 0; // while (shift <= High(FA)) and (FA[shift] = 0) do // Inc(shift); // // if shift <= High(FA) then // begin // if shift > 0 then // begin // for i := Low(FA) to High(FA) - shift do // FA[i] := FA[i + shift]; // for i := High(FA) - shift + 1 to High(FA) do // FA[i] := 0; // end; // // //// Finds GCD of all coefficients. // //gcd := FA[Low(FA)]; // //for i := Low(FA) + 1 to High(FA) do // // if FA[i] <> 0 then // // gcd := TNumberTheory.GreatestCommonDivisor(gcd, FA[i]); // //WriteLn('GCD: ', gcd); // // // //for i := Low(FA) to High(FA) do // // FA[i] := FA[i] div gcd; // end; // // //WriteLn('(', FA[10], ') * x^10 + (', FA[9], ') * x^9 + (', FA[8], ') * x^8 + (', FA[7], ') * x^7 + (', // // FA[6], ') * x^6 + (', FA[5], ') * x^5 + (', FA[4], ') * x^4 + (', FA[3], ') * x^3 + (', FA[2], ') * x^2 + (', // // FA[1], ') * x + (', FA[0], ')'); //end; // //procedure TFirstCollisionPolynomial.Init(constref AHailstone1, AHailstone2, AHailstone3: THailstone; const t_0, t_1, // t_2: Int64); //var // P_00, P_01, P_02, P_10, P_11, P_12, P_20, P_21, P_22, // V_00, V_01, V_02, V_10, V_11, V_12, V_20, V_21, V_22: Int64; // k: array[0..139] of TBigInt; // // For debug calculations // act, a_1, a_2, b_0, b_1, c_0, c_1, d_0, d_1, e_0, e_1, f_0, f_1, f_2: Int64; //begin // // Solving this non-linear equation system, with velocities V_i and start positions P_i: // // V_0 * t_0 + P_0 = V_x * t_0 + P_x // // V_1 * t_1 + P_1 = V_x * t_1 + P_x // // V_2 * t_2 + P_2 = V_x * t_2 + P_x // // Which gives: // // P_x = (V_0 - V_x) * t_0 + P_0 // // V_x = (V_0 * t_0 - V_1 * t_1 + P_0 - P_1) / (t_0 - t_1) // // And with vertex components: // // 1: 0 = (t_1 - t_0) * (V_00 * t_0 - V_20 * t_2 + P_00 - P_20) - (t_2 - t_0) * (V_00 * t_0 - V_10 * t_1 + P_00 - P_10) // // 2: t_1 = (((V_01 - V_21) * t_2 + P_11 - P_21) * t_0 + (P_01 - P_11) * t_2) // // / ((V_01 - V_11) * t_0 + (V_11 - V_21) * t_2 + P_01 - P_21) // // 3: t_2 = (((V_02 - V_12) * t_1 + P_22 - P_12) * t_0 + (P_02 - P_22) * t_1) // // / ((V_02 - V_22) * t_0 + (V_22 - V_12) * t_1 + P_02 - P_12) // // for t_0, t_1, t_2 not pairwise equal. // // With some substitutions depending only on t_0 this gives // // 1: 0 = (t_1 - t_0) * (f_2 - V_20 * t_2) - (t_2 - t_0) * (f_1 - V_10 * t_1) // // 2: t_1 = (b_0 + b_1 * t_2) / (c_0 + c_1 * t_2) // // 3: t_2 = (d_0 + d_1 * t_1) / (e_0 + e_1 * t_1) // // And 3 in 2 gives: // // 4: g_2 * t_1^2 - g_1 * t_1 - g_0 = 0 // // Then, with 4 and 3 in 1 and lengthy calculations with many substitutions (see constants k below, now independent of // // t_0), the following polynomial can be constructed, with t_0 being a positive integer root of this polynomial. // // y = a_10 * x^10 + a_9 * x^9 + ... + a_0 // // P_00 := Round(AHailstone1.Position.data[0]); // P_01 := Round(AHailstone1.Position.data[1]); // P_02 := Round(AHailstone1.Position.data[2]); // P_10 := Round(AHailstone2.Position.data[0]); // P_11 := Round(AHailstone2.Position.data[1]); // P_12 := Round(AHailstone2.Position.data[2]); // P_20 := Round(AHailstone3.Position.data[0]); // P_21 := Round(AHailstone3.Position.data[1]); // P_22 := Round(AHailstone3.Position.data[2]); // V_00 := Round(AHailstone1.Velocity.data[0]); // V_01 := Round(AHailstone1.Velocity.data[1]); // V_02 := Round(AHailstone1.Velocity.data[2]); // V_10 := Round(AHailstone2.Velocity.data[0]); // V_11 := Round(AHailstone2.Velocity.data[1]); // V_12 := Round(AHailstone2.Velocity.data[2]); // V_20 := Round(AHailstone3.Velocity.data[0]); // V_21 := Round(AHailstone3.Velocity.data[1]); // V_22 := Round(AHailstone3.Velocity.data[2]); // // k[0] := P_00 - P_20; // k[1] := P_00 - P_10; // k[2] := P_11 - P_21; // k[3] := P_01 - P_11; // k[4] := P_01 - P_21; // k[5] := P_22 - P_12; // k[6] := P_02 - P_22; // k[7] := P_02 - P_12; // k[8] := V_11 - V_21; // k[9] := V_22 - V_12; // k[10] := V_01 - V_21; // k[11] := V_01 - V_11; // k[12] := V_02 - V_12; // k[13] := V_02 - V_22; // // FH[0] := k[11] * k[9] + k[8] * k[12]; // FH[1] := k[4] * k[9] + k[8] * k[6]; // FH[2] := k[11] * k[13] - k[10] * k[12]; // FH[3] := k[11] * k[7] + k[4] * k[13] + k[8] * k[5] - k[2] * k[9] - k[10] * k[6] - k[3] * k[12]; // FH[4] := k[4] * k[7] - k[3] * k[6]; // FH[5] := k[10] * k[5] + k[2] * k[13]; // FH[6] := k[3] * k[5] + k[2] * k[7]; // // k[14] := V_00 * k[9] - V_20 * k[12]; // k[15] := k[0] * k[9] - V_20 * k[6]; // k[16] := V_00 * k[13]; // k[17] := V_00 * k[7] + k[0] * k[13] - V_20 * k[5]; // k[18] := k[0] * k[7]; // k[19] := k[5] - k[7]; // k[20] := 2 * FH[2] * FH[3]; // k[21] := FH[3] * FH[3]; // k[22] := k[21] + 2 * FH[2] * FH[4]; // k[23] := 2 * FH[3] * FH[4]; // k[24] := 2 * FH[0] * FH[1]; // k[25] := FH[0] * FH[0]; // KILL? // k[26] := FH[5] * k[25]; // KILL? // k[126] := FH[5] * FH[0]; // k[127] := FH[5] * FH[1] + FH[6] * FH[0]; // k[128] := FH[6] * FH[1]; // k[27] := FH[5] * k[24] + FH[6] * k[25]; // KILL? // k[28] := FH[1] * FH[1]; // KILL? // k[29] := FH[5] * k[28] + FH[6] * k[24]; // KILL? // k[30] := FH[6] * k[28]; // KILL? // k[31] := FH[2] * FH[2]; // k[132] := k[20] + 4 * k[126]; // k[133] := k[22] + 4 * k[127]; // k[134] := k[23] + 4 * k[128]; // k[32] := k[31] + 4 * k[26]; // KILL? // k[33] := k[20] + 4 * k[27]; // KILL? // k[34] := k[22] + 4 * k[29]; // KILL? // k[35] := k[23] + 4 * k[30]; // KILL? // k[36] := k[31] + 2 * k[26]; // KILL? // k[37] := k[20] + 2 * k[27]; // KILL? // k[38] := k[22] + 2 * k[29]; // KILL? // k[39] := k[23] + 2 * k[30]; // KILL? // k[137] := k[20] + 2 * k[126]; // k[138] := k[22] + 2 * k[127]; // k[139] := k[23] + 2 * k[128]; // k[40] := k[14] + V_10 * (k[12] - k[9]); // k[41] := k[15] + V_10 * k[6]; // k[42] := k[16] - k[14] - V_10 * k[13] - (k[12] - k[9]) * V_00; // k[43] := k[17] - k[15] + V_10 * k[19] - (k[12] - k[9]) * k[1] - k[6] * V_00; // k[44] := k[18] - k[6] * k[1]; // k[45] := k[42] * FH[0] - k[40] * FH[2]; // k[46] := k[42] * FH[1] + k[43] * FH[0] - k[41] * FH[2] - k[40] * FH[3]; // k[47] := k[43] * FH[1] + k[44] * FH[0] - k[41] * FH[3] - k[40] * FH[4]; // k[48] := k[44] * FH[1] - k[41] * FH[4]; // k[49] := k[42] * FH[2]; // k[50] := k[40] * k[31] - k[49] * FH[0]; // k[51] := k[42] * FH[3] + k[43] * FH[2]; // k[52] := k[40] * k[137] + k[41] * k[31] - k[51] * FH[0] - k[49] * FH[1]; // k[53] := k[42] * FH[4] + k[43] * FH[3] + k[44] * FH[2]; // k[54] := k[40] * k[138] + k[41] * k[137] - k[53] * FH[0] - k[51] * FH[1]; // k[55] := k[43] * FH[4] + k[44] * FH[3]; // k[56] := k[40] * k[139] + k[41] * k[138] - k[55] * FH[0] - k[53] * FH[1]; // k[57] := k[44] * FH[4]; // k[58] := FH[4] * FH[4]; // k[59] := k[40] * k[58] + k[41] * k[139] - k[57] * FH[0] - k[55] * FH[1]; // k[60] := k[41] * k[58] - k[57] * FH[1]; // k[61] := k[13] * V_00 - k[16]; // k[62] := 2 * k[25] * k[61]; // k[63] := k[13] * k[1] - k[19] * V_00 - k[17]; // k[64] := 2 * (k[24] * k[61] + k[25] * k[63]); // k[65] := - k[19] * k[1] - k[18]; // k[66] := 2 * (k[28] * k[61] + k[24] * k[63] + k[25] * k[65]); // k[67] := 2 * (k[28] * k[63] + k[24] * k[65]); // k[68] := 2 * k[28] * k[65]; // k[69] := k[50] + k[62]; // k[70] := k[52] + k[64]; // k[71] := k[54] + k[66]; // k[72] := k[56] + k[67]; // k[73] := k[59] + k[68]; // k[74] := k[45] * k[45]; // k[75] := 2 * k[45] * k[46]; // k[76] := k[46] * k[46] + 2 * k[45] * k[47]; // k[77] := 2 * (k[45] * k[48] + k[46] * k[47]); // k[78] := k[47] * k[47] + 2 * k[46] * k[48]; // k[79] := 2 * k[47] * k[48]; // k[80] := k[48] * k[48]; // // FA[0] := k[58] * k[80] - k[60] * k[60]; // FA[1] := k[134] * k[80] + k[58] * k[79] - 2 * k[73] * k[60]; // FA[2] := k[133] * k[80] + k[134] * k[79] + k[58] * k[78] - k[73] * k[73] - 2 * k[72] * k[60]; // FA[3] := k[133] * k[79] + k[134] * k[78] + k[58] * k[77] + k[132] * k[80] // - 2 * (k[71] * k[60] + k[72] * k[73]); // FA[4] := k[31] * k[80] + k[133] * k[78] + k[134] * k[77] + k[58] * k[76] + k[132] * k[79] - k[72] * k[72] // - 2 * (k[70] * k[60] + k[71] * k[73]); // FA[5] := k[31] * k[79] + k[133] * k[77] + k[134] * k[76] + k[58] * k[75] + k[132] * k[78] // - 2 * (k[69] * k[60] + k[70] * k[73] + k[71] * k[72]); // FA[6] := k[31] * k[78] + k[133] * k[76] + k[134] * k[75] + k[58] * k[74] + k[132] * k[77] - k[71] * k[71] // - 2 * (k[69] * k[73] + k[70] * k[72]); // FA[7] := k[31] * k[77] + k[133] * k[75] + k[134] * k[74] + k[132] * k[76] - 2 * (k[69] * k[72] + k[70] * k[71]); // FA[8] := k[31] * k[76] + k[132] * k[75] + k[133] * k[74] - k[70] * k[70] - 2 * k[69] * k[71]; // FA[9] := k[31] * k[75] + k[132] * k[74] - 2 * k[69] * k[70]; // FA[10] := k[31] * k[74] - k[69] * k[69]; // // // Debug calculations // //a_1 := V_00 * t_0 + P_00 - P_20; // //a_2 := V_00 * t_0 + P_00 - P_10; // //b_0 := (P_11 - P_21) * t_0; // //b_1 := (V_01 - V_21) * t_0 + P_01 - P_11; // //c_0 := (V_01 - V_11) * t_0 + P_01 - P_21; // //c_1 := V_11 - V_21; // //d_0 := (P_22 - P_12) * t_0; // //d_1 := (V_02 - V_12) * t_0 + P_02 - P_22; // //e_0 := (V_02 - V_22) * t_0 + P_02 - P_12; // //e_1 := V_22 - V_12; // //f_2 := c_0 * e_1 + c_1 * d_1; // //f_1 := c_0 * e_0 + c_1 * d_0 - b_0 * e_1 - b_1 * d_1; // //f_0 := b_1 * d_0 + b_0 * e_0; // // // //act := f_2 * t_1 * t_1 + f_1 * t_1 - f_0; // //Write('debug10: ', 0 = act, ' '); // // // //if f_2 <> 0 then // //begin // // act := Round(- f_1 / (2 * f_2) + Sqrt((f_1 / (2 * f_2)) * (f_1 / (2 * f_2)) + f_0 / f_2)); // // Write('debug15: ', t_1 = act); // // act := Round(- f_1 / (2 * f_2) - Sqrt((f_1 / (2 * f_2)) * (f_1 / (2 * f_2)) + f_0 / f_2)); // // Write(' OR ', t_1 = act, ' '); // //end; // // // //act := (e_0 + e_1 * t_1) * t_2 - (d_0 + d_1 * t_1); // //Write('debug20: ', 0 = act, ' '); // // // //act := (a_1 * e_1 - V_20 * d_1 + V_10 * (d_1 - e_1 * t_0)) * t_1 * t_1 // // + (a_1 * e_0 - V_20 * d_0 - t_0 * (a_1 * e_1 - V_20 * d_1) - (d_1 - e_1 * t_0) * a_2 + V_10 * (d_0 - e_0 * t_0)) * t_1 // // + t_0 * (V_20 * d_0 - a_1 * e_0) + (e_0 * t_0 - d_0) * a_2; // //Write('debug30: ', 0 = act, ' '); // // // //act := Round((a_1 * e_1 - V_20 * d_1 + V_10 * (d_1 - e_1 * t_0)) * (f_1 * f_1 + 2 * f_0 * f_2 - f_1 * Sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // + (a_1 * e_0 - V_20 * d_0 - t_0 * (a_1 * e_1 - V_20 * d_1) - (d_1 - e_1 * t_0) * a_2 + V_10 * (d_0 - e_0 * t_0)) * (- f_1 * f_2 + f_2 * Sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // + t_0 * (V_20 * d_0 - a_1 * e_0) * 2 * f_2 * f_2 + (e_0 * t_0 - d_0) * a_2 * 2 * f_2 * f_2); // //Write('debug40: ', 0 = act, ' '); // // // //Write('debug41: ', // // a_1 * k[9] - V_20 * d_1 // // = k[14] * t_0 + k[15], ' '); // //Write('debug42: ', // // d_1 - k[9] * t_0 // // = (k[12] - k[9]) * t_0 + k[6], ' '); // //Write('debug43: ', // // a_1 * e_0 - V_20 * d_0 // // = k[16] * t_0 * t_0 + k[17] * t_0 + k[18], ' '); // //Write('debug44: ', // // d_0 - e_0 * t_0 // // = - k[13] * t_0 * t_0 + k[19] * t_0, ' '); // //Write('debug45: ', // // f_1 * f_1 // // = FH[2] * FH[2] * t_0 * t_0 * t_0 * t_0 + k[20] * t_0 * t_0 * t_0 + k[22] * t_0 * t_0 + k[23] * t_0 + FH[4] * FH[4], ' '); // //Write('debug46: ', // // f_2 * f_2 // // = FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1], ' '); // //Write('debug47: ', // // f_0 * f_2 // // = k[126] * t_0 * t_0 * t_0 + k[127] * t_0 * t_0 + k[128] * t_0, ' '); // //Write('debug48: ', // // f_1 * f_1 + 4 * f_0 * f_2 // // = k[31] * t_0 * t_0 * t_0 * t_0 + k[132] * t_0 * t_0 * t_0 + k[133] * t_0 * t_0 + k[134] * t_0 + k[58], ' '); // //Write('debug49: ', // // f_1 * f_1 + 2 * f_0 * f_2 // // = k[31] * t_0 * t_0 * t_0 * t_0 + k[137] * t_0 * t_0 * t_0 + k[138] * t_0 * t_0 + k[139] * t_0 + k[58], ' '); // // // //act := Round((k[14] * t_0 + k[15] + V_10 * ((k[12] - k[9]) * t_0 + k[6])) * (k[31] * t_0 * t_0 * t_0 * t_0 + k[137] * t_0 * t_0 * t_0 + k[138] * t_0 * t_0 + k[139] * t_0 + k[58] - f_1 * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // + (k[16] * t_0 * t_0 + k[17] * t_0 + k[18] - t_0 * (k[14] * t_0 + k[15]) - ((k[12] - k[9]) * t_0 + k[6]) * a_2 - V_10 * (k[13] * t_0 * t_0 - k[19] * t_0)) * (- f_1 * f_2 + f_2 * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // - 2 * t_0 * (k[16] * t_0 * t_0 + k[17] * t_0 + k[18]) * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1]) + 2 * (k[13] * t_0 * t_0 - k[19] * t_0) * a_2 * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1])); // //Write('debug50: ', 0 = act, ' '); // // // //Write('debug53: ', // // 0 = Round((k[40] * t_0 + k[41]) * (k[31] * t_0 * t_0 * t_0 * t_0 + k[137] * t_0 * t_0 * t_0 + k[138] * t_0 * t_0 + k[139] * t_0 + k[58] - f_1 * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // + ((k[16] - k[14] - V_10 * k[13] - (k[12] - k[9]) * V_00) * t_0 * t_0 + (k[17] - k[15] + V_10 * k[19] - (k[12] - k[9]) * k[1] - k[6] * V_00) * t_0 + k[18] - k[6] * k[1]) * (- f_1 * f_2 + f_2 * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // - 2 * t_0 * (k[16] * t_0 * t_0 + k[17] * t_0 + k[18]) * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1]) + 2 * (k[13] * t_0 * t_0 - k[19] * t_0) * a_2 * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1])), // // ' '); // // // //Write('debug55: ', // // 0 = Round((k[40] * t_0 + k[41]) * (k[31] * t_0 * t_0 * t_0 * t_0 + k[137] * t_0 * t_0 * t_0 + k[138] * t_0 * t_0 + k[139] * t_0 + k[58]) // // - (k[40] * t_0 + k[41]) * f_1 * sqrt(f_1 * f_1 + 4 * f_0 * f_2) // // + (k[42] * t_0 * t_0 + k[43] * t_0 + k[44]) * (- f_1 * f_2 + f_2 * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // - 2 * t_0 * (k[16] * t_0 * t_0 + k[17] * t_0 + k[18]) * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1]) + 2 * (k[13] * t_0 * t_0 - k[19] * t_0) * a_2 * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1])), // // ' '); // // // //Write('debug70: ', // // 0 = Round(((k[42] * t_0 * t_0 + k[43] * t_0 + k[44]) * (FH[0] * t_0 + FH[1]) - (k[40] * t_0 + k[41]) * (FH[2] * t_0 * t_0 + FH[3] * t_0 + FH[4])) * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) // // + (k[40] * t_0 + k[41]) * (k[31] * t_0 * t_0 * t_0 * t_0 + k[137] * t_0 * t_0 * t_0 + k[138] * t_0 * t_0 + k[139] * t_0 + k[58]) // // - (k[42] * t_0 * t_0 + k[43] * t_0 + k[44]) * (FH[2] * t_0 * t_0 + FH[3] * t_0 + FH[4]) * (FH[0] * t_0 + FH[1]) // // - 2 * t_0 * (k[16] * t_0 * t_0 + k[17] * t_0 + k[18]) * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1]) + 2 * (k[13] * t_0 * t_0 - k[19] * t_0) * (V_00 * t_0 + k[1]) * (FH[0] * FH[0] * t_0 * t_0 + k[24] * t_0 + FH[1] * FH[1]), // // ' '); //// //// Write('debug73: ', //// 0 = Round(( //// (k[42] * FH[0] - k[40] * FH[2]) * t_0 * t_0 * t_0 //// + (k[42] * FH[1] + k[43] * FH[0] - k[41] * FH[2] - k[40] * FH[3]) * t_0 * t_0 //// + (k[43] * FH[1] + k[44] * FH[0] - k[41] * FH[3] - k[40] * FH[4]) * t_0 //// + k[44] * FH[1] - k[41] * FH[4] //// ) * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) //// + (k[40] * k[31] - k[42] * FH[2] * FH[0]) * t_0 * t_0 * t_0 * t_0 * t_0 //// + (k[40] * k[137] + k[41] * k[31] - k[42] * FH[3] * FH[0] - k[43] * FH[2] * FH[0] - k[42] * FH[2] * FH[1]) * t_0 * t_0 * t_0 * t_0 //// + (k[40] * k[138] + k[41] * k[137] - k[42] * FH[4] * FH[0] - k[43] * FH[3] * FH[0] - k[44] * FH[2] * FH[0] - k[42] * FH[3] * FH[1] - k[43] * FH[2] * FH[1]) * t_0 * t_0 * t_0 //// + (k[40] * k[139] + k[41] * k[138] - k[43] * FH[4] * FH[0] - k[44] * FH[3] * FH[0] - k[42] * FH[4] * FH[1] - k[43] * FH[3] * FH[1] - k[44] * FH[2] * FH[1]) * t_0 * t_0 //// + (k[40] * k[58] + k[41] * k[139] - k[44] * FH[4] * FH[0] - k[43] * FH[4] * FH[1] - k[44] * FH[3] * FH[1]) * t_0 //// + k[41] * k[58] - k[44] * FH[4] * FH[1] //// + 2 * (k[13] * V_00 * FH[0] * FH[0] - k[16] * FH[0] * FH[0]) * t_0 * t_0 * t_0 * t_0 * t_0 //// + 2 * (k[13] * V_00 * k[24] + k[13] * k[1] * FH[0] * FH[0] - k[19] * V_00 * FH[0] * FH[0] - k[16] * k[24] - k[17] * FH[0] * FH[0]) * t_0 * t_0 * t_0 * t_0 //// + 2 * (k[13] * V_00 * FH[1] * FH[1] + k[13] * k[1] * k[24] - k[19] * V_00 * k[24] - k[19] * k[1] * FH[0] * FH[0] - k[16] * FH[1] * FH[1] - k[17] * k[24] - k[18] * FH[0] * FH[0]) * t_0 * t_0 * t_0 //// + 2 * (k[13] * k[1] * FH[1] * FH[1] - k[19] * V_00 * FH[1] * FH[1] - k[19] * k[1] * k[24] - k[17] * FH[1] * FH[1] - k[18] * k[24]) * t_0 * t_0 //// + 2 * (- k[19] * k[1] * FH[1] * FH[1] - k[18] * FH[1] * FH[1]) * t_0, //// ' '); //// //// Write('debug78: ', //// 0 = Round((k[45] * t_0 * t_0 * t_0 + k[46] * t_0 * t_0 + k[47] * t_0 + k[48]) * sqrt(f_1 * f_1 + 4 * f_0 * f_2)) //// + (k[50] + k[62]) * t_0 * t_0 * t_0 * t_0 * t_0 + (k[52] + k[64]) * t_0 * t_0 * t_0 * t_0 + (k[54] + k[66]) * t_0 * t_0 * t_0 + (k[56] + k[67]) * t_0 * t_0 + (k[59] + k[68]) * t_0 + k[60], //// ' '); //// //// Write('debug80: ', //// 0 = Round((k[45] * t_0 * t_0 * t_0 + k[46] * t_0 * t_0 + k[47] * t_0 + k[48]) * sqrt(k[31] * t_0 * t_0 * t_0 * t_0 + k[132] * t_0 * t_0 * t_0 + k[133] * t_0 * t_0 + k[134] * t_0 + k[58]) //// + k[69] * t_0 * t_0 * t_0 * t_0 * t_0 + k[70] * t_0 * t_0 * t_0 * t_0 + k[71] * t_0 * t_0 * t_0 + k[72] * t_0 * t_0 + k[73] * t_0 + k[60]), //// ' '); //// WriteLn; //// WriteLn(' 0 = ((', k[45], ') * x^3 + (', k[46], ') * x^2 + (', k[47], ') * x + (', k[48], ')) * sqrt((', k[31], ') * x^4 + (', k[132], ') * x^3 + (', k[133], ') * x^2 + (', k[134], ') * x + (', k[58], ')) + (', //// k[69], ') * x^5 + (', k[70], ') * x^4 + (', k[71], ') * x^3 + (', k[72], ') * x^2 + (', k[73], ') * x + (', k[60], ')'); // // Write('debug83: ', // (k[45] * t_0 * t_0 * t_0 + k[46] * t_0 * t_0 + k[47] * t_0 + k[48]) * (k[45] * t_0 * t_0 * t_0 + k[46] * t_0 * t_0 + k[47] * t_0 + k[48]) * (k[31] * t_0 * t_0 * t_0 * t_0 + k[132] * t_0 * t_0 * t_0 + k[133] * t_0 * t_0 + k[134] * t_0 + k[58]) = // (k[69] * t_0 * t_0 * t_0 * t_0 * t_0 + k[70] * t_0 * t_0 * t_0 * t_0 + k[71] * t_0 * t_0 * t_0 + k[72] * t_0 * t_0 + k[73] * t_0 + k[60]) * (k[69] * t_0 * t_0 * t_0 * t_0 * t_0 + k[70] * t_0 * t_0 * t_0 * t_0 + k[71] * t_0 * t_0 * t_0 + k[72] * t_0 * t_0 + k[73] * t_0 + k[60]), // ' '); // Write('debug85: ', // 0 = // ( // k[45] * k[45] * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 // + 2 * k[45] * k[46] * t_0 * t_0 * t_0 * t_0 * t_0 // + k[46] * k[46] * t_0 * t_0 * t_0 * t_0 // + 2 * k[45] * k[47] * t_0 * t_0 * t_0 * t_0 // + 2 * k[45] * k[48] * t_0 * t_0 * t_0 // + 2 * k[46] * k[47] * t_0 * t_0 * t_0 // + k[47] * k[47] * t_0 * t_0 // + 2 * k[46] * k[48] * t_0 * t_0 // + 2 * k[47] * k[48] * t_0 // + k[48] * k[48] // ) * (k[31] * t_0 * t_0 * t_0 * t_0 + k[132] * t_0 * t_0 * t_0 + k[133] * t_0 * t_0 + k[134] * t_0 + k[58]) // - k[69] * k[69] * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 // - 2 * k[69] * k[70] * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 // - (k[70] * k[70] + 2 * k[69] * k[71]) * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 // - 2 * (k[69] * k[72] + k[70] * k[71]) * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 // - (k[71] * k[71] + 2 * k[69] * k[73] + 2 * k[70] * k[72]) * t_0 * t_0 * t_0 * t_0 * t_0 * t_0 // - 2 * (k[69] * k[60] + k[70] * k[73] + k[71] * k[72]) * t_0 * t_0 * t_0 * t_0 * t_0 // - (k[72] * k[72] + 2 * k[70] * k[60] + 2 * k[71] * k[73]) * t_0 * t_0 * t_0 * t_0 // - 2 * (k[71] * k[60] + k[72] * k[73]) * t_0 * t_0 * t_0 // - (k[73] * k[73] + 2 * k[72] * k[60]) * t_0 * t_0 // - 2 * k[73] * k[60] * t_0 // - k[60] * k[60], // ' '); // // WriteLn('debug96: ', EvaluateAt(t_0) = 0); // // NormalizeCoefficients; // // WriteLn('debug99: ', EvaluateAt(t_0) = 0, ' '); //end; // //function TFirstCollisionPolynomial.EvaluateAt(const AT0: Int64): TBigInt; //var // i: Low(FA)..High(FA); //begin // Result := TBigInt.Zero; // for i := High(FA) downto Low(FA) do // Result := Result * AT0 + FA[i]; //end; // //function TFirstCollisionPolynomial.CalcPositiveIntegerRoot: Int64; //var // dividers: TDividers; // factors: TInt64Array; // divider: Int64; //begin // Result := 0; // //factors := TIntegerFactorization.PollardsRhoAlgorithm(FA[0]); // //dividers := TDividers.Create(factors); // // // //try // //for divider in dividers do // //begin // // //WriteLn('Check if ', divider, ' is a root...'); // // if EvaluateAt(divider) = 0 then // // begin // // Result := divider; // // Break; // // end; // //end; // // // //finally // // dividers.Free; // //end; //end; // //function TFirstCollisionPolynomial.CalcT1(const AT0: Int64): Int64; //var // g_0, g_1, g_2: Int64; // g: Extended; //begin // //g_2 := FH[0] * AT0 + FH[1]; // //g_1 := FH[2] * AT0 * AT0 + FH[3] * AT0 + FH[4]; // //g_0 := FH[5] * AT0 * AT0 + FH[6] * AT0; // //g := - g_1 / (2 * g_2); // //Result := Round(g + sqrt(g * g + g_0)); //end; { TNeverTellMeTheOdds } function TNeverTellMeTheOdds.AreIntersecting(constref AHailstone1, AHailstone2: THailstone): Boolean; var m1, m2, x, y: Double; begin Result := False; m1 := AHailstone1.Velocity.Y / AHailstone1.Velocity.X; //m1 := AHailstone1.Velocity.data[1] / AHailstone1.Velocity.data[0]; m2 := AHailstone2.Velocity.Y / AHailstone2.Velocity.X; //m2 := AHailstone2.Velocity.data[1] / AHailstone2.Velocity.data[0]; if m1 <> m2 then begin x := (AHailstone2.Position.Y - m2 * AHailstone2.Position.X - AHailstone1.Position.Y + m1 * AHailstone1.Position.X) / (m1 - m2); //x := (AHailstone2.Position.data[1] - m2 * AHailstone2.Position.data[0] // - AHailstone1.Position.data[1] + m1 * AHailstone1.Position.data[0]) // / (m1 - m2); if (FMin <= x) and (x <= FMax) and (x * Sign(AHailstone1.Velocity.X) >= AHailstone1.Position.X * Sign(AHailstone1.Velocity.X)) //and (x * Sign(AHailstone1.Velocity.data[0]) >= AHailstone1.Position.data[0] * Sign(AHailstone1.Velocity.data[0])) and (x * Sign(AHailstone2.Velocity.X) >= AHailstone2.Position.X * Sign(AHailstone2.Velocity.X)) //and (x * Sign(AHailstone2.Velocity.data[0]) >= AHailstone2.Position.data[0] * Sign(AHailstone2.Velocity.data[0])) then begin y := m1 * (x - AHailstone1.Position.X) + AHailstone1.Position.Y; y := m1 * (x - AHailstone1.Position.X) + AHailstone1.Position.Y; if (FMin <= y) and (y <= FMax) then Result := True end; end; end; // For debug calculations: Const T : array[0..4] of Byte = (5, 3, 4, 6, 1); procedure TNeverTellMeTheOdds.FindRockThrow(const AIndex1, AIndex2, AIndex3: Integer); var i: TVector3DataRange; //i, j, k: Integer; //x0, x1, x2: Extended; //f: TFirstCollisionPolynomial; t0, t1, t2, t0Min, t0Max, t1Min, t1Max, t2Min, t2Max: Int64; boundary: Int64; //p, v: Tvector3_extended; //test: TBigInt; begin //WriteLn; WriteLn(AIndex1, ' ', AIndex2, ' ', AIndex3, ' '); t0Min := FHailstones[AIndex1].GetParameterMinimum(FMin, FMax); t0Max := FHailstones[AIndex1].GetParameterMaximum(FMin, FMax); WriteLn('t0 bounds: ', t0Min, ' ', t0Max); t1Min := FHailstones[AIndex2].GetParameterMinimum(FMin, FMax); t1Max := FHailstones[AIndex2].GetParameterMaximum(FMin, FMax); WriteLn('t1 bounds: ', t1Min, ' ', t1Max); t2Min := FHailstones[AIndex3].GetParameterMinimum(FMin, FMax); t2Max := FHailstones[AIndex3].GetParameterMaximum(FMin, FMax); WriteLn('t2 bounds: ', t2Min, ' ', t2Max); //t0 := t0Min >> 1 + t0Max >> 1; //WriteLn('t0: ', t0); //t1 := t1Min >> 1 + t1Max >> 1; //WriteLn('t1: ', t1); //t2 := t2Min >> 1 + t2Max >> 1; //WriteLn('t2: ', t2); //f := TFirstCollisionPolynomial.Create; //f.Init(FHailstones[AIndex1], FHailstones[AIndex2], FHailstones[AIndex3], T[AIndex1], T[AIndex2], T[AIndex3]); ////t0 := f.CalcPositiveIntegerRoot; ////WriteLn('t0: ', t0, ' ', t0 = T[AIndex1]); ////t1 := f.CalcT1(t0); ////WriteLn(', t1: ', t1); //f.Free; //// V_x = (V_0 * t_0 - V_1 * t_1 + P_0 - P_1) / (t_0 - t_1) //v := (FHailstones[AIndex1].Velocity * t0 - FHailstones[AIndex2].Velocity * t1 // + FHailstones[AIndex1].Position - FHailstones[AIndex2].Position) / (t0 - t1); //// P_x = (V_0 - V_x) * t_0 + P_0 //p := (FHailstones[AIndex1].Velocity - v) * t0 + FHailstones[AIndex1].Position; //FPart2 := Round(p.data[0]) + Round(p.data[1]) + Round(p.data[2]); //for i := 0 to FHailstones.Count - 3 do // for j := i + 1 to FHailstones.Count - 2 do // for k:= j + 1 to FHailstones.Count - 1 do // begin // WriteLn(i, j, k); // solver := TRockThrowSolver.Create(FHailstones[i], FHailstones[j], FHailstones[k], 0); // case i of // 0: x0 := 5; // 1: x0 := 3; // 2: x0 := 4; // end; // f := solver.CalcValue(x0); // solver.Free; // end; //for i := 80 to 120 do //begin // solver := TRockThrowSolver.Create(FHailstones[0], FHailstones[1], FHailstones[2], 0); // x0 := i / 20; // f := solver.CalcValue(x0); // WriteLn(x0, ' ', f.Valid, ' ', f.Value); // solver.Free; //end; end; constructor TNeverTellMeTheOdds.Create(const AMin: Int64; const AMax: Int64); begin FMin := AMin; FMax := AMax; FHailstones := THailstones.Create; end; destructor TNeverTellMeTheOdds.Destroy; begin FHailstones.Free; inherited Destroy; end; procedure TNeverTellMeTheOdds.ProcessDataLine(const ALine: string); begin FHailstones.Add(THailstone.Create(ALine)); end; procedure TNeverTellMeTheOdds.Finish; var i, j, k: Integer; begin for i := 0 to FHailstones.Count - 2 do for j := i + 1 to FHailstones.Count - 1 do if AreIntersecting(FHailstones[i], FHailstones[j]) then Inc(FPart1); //for i := 0 to FHailstones.Count - 1 do // for j := 0 to FHailstones.Count - 1 do // for k := 0 to FHailstones.Count - 1 do // if (i <> j) and (i <> k) and (j <> k) then // FindRockThrow(i, j, k); FindRockThrow(0, 1, 2); end; function TNeverTellMeTheOdds.GetDataFileName: string; begin Result := 'never_tell_me_the_odds.txt'; end; function TNeverTellMeTheOdds.GetPuzzleName: string; begin Result := 'Day 24: Never Tell Me The Odds'; end; end.