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Problem29.m

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+function [] = Problem29()
+%ProjectEuler/Octave/Problem29.m
+%Matthew Ellison
+% Created: 10-16-19
+%Modified: 10-20-19
+%How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
+%{
+	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/>.
+%}
+
+
+%Setup your variables
+BOTTOM_A = 2;	%The lowest possible value for A
+TOP_A = 100;		%The highest possible value for A
+BOTTOM_B = 2;	%The lowest possible value for B
+TOP_B = 100;		%The highest possible value for B
+uniq = {};		%A table to hold all of the unique answers for the equation
+currentNum = [];%Holds the answer to the equation for a particular loop
+
+
+%Start the timer
+startTime = clock();
+
+%Start with the lowest A and move towards the largest
+for currentA = BOTTOM_A : TOP_A
+	currentA
+	%Start with the lowest B and move towards the largest
+	for currentB = BOTTOM_B : TOP_B
+		%Get the number
+		%Start with the base number and multiply until you reach the correct power
+		currentPower = 0;
+		carry = 0;
+		currentNum = [1];
+		while(currentPower < currentB)
+			counter = 1;
+			%Loop through every element in the list and multiply it by the current A
+			while(counter <= size(currentNum)(2))
+				currentNum(counter) = (currentNum(counter) * currentA) + carry;
+				carry = 0;
+				%If one fo the elements is too large you need to carry that to the next element
+				while(currentNum(counter) >= 10)
+					currentNum(counter) -= 10;
+					++carry;
+				end
+				++counter;
+			end
+			%If you ahve something to carry after everything has been multiplied you need to add a new column
+			while(carry > 0)
+				currentNum(end + 1) = carry;
+				carry = 0;
+				%If one fo the elements is too large you need to carry that to the next element
+				while(currentNum(end) >= 10)
+					currentNum(end) -= 10;
+					++carry;
+				end
+			end
+			++currentPower;
+		end
+		%If the number isn't in the list add it
+		if(~isFound(uniq, currentNum))
+			uniq(end + 1) = currentNum;
+		end
+	end
+end
+
+%Stop the timer
+endTime = clock();
+
+%Print the results
+printf("The number of unique values generated by a^b for %d <= a <= %d and %d <= b <= %d is %d\n", BOTTOM_A, TOP_A, BOTTOM_B, TOP_B, size(uniq)(2));
+printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))
+
+end
+
+
+function [found] = isFound(array, key)
+	found = false;	%Start with a false. It only turns true if you find key in array
+	for location = 1 : size(array)(2)
+		if(size(key)(2) != size(array{location})(2))
+			continue;
+		elseif(key == array{location})
+			found = true;
+			return;
+		end
+	end
+end
+
+%{
+This has not run to completion because it would take an insane amount of time
+but it got the correct results on several subsets (compared with my python code)
+so it should come up with the same answer.
+%}