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Moved ProjectEuler to its own repository
This commit is contained in:
@@ -1,45 +0,0 @@
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//ProjectEuler/C++/Problem1.cpp
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//Matthew Ellison
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// Created: 9-28-18
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//Modified: 9-28-18
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//What is the sum of all the multiples of 3 or 5 that are less than 1000
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#include <iostream>
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#include <vector>
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#include <chrono>
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int main(){
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unsigned long fullSum = 0; //For the sum of all the numbers
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std::vector<unsigned long> numbers; //Holds all the numbers
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std::chrono::high_resolution_clock::time_point startTime = std::chrono::high_resolution_clock::now();
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//Step through every number < 1000 and see if either 3 or 5 divide it evenly
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for(int cnt = 0;cnt < 1000;++cnt){
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//If either divides it then add it to the vector
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if((cnt % 3) == 0){
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numbers.push_back(cnt);
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}
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else if((cnt % 5) == 0){
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numbers.push_back(cnt);
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}
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}
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//Get the sum of all numbers
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for(unsigned long num : numbers){
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fullSum += num;
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}
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//Calculate the time needed to run the algorithm
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std::chrono::high_resolution_clock::time_point endTime = std::chrono::high_resolution_clock::now();
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std::chrono::high_resolution_clock::duration dur = std::chrono::duration_cast<std::chrono::nanoseconds>(endTime - startTime);
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//Print the output
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std::cout << "The sum of all the numbers < 1000 that are divisible by 3 or 5 is " << fullSum
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<< "\nIt took " << dur.count() << " nanoseconds to run this algorithm" << std::endl;
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std::cin.get();
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return 0;
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}
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@@ -1,57 +0,0 @@
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//ProjectEuler/C++/Problem12.cpp
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//Matthew Ellison
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// Created: 9-27-18
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//Modified: 9-28-18
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//This file contains the program to calculate the answer to Problem 12 on ProjectEuler.net
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#include <iostream>
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#include <chrono> //For the timer
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//Counter how many divisors number has
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unsigned long countDivisors(unsigned long number);
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int main(){
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bool found = false; //To flag whether the number has been found
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unsigned long sum = 1; //The sum of the numbers up to counter
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unsigned long counter = 2; //The next number to be added to sum
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const unsigned long goalDivisors = 500; //The number of divisors that is being sought
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std::chrono::high_resolution_clock::time_point startTime = std::chrono::high_resolution_clock::now();
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while(!found){
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//If the number of divisors is correct set the flag
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if(countDivisors(sum) > goalDivisors){
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found = true;
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}
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//Otherwise add to the sum and increase the next numeber
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else{
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sum += counter;
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++counter;
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}
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}
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std::chrono::high_resolution_clock::time_point endTime = std::chrono::high_resolution_clock::now();
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//Print the results
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std::cout << "The triangular number " << sum << " is made with all number >= " << counter - 1 << " and has " << countDivisors << " divisors" << std::endl;
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std::cout << "The problem took " << std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::high_resolution_clock::duration(endTime - startTime)).count() << " milliseconds" << std::endl;
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std::cin.get();
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return 0;
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}
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unsigned long countDivisors(unsigned long number){
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unsigned long numDivisors = 0; //Holds the number of divisors
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//You only need to go to sqrt(number). cnt * cnt is faster than sqrt()
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for(int cnt = 1;cnt * cnt < number;++cnt){
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//Check if the counter evenly divides the number
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//If it does the counter and the other number are both divisors
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if((number % cnt) == 0){
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numDivisors += 2;
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}
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}
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return numDivisors;
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}
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@@ -1,43 +0,0 @@
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//ProjectEuler/C++/Problem2.cpp
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//Matthew Ellison
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// Created: 9-28-18
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//Modified: 9-28-18
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//The sum of the even Fibonacci numbers less than 4,000,000
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#include <iostream>
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#include <vector>
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#include <chrono>
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int main(){
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unsigned long fullSum = 2; //Holds the sum of all the numbers
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std::vector<unsigned long> fib = {1, 1}; //Holds the Fibonacci numbers
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unsigned long nextFib = 2; //Holds the next Fibonacci number
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std::chrono::high_resolution_clock::time_point startTime = std::chrono::high_resolution_clock::now(); //Start the timer
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while(nextFib < 4000000){
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//If it is an even number add it to the sum
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if(nextFib % 2){
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fullSum += nextFib;
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}
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//Move all the fib numbers down and calculate the next one
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fib.at(0) = fib.at(1);
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fib.at(1) = nextFib;
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nextFib = fib.at(1) + fib.at(0);
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//You could do this keeping all the fib numbers and sum at the end,
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//but this way will be faster because you are only handling every number twice
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//and you don't have to expand the vector
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}
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//Calculate the time needed for the algorithm
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std::chrono::high_resolution_clock::time_point endTime = std::chrono::high_resolution_clock::now(); //End the timer
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std::chrono::high_resolution_clock::duration dur = std::chrono::duration_cast<std::chrono::nanoseconds>(endTime - startTime);
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//Print the resultss
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std::cout << "The sum of the even Fibonacci numbers less than 4,000,000 is " << fullSum
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<< "\nIt took " << dur.count() << " nanoseconds to run this algorithm" << std::endl;
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//Pause before ending
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std::cin.get();
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return 0;
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}
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@@ -1,104 +0,0 @@
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//ProjectEuler/C++/Problem3.cpp
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//Matthew Ellison
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// Created: 9-28-18
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//Modified: 9-28-18
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//The largest prime factor of 600851475143
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#include <iostream>
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#include <cmath>
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#include <vector>
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#include <chrono>
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std::vector<unsigned long long> generatePrimes(const unsigned long long number);
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unsigned long long findLargest(const std::vector<unsigned long long> list);
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int main(){
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const unsigned long long goalNumber = 600851475143; //The number you are trying to find the factors of
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std::vector<unsigned long long> primes; //Holds the list of prime numbers
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std::vector<unsigned long long> factors; //Holds the factors of goalNumber
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unsigned long long number = goalNumber; //The number that is left after taking the prime numbers out
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bool found = false;
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std::chrono::high_resolution_clock::time_point startTime = std::chrono::high_resolution_clock::now();
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//Generate the primes
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primes = generatePrimes(ceil(sqrt(goalNumber)));
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//Check the primes against the number
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//62113 numbers at this point
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while(!found){
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//Loop through the list of primes
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for(int cnt = 0;cnt < primes.size();){
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//See if after dividing a prime out it is left with a whole number
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if((number % primes.at(cnt)) == 0){
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number /= primes.at(cnt);
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factors.push_back(primes.at(cnt));
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}
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//If you didn't find a prime then advance to the next possible number
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//If you did find a prime then stay where you are in the list incase it occurs more than once
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else{
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++cnt;
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}
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}
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//If the remaining number is 1 then you just added the last number to the factors
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if(number == 1){
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found = true;
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}
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}
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//Look for the largest number in the vector
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unsigned long long maxNum = findLargest(factors);
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//Calculate the amount of time it took to run the algorithm
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std::chrono::high_resolution_clock::time_point endTime = std::chrono::high_resolution_clock::now();
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std::chrono::high_resolution_clock::duration dur = std::chrono::duration_cast<std::chrono::milliseconds>(endTime - startTime);
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//Print the results
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std::cout << "The largest factor of the number " << goalNumber << " is " << maxNum
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<< "\nIt took " << dur.count() << " milliseconds to run this algorith" << std::endl;
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//Pause before exiting
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std::cin.get();
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return 0;
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}
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std::vector<unsigned long long> generatePrimes(const unsigned long long goalNumber){
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std::vector<unsigned long long> primes;
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bool foundFactor = false;
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//Start at 2 so we can skip 1
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if(goalNumber >= 2){
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primes.push_back(2);
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}
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//We can skip all of the even numbers
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for(unsigned long long possiblePrime = 3;possiblePrime < goalNumber;possiblePrime += 2){
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//Step through every element in the current primes. If you don't find anything that divides it, it must be a prime itself
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for(int cnt = 0;(cnt < primes.size()) && ((primes.at(cnt) * primes.at(cnt)) < goalNumber);++cnt){
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if(fmod(((double)possiblePrime / primes.at(cnt)), 1) == 0){
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foundFactor = true;
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break;
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}
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}
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//If you didn't find a factor then it must be prime
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if(!foundFactor){
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primes.push_back(possiblePrime);
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}
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//If you did find a factor you need to reset the flag
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else{
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foundFactor = false;
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}
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}
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return primes;
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}
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unsigned long long findLargest(const std::vector<unsigned long long> list){
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unsigned long long maxNum = 0;
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for(unsigned long long num : list){
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if(num > maxNum){
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maxNum = num;
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}
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}
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return maxNum;
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}
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@@ -1,30 +0,0 @@
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%ProjectEuler/Problem1.m
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%This is a script to answer Problem 1 for Project Euler
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%What is the sum of all the multiples of 3 or 5 that are less than 1000
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%Setup your variables
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fullSum = 0; %To hold the sum of all the numbers
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numbers = 0; %To hold all of the numbers
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counter = 0; %The number. It must stay below 1000
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while(counter < 1000)
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%See if the number is a multiple of 3
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if(mod(counter, 3) == 0)
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numbers(end + 1) = counter;
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%See if the number is a multiple of 5
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elseif(mod(counter, 5) == 0)
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numbers(end + 1) = counter;
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end
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%Increment the number
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++counter;
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end
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%When done this way it removes the possibility of duplicate numbers
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fullSum = sum(numbers);
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ans = fullSum
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%Cleanup your variables
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clear fullSum;
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clear numbers;
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clear counter;
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@@ -1,6 +0,0 @@
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%ProjectEuler/Problem10.m
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%This is a script to answer Problem 10 for Project Euler
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%Find the sum of all the primes below two million.
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%Print the answer
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sum(primes(2000000))
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@@ -1,152 +0,0 @@
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%ProjectEuler/Problem11.m
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%This is a script to answer Problem 11 for Project Euler
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%What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
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%{
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08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
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49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
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81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
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52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
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22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
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24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
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32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
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67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
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24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
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21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
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78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
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16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
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86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
|
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19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
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04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
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88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
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04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
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20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
|
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20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
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01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
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%}
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%Create your variables
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grid = [08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08;
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49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00;
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81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65;
|
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52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91;
|
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22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80;
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24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50;
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32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70;
|
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67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21;
|
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24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72;
|
||||
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95;
|
||||
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92;
|
||||
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57;
|
||||
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58;
|
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19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40;
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04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66;
|
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88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69;
|
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04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36;
|
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20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16;
|
||||
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54;
|
||||
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48];
|
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currentLocation = [1, 1]; %The location you are checking now
|
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currentProduct = [0 0 0 0]; %The product you are ucrrently looking at
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greatestProduct = [0 0 0 0]; %The greatest product of values you have found
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finished = false;
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%Loop until you reach the last element
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startTime = clock();
|
||||
while(~finished)
|
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left = false;
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right = false;
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down = false;
|
||||
|
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%Check which directions you can go
|
||||
%When moving you will be moving 4 locations
|
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if((currentLocation(2) - 3) >= 1)
|
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left = true;
|
||||
end
|
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if((currentLocation(2) + 3) <= size(grid)(2))
|
||||
right = true;
|
||||
end
|
||||
if((currentLocation(1) + 3) <= size(grid)(1))
|
||||
down = true;
|
||||
end
|
||||
|
||||
%Check the possible directions and check against greatest
|
||||
%Left
|
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if(left)
|
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currentProduct = grid(currentLocation(1),currentLocation(2):-1:(currentLocation(2) - 3));
|
||||
%If the current numbers' product is greater than the greatest product so far, replace it
|
||||
if(prod(currentProduct) > prod(greatestProduct))
|
||||
greatestProduct = currentProduct;
|
||||
end
|
||||
end
|
||||
%Right
|
||||
if(right)
|
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currentProduct = grid(currentLocation(1), currentLocation(2):(currentLocation(2) + 3));
|
||||
%If the current numbers' product is greater than the greatest product so far, replace it
|
||||
if(prod(currentProduct) > prod(greatestProduct))
|
||||
greatestProduct = currentProduct;
|
||||
end
|
||||
end
|
||||
%Down
|
||||
if(down)
|
||||
currentProduct = grid(currentLocation(1):(currentLocation(1) + 3), currentLocation(2));
|
||||
%If the current numbers' product is greater than the greatest product so far, replace it
|
||||
if(prod(currentProduct) > prod(greatestProduct))
|
||||
greatestProduct = currentProduct;
|
||||
end
|
||||
end
|
||||
%LeftDown
|
||||
if(left && down)
|
||||
currentProduct(1) = grid(currentLocation(1), currentLocation(2));
|
||||
currentProduct(2) = grid(currentLocation(1) + 1,currentLocation(2) - 1);
|
||||
currentProduct(3) = grid(currentLocation(1) + 2,currentLocation(2) - 2);
|
||||
currentProduct(4) = grid(currentLocation(1) + 3,currentLocation(2) - 3);
|
||||
%If the current numbers' product is greater than the greatest product so far, replace it
|
||||
if(prod(currentProduct) > prod(greatestProduct))
|
||||
greatestProduct = currentProduct;
|
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end
|
||||
end
|
||||
%RightDown
|
||||
if(right && down)
|
||||
currentProduct(1) = grid(currentLocation(1), currentLocation(2));
|
||||
currentProduct(2) = grid(currentLocation(1) + 1,currentLocation(2) + 1);
|
||||
currentProduct(3) = grid(currentLocation(1) + 2,currentLocation(2) + 2);
|
||||
currentProduct(4) = grid(currentLocation(1) + 3,currentLocation(2) + 3);
|
||||
%If the current numbers' product is greater than the greatest product so far, replace it
|
||||
if(prod(currentProduct) > prod(greatestProduct))
|
||||
greatestProduct = currentProduct;
|
||||
end
|
||||
end
|
||||
|
||||
%Move to the next column
|
||||
++currentLocation(2);
|
||||
%If you have moved too far in the columns move back to the beginning and to the next row
|
||||
if(currentLocation(2) > size(grid)(2))
|
||||
currentLocation(2) = 1;
|
||||
++currentLocation(1);
|
||||
end
|
||||
%If the row is currently greater than what is available you have traversed the list
|
||||
if(currentLocation(1) > size(grid)(1))
|
||||
finished = true;
|
||||
end
|
||||
end
|
||||
greatestProduct = reshape(greatestProduct, 1, 4); %For some reason it is coming out a 4X1 instead of 1X4
|
||||
endTime = clock();
|
||||
|
||||
%Print the result
|
||||
totalTime = etime(endTime, startTime)
|
||||
greatestProduct
|
||||
prod(greatestProduct)
|
||||
|
||||
%Cleanup the variables
|
||||
clear down;
|
||||
clear right;
|
||||
clear left;
|
||||
clear finished;
|
||||
clear startTime;
|
||||
clear endTime;
|
||||
clear totalTime;
|
||||
clear grid;
|
||||
clear greatestProduct;
|
||||
clear currentLocation;
|
||||
clear currentProduct;
|
||||
@@ -1,51 +0,0 @@
|
||||
%ProjectEuler/Problem12.m
|
||||
%This is a script to answer Problem 12 for Project Euler
|
||||
%What is the value of the first triangle number to have over five hundred divisors?
|
||||
|
||||
%Setup your variables
|
||||
counter = 1; %To hold the current number you have counted up to
|
||||
number = 0; %To hold the current triangle number
|
||||
found = false; %To tell when the answer has been found
|
||||
numDivisors = 0;
|
||||
maxDivisors = 0;
|
||||
maxCounter = 0;
|
||||
|
||||
|
||||
startTime = clock();
|
||||
while(~found)
|
||||
%Get your next triangle number
|
||||
number = sym(sum([1:counter]));
|
||||
|
||||
%See if it has 500 divisors
|
||||
numDivisors = size(divisors(number))(2);
|
||||
if(numDivisors > maxDivisors)
|
||||
maxDivisors = numDivisors;
|
||||
maxCounter = counter;
|
||||
end
|
||||
if(numDivisors > 500)
|
||||
found = true;
|
||||
else
|
||||
counter = counter + 1;
|
||||
end
|
||||
end
|
||||
endTime = clock();
|
||||
|
||||
%Print your result
|
||||
totalTime = etime(endTime, startTime)
|
||||
topNumber = counter
|
||||
double(number)
|
||||
|
||||
%Cleanup your variables
|
||||
clear counter;
|
||||
clear number;
|
||||
clear found;
|
||||
clear topNumber;
|
||||
clear startTime;
|
||||
clear endTime;
|
||||
clear totalTime;
|
||||
clear numDivisors;
|
||||
clear maxDivisors;
|
||||
clear maxCounter;
|
||||
|
||||
%This will take 6-7 hours to run. I got the C++ answer in 2.8 seconds
|
||||
%Try to find a more efficient way to run this
|
||||
@@ -1,52 +0,0 @@
|
||||
%ProjectEuler/Problem12.m
|
||||
%This is a script to answer Problem 12 for Project Euler
|
||||
%What is the value of the first triangle number to have over five hundred divisors?
|
||||
|
||||
found = false;
|
||||
numSum = 1;
|
||||
counter = 2;
|
||||
numDivisors = 0;
|
||||
goalDivisors = 500;
|
||||
|
||||
startTime = clock();
|
||||
while(~found)
|
||||
%Count the number of divisors
|
||||
numDivisors = 0;
|
||||
divCounter = 0;
|
||||
while((divCounter * divCounter) < numSum)
|
||||
if(mod(numSum, divCounter) == 0)
|
||||
numDivisors += 2;
|
||||
end
|
||||
++divCounter;
|
||||
end
|
||||
|
||||
%Check if there are enough divisors
|
||||
if(numDivisors > goalDivisors)
|
||||
found = true;
|
||||
else
|
||||
numSum += counter;
|
||||
++counter;
|
||||
end
|
||||
end
|
||||
endTime = clock();
|
||||
|
||||
%Print the result
|
||||
number = numSum
|
||||
highestNumber = counter - 1
|
||||
numDivisors = numDivisors
|
||||
totalTime = etime(endTime, startTime)
|
||||
|
||||
%Cleanup the variables
|
||||
clear found;
|
||||
clear numSum;
|
||||
clear counter;
|
||||
clear numDivisors;
|
||||
clear goalDivisors;
|
||||
clear startTime;
|
||||
clear endTime;
|
||||
clear totalTime;
|
||||
clear numDivisors;
|
||||
clear divCounter;
|
||||
clear ans;
|
||||
|
||||
%Returns result in 7.5 minutes
|
||||
@@ -1,214 +0,0 @@
|
||||
%ProjectEuler/Problem13.m
|
||||
%This is a script to answer Problem 13 for Project Euler
|
||||
%Work out the first ten digits of the sum of the following one-hundred 50-digit numbers
|
||||
%{
|
||||
37107287533902102798797998220837590246510135740250
|
||||
46376937677490009712648124896970078050417018260538
|
||||
74324986199524741059474233309513058123726617309629
|
||||
91942213363574161572522430563301811072406154908250
|
||||
23067588207539346171171980310421047513778063246676
|
||||
89261670696623633820136378418383684178734361726757
|
||||
28112879812849979408065481931592621691275889832738
|
||||
44274228917432520321923589422876796487670272189318
|
||||
47451445736001306439091167216856844588711603153276
|
||||
70386486105843025439939619828917593665686757934951
|
||||
62176457141856560629502157223196586755079324193331
|
||||
64906352462741904929101432445813822663347944758178
|
||||
92575867718337217661963751590579239728245598838407
|
||||
58203565325359399008402633568948830189458628227828
|
||||
80181199384826282014278194139940567587151170094390
|
||||
35398664372827112653829987240784473053190104293586
|
||||
86515506006295864861532075273371959191420517255829
|
||||
71693888707715466499115593487603532921714970056938
|
||||
54370070576826684624621495650076471787294438377604
|
||||
53282654108756828443191190634694037855217779295145
|
||||
36123272525000296071075082563815656710885258350721
|
||||
45876576172410976447339110607218265236877223636045
|
||||
17423706905851860660448207621209813287860733969412
|
||||
81142660418086830619328460811191061556940512689692
|
||||
51934325451728388641918047049293215058642563049483
|
||||
62467221648435076201727918039944693004732956340691
|
||||
15732444386908125794514089057706229429197107928209
|
||||
55037687525678773091862540744969844508330393682126
|
||||
18336384825330154686196124348767681297534375946515
|
||||
80386287592878490201521685554828717201219257766954
|
||||
78182833757993103614740356856449095527097864797581
|
||||
16726320100436897842553539920931837441497806860984
|
||||
48403098129077791799088218795327364475675590848030
|
||||
87086987551392711854517078544161852424320693150332
|
||||
59959406895756536782107074926966537676326235447210
|
||||
69793950679652694742597709739166693763042633987085
|
||||
41052684708299085211399427365734116182760315001271
|
||||
65378607361501080857009149939512557028198746004375
|
||||
35829035317434717326932123578154982629742552737307
|
||||
94953759765105305946966067683156574377167401875275
|
||||
88902802571733229619176668713819931811048770190271
|
||||
25267680276078003013678680992525463401061632866526
|
||||
36270218540497705585629946580636237993140746255962
|
||||
24074486908231174977792365466257246923322810917141
|
||||
91430288197103288597806669760892938638285025333403
|
||||
34413065578016127815921815005561868836468420090470
|
||||
23053081172816430487623791969842487255036638784583
|
||||
11487696932154902810424020138335124462181441773470
|
||||
63783299490636259666498587618221225225512486764533
|
||||
67720186971698544312419572409913959008952310058822
|
||||
95548255300263520781532296796249481641953868218774
|
||||
76085327132285723110424803456124867697064507995236
|
||||
37774242535411291684276865538926205024910326572967
|
||||
23701913275725675285653248258265463092207058596522
|
||||
29798860272258331913126375147341994889534765745501
|
||||
18495701454879288984856827726077713721403798879715
|
||||
38298203783031473527721580348144513491373226651381
|
||||
34829543829199918180278916522431027392251122869539
|
||||
40957953066405232632538044100059654939159879593635
|
||||
29746152185502371307642255121183693803580388584903
|
||||
41698116222072977186158236678424689157993532961922
|
||||
62467957194401269043877107275048102390895523597457
|
||||
23189706772547915061505504953922979530901129967519
|
||||
86188088225875314529584099251203829009407770775672
|
||||
11306739708304724483816533873502340845647058077308
|
||||
82959174767140363198008187129011875491310547126581
|
||||
97623331044818386269515456334926366572897563400500
|
||||
42846280183517070527831839425882145521227251250327
|
||||
55121603546981200581762165212827652751691296897789
|
||||
32238195734329339946437501907836945765883352399886
|
||||
75506164965184775180738168837861091527357929701337
|
||||
62177842752192623401942399639168044983993173312731
|
||||
32924185707147349566916674687634660915035914677504
|
||||
99518671430235219628894890102423325116913619626622
|
||||
73267460800591547471830798392868535206946944540724
|
||||
76841822524674417161514036427982273348055556214818
|
||||
97142617910342598647204516893989422179826088076852
|
||||
87783646182799346313767754307809363333018982642090
|
||||
10848802521674670883215120185883543223812876952786
|
||||
71329612474782464538636993009049310363619763878039
|
||||
62184073572399794223406235393808339651327408011116
|
||||
66627891981488087797941876876144230030984490851411
|
||||
60661826293682836764744779239180335110989069790714
|
||||
85786944089552990653640447425576083659976645795096
|
||||
66024396409905389607120198219976047599490197230297
|
||||
64913982680032973156037120041377903785566085089252
|
||||
16730939319872750275468906903707539413042652315011
|
||||
94809377245048795150954100921645863754710598436791
|
||||
78639167021187492431995700641917969777599028300699
|
||||
15368713711936614952811305876380278410754449733078
|
||||
40789923115535562561142322423255033685442488917353
|
||||
44889911501440648020369068063960672322193204149535
|
||||
41503128880339536053299340368006977710650566631954
|
||||
81234880673210146739058568557934581403627822703280
|
||||
82616570773948327592232845941706525094512325230608
|
||||
22918802058777319719839450180888072429661980811197
|
||||
77158542502016545090413245809786882778948721859617
|
||||
72107838435069186155435662884062257473692284509516
|
||||
20849603980134001723930671666823555245252804609722
|
||||
53503534226472524250874054075591789781264330331690
|
||||
%}
|
||||
|
||||
%Variables
|
||||
nums = [37107287533902102798797998220837590246510135740250,
|
||||
46376937677490009712648124896970078050417018260538,
|
||||
74324986199524741059474233309513058123726617309629,
|
||||
91942213363574161572522430563301811072406154908250,
|
||||
23067588207539346171171980310421047513778063246676,
|
||||
89261670696623633820136378418383684178734361726757,
|
||||
28112879812849979408065481931592621691275889832738,
|
||||
44274228917432520321923589422876796487670272189318,
|
||||
47451445736001306439091167216856844588711603153276,
|
||||
70386486105843025439939619828917593665686757934951,
|
||||
62176457141856560629502157223196586755079324193331,
|
||||
64906352462741904929101432445813822663347944758178,
|
||||
92575867718337217661963751590579239728245598838407,
|
||||
58203565325359399008402633568948830189458628227828,
|
||||
80181199384826282014278194139940567587151170094390,
|
||||
35398664372827112653829987240784473053190104293586,
|
||||
86515506006295864861532075273371959191420517255829,
|
||||
71693888707715466499115593487603532921714970056938,
|
||||
54370070576826684624621495650076471787294438377604,
|
||||
53282654108756828443191190634694037855217779295145,
|
||||
36123272525000296071075082563815656710885258350721,
|
||||
45876576172410976447339110607218265236877223636045,
|
||||
17423706905851860660448207621209813287860733969412,
|
||||
81142660418086830619328460811191061556940512689692,
|
||||
51934325451728388641918047049293215058642563049483,
|
||||
62467221648435076201727918039944693004732956340691,
|
||||
15732444386908125794514089057706229429197107928209,
|
||||
55037687525678773091862540744969844508330393682126,
|
||||
18336384825330154686196124348767681297534375946515,
|
||||
80386287592878490201521685554828717201219257766954,
|
||||
78182833757993103614740356856449095527097864797581,
|
||||
16726320100436897842553539920931837441497806860984,
|
||||
48403098129077791799088218795327364475675590848030,
|
||||
87086987551392711854517078544161852424320693150332,
|
||||
59959406895756536782107074926966537676326235447210,
|
||||
69793950679652694742597709739166693763042633987085,
|
||||
41052684708299085211399427365734116182760315001271,
|
||||
65378607361501080857009149939512557028198746004375,
|
||||
35829035317434717326932123578154982629742552737307,
|
||||
94953759765105305946966067683156574377167401875275,
|
||||
88902802571733229619176668713819931811048770190271,
|
||||
25267680276078003013678680992525463401061632866526,
|
||||
36270218540497705585629946580636237993140746255962,
|
||||
24074486908231174977792365466257246923322810917141,
|
||||
91430288197103288597806669760892938638285025333403,
|
||||
34413065578016127815921815005561868836468420090470,
|
||||
23053081172816430487623791969842487255036638784583,
|
||||
11487696932154902810424020138335124462181441773470,
|
||||
63783299490636259666498587618221225225512486764533,
|
||||
67720186971698544312419572409913959008952310058822,
|
||||
95548255300263520781532296796249481641953868218774,
|
||||
76085327132285723110424803456124867697064507995236,
|
||||
37774242535411291684276865538926205024910326572967,
|
||||
23701913275725675285653248258265463092207058596522,
|
||||
29798860272258331913126375147341994889534765745501,
|
||||
18495701454879288984856827726077713721403798879715,
|
||||
38298203783031473527721580348144513491373226651381,
|
||||
34829543829199918180278916522431027392251122869539,
|
||||
40957953066405232632538044100059654939159879593635,
|
||||
29746152185502371307642255121183693803580388584903,
|
||||
41698116222072977186158236678424689157993532961922,
|
||||
62467957194401269043877107275048102390895523597457,
|
||||
23189706772547915061505504953922979530901129967519,
|
||||
86188088225875314529584099251203829009407770775672,
|
||||
11306739708304724483816533873502340845647058077308,
|
||||
82959174767140363198008187129011875491310547126581,
|
||||
97623331044818386269515456334926366572897563400500,
|
||||
42846280183517070527831839425882145521227251250327,
|
||||
55121603546981200581762165212827652751691296897789,
|
||||
32238195734329339946437501907836945765883352399886,
|
||||
75506164965184775180738168837861091527357929701337,
|
||||
62177842752192623401942399639168044983993173312731,
|
||||
32924185707147349566916674687634660915035914677504,
|
||||
99518671430235219628894890102423325116913619626622,
|
||||
73267460800591547471830798392868535206946944540724,
|
||||
76841822524674417161514036427982273348055556214818,
|
||||
97142617910342598647204516893989422179826088076852,
|
||||
87783646182799346313767754307809363333018982642090,
|
||||
10848802521674670883215120185883543223812876952786,
|
||||
71329612474782464538636993009049310363619763878039,
|
||||
62184073572399794223406235393808339651327408011116,
|
||||
66627891981488087797941876876144230030984490851411,
|
||||
60661826293682836764744779239180335110989069790714,
|
||||
85786944089552990653640447425576083659976645795096,
|
||||
66024396409905389607120198219976047599490197230297,
|
||||
64913982680032973156037120041377903785566085089252,
|
||||
16730939319872750275468906903707539413042652315011,
|
||||
94809377245048795150954100921645863754710598436791,
|
||||
78639167021187492431995700641917969777599028300699,
|
||||
15368713711936614952811305876380278410754449733078,
|
||||
40789923115535562561142322423255033685442488917353,
|
||||
44889911501440648020369068063960672322193204149535,
|
||||
41503128880339536053299340368006977710650566631954,
|
||||
81234880673210146739058568557934581403627822703280,
|
||||
82616570773948327592232845941706525094512325230608,
|
||||
22918802058777319719839450180888072429661980811197,
|
||||
77158542502016545090413245809786882778948721859617,
|
||||
72107838435069186155435662884062257473692284509516,
|
||||
20849603980134001723930671666823555245252804609722,
|
||||
53503534226472524250874054075591789781264330331690];
|
||||
|
||||
format long; %You need to be able to see 10 digits
|
||||
sum(nums)
|
||||
format short; %Set it back to normal
|
||||
|
||||
%Cleanup the variables
|
||||
clear nums;
|
||||
@@ -1,27 +0,0 @@
|
||||
%ProjectEuler/Problem2.m
|
||||
%This is a script to answer Problem 2 for Project Euler
|
||||
%The sum of the even Fibonacci numbers less than 4,000,000
|
||||
|
||||
%Setup your Variables
|
||||
fib = [1, 1, 2]; %Holds the Fibonacci numbers
|
||||
currentFib = fib(end) + fib(end - 1); %The current Fibonacci number to be tested
|
||||
evenFib = [2]; %A subset of the even Fibonacci numbers
|
||||
|
||||
while(currentFib < 4000000)
|
||||
%Add the number to the list
|
||||
fib(end + 1) = currentFib;
|
||||
%If the number is even add it to the even list as well
|
||||
if(mod(currentFib, 2) == 0)
|
||||
evenFib(end + 1) = currentFib;
|
||||
end
|
||||
|
||||
%Set the next Fibonacci
|
||||
currentFib = fib(end) + fib(end - 1);
|
||||
end
|
||||
|
||||
sum(evenFib)
|
||||
|
||||
%Cleanup your variables
|
||||
clear fib;
|
||||
clear currentFib;
|
||||
clear evenFib;
|
||||
@@ -1,48 +0,0 @@
|
||||
%ProjectEuler/Problem3.m
|
||||
%This is a script to answer Problem 3 for Project Euler
|
||||
%The largest prime factor of 600851475143
|
||||
|
||||
%Setup your variables
|
||||
number = 600851475143; %The number we are trying to find the greatest prime factor of
|
||||
primeNums = []; %A list of prime numbers. Will include all prime numbers <= number
|
||||
factors = []; %For the list of factors of number
|
||||
tempNum = number; %Used to track the current value if all of the factors were taken out of number
|
||||
%number = 16; %Used for a test case
|
||||
|
||||
%Get the prime numbers up to sqrt(number). If it is not prime there must be a value <= sqrt
|
||||
primeNums = primes(sqrt(number));
|
||||
|
||||
%Setup the loop
|
||||
counter = 1;
|
||||
%Start with the lowest number and work your way up. When you reach a number > size(primeNums) you have found all of the factors
|
||||
while(counter <= size(primeNums)(2))
|
||||
|
||||
%Divide the number by the next prime number in the list
|
||||
answer = (tempNum/primeNums(counter));
|
||||
|
||||
%If it is a whole number add it to the factors
|
||||
if(mod(answer,1) == 0)
|
||||
factors(end + 1) = primeNums(counter);
|
||||
%Set tempNum so that it reflects number/factors
|
||||
tempNum = tempNum / primeNums(counter);
|
||||
%Keep the counter where it is in case a factor appears more than once
|
||||
%Get the new set of prime numbers
|
||||
primeNums = primes(sqrt(tempNum));
|
||||
else
|
||||
%If it was not an integer increment the counter
|
||||
++counter;
|
||||
end
|
||||
end
|
||||
%When the last number is not divisible by a prime number it must be a prime number
|
||||
factors(end + 1) = tempNum;
|
||||
|
||||
%Print the answer
|
||||
max(factors)
|
||||
|
||||
%Cleanup your variables
|
||||
clear counter;
|
||||
clear tempNum;
|
||||
clear answer;
|
||||
clear number;
|
||||
clear primeNums;
|
||||
clear factors;
|
||||
@@ -1,50 +0,0 @@
|
||||
%ProjectEuler/Problem4.m
|
||||
%This is a script to answer Problem 4 for Project Euler
|
||||
%Find the largest palindrome made from the product of two 3-digit numbers
|
||||
|
||||
%Make your variables
|
||||
answer = 0; %For the product of the two numbers
|
||||
numbers = [100:999]; %Create an array with a list of all 3 digit numbers
|
||||
palindromes = []; %Holds all the numbers that are palindromes
|
||||
%Create 2 counters for an inner loop and an outer loop
|
||||
%This allows you to multiply 2 numbers from the same array
|
||||
outerCounter = 1;
|
||||
innerCounter = 1;
|
||||
|
||||
startTime = clock(); %This is for timing purposes
|
||||
while(outerCounter < size(numbers)(2))
|
||||
innerCounter = outerCounter; %Once you have multiplied 2 numbers there is no need to multiply them again, so skip what has already been done
|
||||
while(innerCounter < size(numbers)(2))
|
||||
%Multiply the two numbers
|
||||
answer = numbers(outerCounter) * numbers(innerCounter);
|
||||
|
||||
%See if the number is a palindromes
|
||||
%%WARNING - Ocatave does not have a Reverse function. I had to create one that reversed strings
|
||||
if(num2str(answer) == Reverse(num2str(answer)))
|
||||
%Add it to the palindromes list
|
||||
palindromes(end + 1) = answer;
|
||||
end
|
||||
++innerCounter; %Increment
|
||||
end
|
||||
++outerCounter; %Increment
|
||||
end
|
||||
endTime = clock(); %This is for timing purposes
|
||||
timeTaken = etime(endTime - startTime) %This is for timing purposes
|
||||
|
||||
max(palindromes)
|
||||
|
||||
%Cleanup your variables
|
||||
clear outerCounter;
|
||||
clear innerCounter;
|
||||
clear answer;
|
||||
clear numbers;
|
||||
clear palindromes;
|
||||
clear startTime;
|
||||
clear endTime;
|
||||
clear timeTaken;
|
||||
|
||||
|
||||
%This way is slow. I would like to find a faster way
|
||||
%{
|
||||
The palindrome can be written as: abccba Which then simpifies to: 100000a + 10000b + 1000c + 100c + 10b + a And then: 100001a + 10010b + 1100c Factoring out 11, you get: 11(9091a + 910b + 100c) So the palindrome must be divisible by 11. Seeing as 11 is prime, at least one of the numbers must be divisible by 11
|
||||
%}
|
||||
@@ -1,43 +0,0 @@
|
||||
%ProjectEuler/Problem5.m
|
||||
%This is a script to answer Problem 5 for Project Euler
|
||||
%What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
|
||||
|
||||
%Create your variables
|
||||
nums = [1:20];
|
||||
factors = [1]; %The factors that are already in the number
|
||||
list = []; %For a temperary list of the factors of the current number
|
||||
counter = 1;
|
||||
|
||||
%You need to find the factors of all the numbers from 1->20
|
||||
while(counter <= size(nums)(2))
|
||||
list = factor(nums(counter));
|
||||
|
||||
%Search factors and try to match all elements in list
|
||||
listCnt = 1;
|
||||
factorCnt = 1;
|
||||
while(listCnt <= size(list)(2))
|
||||
if((factorCnt > size(factors)(2)) || (factors(factorCnt) > list(listCnt)))
|
||||
%If it was not found add the factor to the list for the number and reset the counters
|
||||
factors(end + 1) = list(listCnt);
|
||||
factors = sort(factors);
|
||||
factorCnt = 1;
|
||||
listCnt = 1;
|
||||
elseif(factors(factorCnt) == list(listCnt))
|
||||
++listCnt;
|
||||
++factorCnt;
|
||||
else
|
||||
++factorCnt;
|
||||
end
|
||||
end
|
||||
++counter;
|
||||
end
|
||||
|
||||
prod(factors)
|
||||
|
||||
%Cleanup your variables
|
||||
clear counter;
|
||||
clear factorCnt;
|
||||
clear listCnt;
|
||||
clear list;
|
||||
clear nums;
|
||||
clear factors;
|
||||
@@ -1,21 +0,0 @@
|
||||
%ProjectEuler/Problem4.m
|
||||
%This is a script to answer Problem 4 for Project Euler
|
||||
%Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
|
||||
|
||||
%Setup your variables
|
||||
nums = [1:100];
|
||||
squares = nums.^2; %Square every number in the list nums
|
||||
sumOfSquares = sum(squares); %Get the sum of all the elements in the list squares
|
||||
squareOfSums = sum(nums)^2; %Get the sum of all the elements in the list nums and square the answer
|
||||
value = abs(squareOfSums - sumOfSquares); %Get the difference of the 2 numbers
|
||||
%This could all be done on one line, but this is less confusing
|
||||
|
||||
%Print the value
|
||||
value
|
||||
|
||||
%Cleanup your variables
|
||||
clear nums;
|
||||
clear squares;
|
||||
clear sumOfSquares;
|
||||
clear squareOfSums;
|
||||
clear value;
|
||||
@@ -1,21 +0,0 @@
|
||||
%ProjectEuler/Problem7.m
|
||||
%This is a script to answer Problem 7 for Project Euler
|
||||
%What is the 10001th prime number?
|
||||
|
||||
%Setup the variables
|
||||
counter = 1000;
|
||||
primeList = [];
|
||||
|
||||
%Cycle through the prime numbers until you get the correct number
|
||||
while(size(primeList)(2) < 10001)
|
||||
primeList = primes(counter);
|
||||
counter += 1000;
|
||||
end
|
||||
|
||||
%Print the number
|
||||
primeList(10001)
|
||||
|
||||
%Cleanup the variables
|
||||
clear ans;
|
||||
clear counter;
|
||||
clear primeList;
|
||||
@@ -1,63 +0,0 @@
|
||||
%ProjectEuler/Problem8.m
|
||||
%This is a script to answer Problem 8 for Project Euler
|
||||
%Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
|
||||
%{
|
||||
73167176531330624919225119674426574742355349194934
|
||||
96983520312774506326239578318016984801869478851843
|
||||
85861560789112949495459501737958331952853208805511
|
||||
12540698747158523863050715693290963295227443043557
|
||||
66896648950445244523161731856403098711121722383113
|
||||
62229893423380308135336276614282806444486645238749
|
||||
30358907296290491560440772390713810515859307960866
|
||||
70172427121883998797908792274921901699720888093776
|
||||
65727333001053367881220235421809751254540594752243
|
||||
52584907711670556013604839586446706324415722155397
|
||||
53697817977846174064955149290862569321978468622482
|
||||
83972241375657056057490261407972968652414535100474
|
||||
82166370484403199890008895243450658541227588666881
|
||||
16427171479924442928230863465674813919123162824586
|
||||
17866458359124566529476545682848912883142607690042
|
||||
24219022671055626321111109370544217506941658960408
|
||||
07198403850962455444362981230987879927244284909188
|
||||
84580156166097919133875499200524063689912560717606
|
||||
05886116467109405077541002256983155200055935729725
|
||||
71636269561882670428252483600823257530420752963450
|
||||
%}
|
||||
|
||||
%Setup your variables
|
||||
%The string of the number
|
||||
number = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450';
|
||||
counter = 1; %Location of the first digit in the series
|
||||
productNumbers = ['']; %The numbers in the current product
|
||||
greatestProduct = []; %The numbers in the greatest product
|
||||
|
||||
%Loop through the string until every element has been tested
|
||||
while((counter + 12) < size(number)(2))
|
||||
innerCounter = 0;
|
||||
productNumbers = ['']; %Clear the variable
|
||||
while(innerCounter < 13)
|
||||
%Octave throws an error if you don't take this round about way of adding the characters to the array
|
||||
tempChar = ''; %Throw away variable
|
||||
tempChar = [number(counter + innerCounter), ' ']; %Add the next number to what you already have and add a space at the end
|
||||
productNumbers = [productNumbers, tempChar];
|
||||
++innerCounter;
|
||||
end
|
||||
productNumbers = str2num(productNumbers); %Convert the characters to numbers
|
||||
%Check whether the current product is greater than the current greatest product
|
||||
if(prod(productNumbers) > prod(greatestProduct))
|
||||
greatestProduct = productNumbers;
|
||||
end
|
||||
++counter;
|
||||
end
|
||||
|
||||
%Print the result
|
||||
greatestProduct
|
||||
prod(greatestProduct)
|
||||
|
||||
%Cleanup your variables
|
||||
clear number;
|
||||
clear counter;
|
||||
clear productNumbers;
|
||||
clear greatestProduct;
|
||||
clear tempChar;
|
||||
clear innerCounter;
|
||||
@@ -1,39 +0,0 @@
|
||||
%ProjectEuler/Problem9.m
|
||||
%This is a script to answer Problem 9 for Project Euler
|
||||
%There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
|
||||
|
||||
%Create the variable
|
||||
a = 1;
|
||||
b = 0;
|
||||
c = 0;
|
||||
found = false;
|
||||
|
||||
%Start with the smallest possible a
|
||||
while((a < 1000) && ~found)
|
||||
b = a + 1; %b must be > a
|
||||
c = sqrt(a^2 + b^2); %c^2 = a^2 + b^2
|
||||
%Loop through all possible b's. When the sum of a, b, c is > 1000. You done have the number. Try the next a
|
||||
while(((a + b + c) <= 1000) && ~found)
|
||||
%If the sum == 1000 you found the numbers
|
||||
if((a + b + c) == 1000)
|
||||
found = true;
|
||||
%Otherwise try the next b and recalculate c
|
||||
else
|
||||
++b;
|
||||
c = sqrt(a^2 + b^2);
|
||||
end
|
||||
end
|
||||
%If you haven't found the numbers yet, increment a and try again
|
||||
if(~found)
|
||||
++a;
|
||||
end
|
||||
end
|
||||
|
||||
%print the result
|
||||
a * b * c
|
||||
|
||||
%Cleanup the variables
|
||||
clear a;
|
||||
clear b;
|
||||
clear c;
|
||||
clear found;
|
||||
@@ -1,19 +0,0 @@
|
||||
function [rString] = Reverse(str)
|
||||
%Reverse(string)
|
||||
%This function Reverse the order of the elements in an array
|
||||
%It was specifically designed for a string, but should work on other 1xX arrays
|
||||
%
|
||||
|
||||
if(nargin ~= 1)
|
||||
error('That is not a valid number of arguments')
|
||||
return;
|
||||
end
|
||||
|
||||
counter = size(str)(2); %Set the counter to the last element in string
|
||||
%Loop until the counter reaches 0
|
||||
while(counter > 0)
|
||||
%Add the current element of string to rString
|
||||
rString(end + 1) = str(counter);
|
||||
--counter;
|
||||
end
|
||||
end
|
||||
Reference in New Issue
Block a user