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DATA STRUCTURE AND ALGORITHM Recursive Euclid Algorithm CẤU TRÚC DỮ LIỆU VÀ GIẢI THUẬT Thực hiệu thuật toán Euclid đệ qui Dr Dao Nam Anh Data Structure and Algorithm Resource - Reference Slides adapted from Robert Sedgewick, and Kevin Wayne Major Reference: • Robert Sedgewick, and Kevin Wayne, “Algorithms” Princeton University, 2011, Addison Wesley • Algorithm in C (Parts 1-5 Bundle)- Third Edition by Robert Sedgewick, Addison-Wesley Data Structure and Algorithm Recursive Euclid Algorithm Tìm ước số chung lớn hai số nguyên public class Euclid { public static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } public static void main(String[] args) { int p = Integer.parseInt(args[0]); int q = Integer.parseInt(args[1]); System.out.println(gcd(p, q)); } } Data Structure and Algorithm p = 1272, q = 216 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm p = 1272, q = 216 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm p = 1272, q = 216 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm p = 1272, q = 216 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 1272 = 216 + 192 p = 216, q = 192 environment gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm p = 1272, q = 216 environment p = 216, q = 192 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm p = 1272, q = 216 environment p = 216, q = 192 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm 10 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm 11 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm 12 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } p = 24, q = environment gcd(1272, 216) gcd(24, 0) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm 13 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } p = 24, q = environment gcd(1272, 216) gcd(24, 0) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm 14 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 p = 24, q = environment gcd(1272, 216) gcd(24, 0) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } Data Structure and Algorithm 15 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 Data Structure and Algorithm 16 p = 1272, q = 216 environment p = 216, q = 192 environment p = 192, q = 24 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 gcd(192, 24) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 Data Structure and Algorithm 17 p = 1272, q = 216 environment p = 216, q = 192 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 Data Structure and Algorithm 18 p = 1272, q = 216 environment p = 216, q = 192 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 gcd(216, 192) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 Data Structure and Algorithm 19 p = 1272, q = 216 environment gcd(1272, 216) static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } 24 Data Structure and Algorithm 20 p = 1272, q = 216 gcd(1272, 216) environment static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); }24 public class Euclid { public static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); } } public static void main(String[] args) { int p = Integer.parseInt(args[0]); 24 int q = Integer.parseInt(args[1]); System.out.println(gcd(p, q)); } 24 % java Euclid 1272 216 24 Data Structure and Algorithm 21 ... Algorithm in C (Parts 1-5 Bundle)- Third Edition by Robert Sedgewick, Addison-Wesley Data Structure and Algorithm Recursive Euclid Algorithm Tìm ước số chung lớn hai số nguyên public class Euclid { public... static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q); }24 public class Euclid { public static int gcd(int p, int q) { if (q == 0) return p; else return gcd(q, p % q);... Integer.parseInt(args[0]); 24 int q = Integer.parseInt(args[1]); System.out.println(gcd(p, q)); } 24 % java Euclid 1272 216 24 Data Structure and Algorithm 21