在中文区讲解这两个算法的博客虽然不少,但是让人看得像是在云里雾里的。 本文通过一个详细的计算过程来讲解辗转相除法(即欧几里得算法),以及拓展的欧几里得算法/Extended Euclidean algorithm。这两个算法有很强的关联,因此请读者先看完辗转相除法再看拓展的欧几里得算法。 辗转相除法(即欧几里得算法) 目的:计算两个...
扩展欧几里德算法 基本算法:对于不完全为 0 的非负整数 a,b,gcd(a,b)表示 a,b 的最大公约数,必然存在整数对 x,y ,使得 gcd(a,b)=ax+by。 证明:设 a>b。 1,显然当 b=0,gcd(a,b)=a。此时 x=1,y=0; 2,ab!=0 时 设ax1+by1=gcd(a,b); bx2+(a mod b)y2=gcd(b,a mod b);...
扩展欧几里德算法 基本算法:对于不完全为 0 的非负整数 a,b,gcd(a,b)表示 a,b 的最大公约数,必然存在整数对 x,y ,使得 gcd(a,b)=ax+by。 证明:设 a>b。 1,显然当 b=0,gcd(a,b)=a。此时 x=1,y=0; 2,ab!=0 时 设ax1+by1=gcd(a,b); bx2+(a mod b)y2=gcd(b,a mod b);...
In mathematics, the Euclidean algorithm[a], or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder. It is named after the ancient Greek mathematician Euclid, who firs...
算法进阶【第九期】数学算法:Extended Euclidean Algorithm扩展欧几里得算法 喵喵提醒版 爆零是一种宿命,枚举是一种思想,打表是一种勇气,骗分是一种日常,刷题是一种出路,AC是一种原谅,AK是一种梦想,搜索是一种信仰,剪枝是一种精神,弃赛是一种颓废,吊打是一种必然,进队是一种奢望,B站是一种解放。
The Extended Euclidean AlgorithmExtended, TheAlgorithm, EuclideanAlgorithm, Extended EuclideanEuclidean, TheAlgorithm, The EuclideanAlgorithm, Division
We know that by means of extended euclidean algorithmxandycan be calculated fromax + by = gcd(a, b).The formula is: x=prev_y;y=prev_x-(a/b)*x; and the code is: intgcd(inta,intb,int&x,int&y){if(b==0){x=1;y=0;returna;}intx1,y1;intd=gcd(b,a%b,x1,y1);x=y1;y...
Example of Extended Euclidean AlgorithmRecall that gcd(84, 33) = gcd(33, 18) = gcd(18, 15) = gcd(15, 3) = gcd(3, 0) = 3 We work backwards to write 3 as a linear combination of 84 and 33: 3 = 18 − 15 [Now 3 is a linear combination of 18 and 15] = 18 − (33...
euclid-algo refactor adapter to euclids algorithm Jul 1, 2022 .gitignore initial commit extended euclids algorithm Jul 1, 2022 About Implementation of the extended "Euclidean" algorithm. Topics university university-course extended-euclidean-algorithm university-assignment euclidean-algorithm euclid-algorit...
Pure-Python extended Euclidean algorithm implementation that accepts any number of integer arguments. - lapets/egcd