Added solution to problem 27

This commit is contained in:
2020-09-11 14:02:49 -04:00
parent 450524fcc1
commit b0e6fbe76a
3 changed files with 141 additions and 2 deletions

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@@ -32,7 +32,7 @@ namespace ProjectEulerCS{
private static readonly List<int> _PROBLEM_NUMBERS = new List<int>()
{ 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<int> 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;

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@@ -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

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@@ -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 <https://www.gnu.org/licenses/>.
*/
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<int> 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<int>();
}
//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
*/