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Problem30.lua

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+--ProjectEuler/lua/Problem29.lua
+-- Created: 10-28-19
+--Modified: 10-28-19
+--Find the sum of all the numbers that can be written as the sum of the fifth powers of their digits.
+--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
+--[[
+	Copyright (C) 2019  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/>.
+]]
+
+
+require "Stopwatch"
+
+
+--Returns a table with the individual digits of the number passed to it
+function getDigits(num)
+	local listOfDigits = {};	--This table holds the individual digits of num
+	--The easiest way to get the individual digits of a number is by converting it to a string
+	local digits = tostring(num);
+	--Start with the first digit, convert it to an integer, store it in the table, and move to the next digit
+	for cnt = 1, #digits do
+		table.insert(listOfDigits, tonumber(string.sub(digits, cnt, cnt)));
+	end
+	--Return the table of digits
+	return listOfDigits;
+end
+
+--Gets the sum of a table of numbers
+function getSumOfTable(ary)
+	local sum = 0;	--Start the sum at 0 so you can add to it
+	--Add every number in the table to the sum
+	for cnt = 1, #ary do
+		sum = sum + ary[cnt];
+	end
+	--Return the sum
+	return sum;
+end
+
+
+--Setup the variables
+local timer = Stopwatch:create();
+local TOP_NUM = 1000000;	--This is the largest number that will be checked
+local BOTTOM_NUM = 2;	--Starts with 2 because 0 and 1 don't count
+local POWER_RAISED = 5;	--This is the power that the digits are raised to
+local sumOfFifthNumbers = {};	--This is a table of the numbers that are the sum of the fifth power of their digits
+
+--Start the timer
+timer:start();
+
+--Start with the lowest number and increment until you reach the largest number
+for currentNum = BOTTOM_NUM, TOP_NUM do
+	--Get the digits of the number
+	local digits = getDigits(currentNum);
+	--Get the sum of the powers
+	local sumOfPowers = 0;
+	for cnt = 1, #digits do
+		sumOfPowers = sumOfPowers + math.pow(digits[cnt], POWER_RAISED);
+	end
+	--Check if the sum of the powers is the same as the number
+	--If it is add it to the list, otherwise continue to the next number
+	if(sumOfPowers == currentNum) then
+		table.insert(sumOfFifthNumbers, currentNum);
+	end
+end
+
+--Stop the timer
+timer:stop();
+
+--Print the results
+io.write("The sum of all the numbers that can be written as the sum of the fifth powers of their digits is " .. getSumOfTable(sumOfFifthNumbers) .. '\n');
+io.write("It took " .. timer:getString() .. " to run this algorithm\n");
+
+
+--[[ Results:
+The sum of all the numbers that can be written as the sum of the fifth powers of their digits is 443839
+It took 2.706 seconds to run this algorithm
+]]