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46 lines
860 B
C++
46 lines
860 B
C++
//
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// Factors.hpp
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// Clock Signal
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//
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// Created by Thomas Harte on 29/07/2016.
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// Copyright © 2016 Thomas Harte. All rights reserved.
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//
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#ifndef Factors_hpp
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#define Factors_hpp
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namespace NumberTheory {
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/*!
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@returns The greatest common divisor of @c a and @c b as computed by Euclid's algorithm.
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*/
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template<class T> T greatest_common_divisor(T a, T b) {
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if(a < b) {
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T swap = b;
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b = a;
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a = swap;
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}
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while(1) {
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if(!a) return b;
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if(!b) return a;
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T remainder = a%b;
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a = b;
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b = remainder;
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}
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}
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/*!
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@returns The least common multiple of @c a and @c b computed indirectly via Euclid's greatest
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common divisor algorithm.
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*/
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template<class T> T least_common_multiple(T a, T b) {
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if(a == b) return a;
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T gcd = greatest_common_divisor<T>(a, b);
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return (a / gcd) * (b / gcd) * gcd;
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}
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}
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#endif /* Factors_hpp */
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