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Added solution to problem 33
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@@ -36,7 +36,7 @@ public class ProblemSelection{
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public static final ArrayList<Integer> PROBLEM_NUMBERS = new ArrayList<Integer>(Arrays.asList( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
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11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
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21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
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31, 32, 67));
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31, 32, 33, 67));
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//Returns the problem corresponding to the given problem number
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public static Problem getProblem(Integer problemNumber){
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@@ -74,6 +74,7 @@ public class ProblemSelection{
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case 30 : problem = new Problem30(); break;
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case 31 : problem = new Problem31(); break;
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case 32 : problem = new Problem32(); break;
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case 33 : problem = new Problem33(); break;
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case 67 : problem = new Problem67(); break;
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}
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return problem;
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166
src/main/java/mattrixwv/ProjectEuler/Problems/Problem33.java
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166
src/main/java/mattrixwv/ProjectEuler/Problems/Problem33.java
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@@ -0,0 +1,166 @@
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//ProjectEulerJava/src/main/java/mattrixwv/ProjectEuler/Problems/Problem33.java
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//Matthew Ellison
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// Created: 02-05-21
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//Modified: 02-07-21
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/*
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The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s
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We shall consider fractions like, 30/50 = 3/5, to be trivial examples
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There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator
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If the product of these four fractions is given in its lowest common terms, find the value of the denominator
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*/
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//Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/JavaClasses
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/*
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Copyright (C) 2021 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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*/
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package mattrixwv.ProjectEuler.Problems;
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import java.util.ArrayList;
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import mattrixwv.Algorithms;
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import mattrixwv.ProjectEuler.Unsolved;
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public class Problem33 extends Problem{
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//Variables
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//Static variables
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private static final int MIN_NUMERATOR = 10; //The lowest the numerator can be
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private static final int MAX_NUMERATOR = 98; //The highest the numerator can be
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private static final int MIN_DENOMINATOR = 11; //The lowest the denominator can be
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private static final int MAX_DENOMINATOR = 99; //The highest the denominator can be
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//Instance variables
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private ArrayList<Integer> numerators; //Holds the numerators that were found
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private ArrayList<Integer> denominators; //Holds the denominators that were found
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private int prodDenominator; //Holds the answer to the question
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//Functions
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//Constructor
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public Problem33(){
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super("If the product of these four fractions is given in its lowest common terms, find the value of the denominator");
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prodDenominator = 1;
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numerators = new ArrayList<Integer>();
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denominators = new ArrayList<Integer>();
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}
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//Operational functions
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//Solve the problem
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@Override
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public void solve(){
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//If the problem has already been solved do nothing and end the function
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if(solved){
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return;
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}
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//Start the timer
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timer.start();
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//Search every possible numerator/denominator pair
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for(int denominator = MIN_DENOMINATOR;denominator <= MAX_DENOMINATOR;++denominator){
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for(int numerator = MIN_NUMERATOR;(numerator < denominator) && (numerator <= MAX_NUMERATOR);++numerator){
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String denom = Integer.toString(denominator);
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String num = Integer.toString(numerator);
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int tempNum = 0;
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int tempDenom = 1;
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//Check that this isn't a trivial example
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if((num.charAt(1) == '0') && (denom.charAt(1) == '0')){
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continue;
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}
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//Remove the offending digits if they exist
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else if(num.charAt(0) == denom.charAt(0)){
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tempNum = num.charAt(1) - 48;
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tempDenom = denom.charAt(1) - 48;
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}
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else if(num.charAt(0) == denom.charAt(1)){
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tempNum = num.charAt(1) - 48;
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tempDenom = denom.charAt(0) - 48;
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}
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else if(num.charAt(1) == denom.charAt(0)){
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tempNum = num.charAt(0) - 48;
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tempDenom = denom.charAt(1) - 48;
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}
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else if(num.charAt(1) == denom.charAt(1)){
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tempNum = num.charAt(0) - 48;
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tempDenom = denom.charAt(0) - 48;
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}
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//Test if the new fraction is the same as the old one
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if(((double)tempNum / (double)tempDenom) == ((double)numerator / (double)denominator)){
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numerators.add(numerator);
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denominators.add(denominator);
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}
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}
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}
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//Get the product of the numbers
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int numProd = Algorithms.getProd(numerators);
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int denomProd = Algorithms.getProd(denominators);
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//Get the gcd to reduce to lowest terms
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int gcd = Algorithms.gcd(numProd, denomProd);
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//Save the denominator
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prodDenominator = denomProd / gcd;
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//Stop the timer
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timer.stop();
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//Throw a flag to show the problem is solved
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solved = true;
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}
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//Reset the problem so it can be run again
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@Override
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public void reset(){
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super.reset();
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numerators.clear();
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denominators.clear();
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}
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//Gets
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//Returns the result of solving the problem
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@Override
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public String getResult(){
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if(!solved){
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throw new Unsolved();
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}
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return String.format("The denominator of the product is %d", prodDenominator);
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}
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//Returns the list of numerators
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ArrayList<Integer> getNumerators(){
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw new Unsolved();
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}
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return numerators;
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}
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//Returns the list of denominators
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ArrayList<Integer> getDenominators(){
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw new Unsolved();
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}
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return denominators;
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}
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//Returns the answer to the question
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int getProdDenominator(){
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw new Unsolved();
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}
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return prodDenominator;
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}
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}
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/* Results:
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The denominator of the product is 100
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It took an average of 522.671 microseconds to run this problem through 100 iterations
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*/
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