diff --git a/ProjectEuler/Problem4.m b/ProjectEuler/Problem4.m new file mode 100644 index 0000000..945e461 --- /dev/null +++ b/ProjectEuler/Problem4.m @@ -0,0 +1,41 @@ +%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; + +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 + +clear outerCounter; +clear innerCounter; +clear answer; +clear numbers; + +max(palindromes) + +%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 +%} diff --git a/ProjectEuler/Problem5.m b/ProjectEuler/Problem5.m new file mode 100644 index 0000000..1391905 --- /dev/null +++ b/ProjectEuler/Problem5.m @@ -0,0 +1,45 @@ +%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 +value = 0; %The value that is evenly divisible +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 + +%Cleanup your variables +clear counter; +clear factorCnt; +clear listCnt; +clear list; +clear nums; +clear ans; %Appears whenever you use increment + +value = prod(factors); +value diff --git a/ProjectEuler/Reverse.m b/ProjectEuler/Reverse.m new file mode 100644 index 0000000..9a02df0 --- /dev/null +++ b/ProjectEuler/Reverse.m @@ -0,0 +1,19 @@ +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