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106 lines
3.3 KiB
Matlab
106 lines
3.3 KiB
Matlab
function [] = Problem29()
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%ProjectEuler/Octave/Problem29.m
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%Matthew Ellison
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% Created: 10-16-19
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%Modified: 10-20-19
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%How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
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%{
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Copyright (C) 2019 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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%Setup your variables
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BOTTOM_A = 2; %The lowest possible value for A
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TOP_A = 100; %The highest possible value for A
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BOTTOM_B = 2; %The lowest possible value for B
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TOP_B = 100; %The highest possible value for B
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uniq = {}; %A table to hold all of the unique answers for the equation
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currentNum = [];%Holds the answer to the equation for a particular loop
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%Start the timer
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startTime = clock();
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%Start with the lowest A and move towards the largest
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for currentA = BOTTOM_A : TOP_A
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currentA
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%Start with the lowest B and move towards the largest
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for currentB = BOTTOM_B : TOP_B
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%Get the number
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%Start with the base number and multiply until you reach the correct power
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currentPower = 0;
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carry = 0;
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currentNum = [1];
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while(currentPower < currentB)
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counter = 1;
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%Loop through every element in the list and multiply it by the current A
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while(counter <= size(currentNum)(2))
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currentNum(counter) = (currentNum(counter) * currentA) + carry;
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carry = 0;
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%If one fo the elements is too large you need to carry that to the next element
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while(currentNum(counter) >= 10)
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currentNum(counter) -= 10;
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++carry;
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end
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++counter;
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end
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%If you ahve something to carry after everything has been multiplied you need to add a new column
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while(carry > 0)
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currentNum(end + 1) = carry;
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carry = 0;
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%If one fo the elements is too large you need to carry that to the next element
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while(currentNum(end) >= 10)
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currentNum(end) -= 10;
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++carry;
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end
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end
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++currentPower;
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end
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%If the number isn't in the list add it
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if(~isFound(uniq, currentNum))
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uniq(end + 1) = currentNum;
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end
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end
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end
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%Stop the timer
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endTime = clock();
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%Print the results
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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));
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printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))
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end
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function [found] = isFound(array, key)
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found = false; %Start with a false. It only turns true if you find key in array
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for location = 1 : size(array)(2)
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if(size(key)(2) != size(array{location})(2))
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continue;
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elseif(key == array{location})
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found = true;
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return;
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end
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end
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end
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%{
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This has not run to completion because it would take an insane amount of time
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but it got the correct results on several subsets (compared with my python code)
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so it should come up with the same answer.
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%}
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