From b0e6fbe76a342c7902284ee34c56aef6a8099b2f Mon Sep 17 00:00:00 2001 From: Mattrixwv Date: Fri, 11 Sep 2020 14:02:49 -0400 Subject: [PATCH] Added solution to problem 27 --- ProjectEulerCS/ProblemSelection.cs | 3 +- ProjectEulerCS/Problems/Problem26.cs | 2 +- ProjectEulerCS/Problems/Problem27.cs | 138 +++++++++++++++++++++++++++ 3 files changed, 141 insertions(+), 2 deletions(-) create mode 100644 ProjectEulerCS/Problems/Problem27.cs diff --git a/ProjectEulerCS/ProblemSelection.cs b/ProjectEulerCS/ProblemSelection.cs index 46aa10f..3982167 100644 --- a/ProjectEulerCS/ProblemSelection.cs +++ b/ProjectEulerCS/ProblemSelection.cs @@ -32,7 +32,7 @@ namespace ProjectEulerCS{ private static readonly List _PROBLEM_NUMBERS = new List() { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, - 20, 21, 22, 23, 24, 25, 26, 67}; + 20, 21, 22, 23, 24, 25, 26, 27, 67}; public static System.Collections.Generic.List PROBLEM_NUMBERS{ get { return _PROBLEM_NUMBERS; } } @@ -67,6 +67,7 @@ namespace ProjectEulerCS{ case 24: problem = new Problem24(); break; case 25: problem = new Problem25(); break; case 26: problem = new Problem26(); break; + case 27: problem = new Problem27(); break; case 67: problem = new Problem67(); break; } return problem; diff --git a/ProjectEulerCS/Problems/Problem26.cs b/ProjectEulerCS/Problems/Problem26.cs index d9e84b7..3fe3036 100644 --- a/ProjectEulerCS/Problems/Problem26.cs +++ b/ProjectEulerCS/Problems/Problem26.cs @@ -2,7 +2,7 @@ //Matthew Ellison // Created: 09-11-20 //Modified: 09-11-20 -//What is the index of the first term in the Fibonacci sequence to contain 1000 digits? +//Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part. //Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/CSClasses /* Copyright (C) 2020 Matthew Ellison diff --git a/ProjectEulerCS/Problems/Problem27.cs b/ProjectEulerCS/Problems/Problem27.cs new file mode 100644 index 0000000..902ffff --- /dev/null +++ b/ProjectEulerCS/Problems/Problem27.cs @@ -0,0 +1,138 @@ +//ProjectEuler/ProjectEulerCS/src/Problems/Problem27.cs +//Matthew Ellison +// Created: 09-11-20 +//Modified: 09-11-20 +//Find the product of the coefficients, |a| < 1000 and |b| <= 1000, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0. +//Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/CSClasses +/* + Copyright (C) 2020 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser 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 Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +*/ + + +using System.Collections.Generic; + + +namespace ProjectEulerCS.Problems{ + public class Problem27 : Problem{ + //Variables + //Static variables + private const int LARGEST_POSSIBLE_A = 999; + private const int LARGEST_POSSIBLE_B = 1000; + //Instance variables + private int topA; //The A for the most n's generated + private int topB; //THe B for the most n's generated + private int topN; //The most n's generated + private List primes; //A list of all primes that could possibly be generated with this formula + public int TOP_A{ + get{ + if(!solved){ + throw new Unsolved(); + } + return topA; + } + } + public int TOP_B{ + get{ + if(!solved){ + throw new Unsolved(); + } + return topB; + } + } + public int TOP_N{ + get{ + if(!solved){ + throw new Unsolved(); + } + return topN; + } + } + public override string Result{ + get{ + if(!solved){ + throw new Unsolved(); + } + return $"The greatest number of primes found is {topN}\nIt was found with A = {topA}, B = {topB}\nThe product of A and B is {topA * topB}"; + } + } + + //Functions + //Constructor + public Problem27() : base($"Find the product of the coefficients, |a| <= {LARGEST_POSSIBLE_A} and |b| <= {LARGEST_POSSIBLE_B}, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0"){ + topA = 0; + topB = 0; + topN = 0; + primes = new List(); + } + //Operational functions + //Solve the problem + public override void Solve(){ + //If the problem has already been solved do nothing and end the function + if(solved){ + return; + } + + //Start the timer + timer.Start(); + + //Get the primes + primes = mee.Algorithms.GetPrimes(12000); + + //Start with the lowest possible A and check all possibilities after that + for(int a = -LARGEST_POSSIBLE_A;a <= LARGEST_POSSIBLE_A;++a){ + //Start with the lowest possible B and check all possibilities after that + for(int b = -LARGEST_POSSIBLE_B;b <= LARGEST_POSSIBLE_B;++b){ + //Start with n=0 and check the formula to see how many primes you can get with concecutive n's + int n = 0; + int quadratic = (n * n) + (a * n) + b; + while(primes.Contains(quadratic)){ + ++n; + quadratic = (n * n) + (a * n) + b; + } + --n; //Negate an n because the last formula failed' + + //Set all the largest numbers if this created more primes than any other + if(n > topN){ + topN = n; + topB = b; + topA = a; + } + } + } + + //Top the timer + timer.Stop(); + + //Throw a flag to show the problem is solved + solved = true; + } + //Reset the problem so it can be run again + public override void Reset(){ + base.Reset(); + topA = 0; + topB = 0; + topN = 0; + primes.Clear(); + } + } +} + +/* Result: +The greatest number of primes found is 70 +It was found with A = -61, B = 971 +The product of A and B is -59231 +It took an average of 1.394 seconds to run this problem through 100 iterations +*/