The Euclidean algorithm finds the greatest common divisor by replacing a pair with the smaller number and the remainder.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | "use strict"; // Euclidean GCD in JavaScript // // PURPOSE // The Euclidean algorithm finds the greatest common divisor by replacing a pair with the // smaller number and the remainder. Common divisors are preserved by this replacement. // // METHOD // Repeatedly compute a modulo b, move b into a, and put the remainder into b. Stop when b is // zero; the last nonzero value divides both original inputs. // // COMPLEXITY // O(log(min(a,b))) arithmetic steps for positive inputs, O(1) auxiliary space. // // CONTRACT // a and b are nonnegative integers. Defines gcd(0,0) as 0. Avoid negative values because // remainder conventions vary by language. // Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex // counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers. // Sorted order, correct tree topology, and caller-owned data-structure invariants are // preconditions; checking them on every query would change query complexity. // Scalar and shape checks are included. Value-range checks are included where needed to // prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000 // workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python // uses arbitrary precision. Native allocation failures propagate. In-place outputs may be // partly updated after arithmetic failure. These are single-threaded, in-memory // implementations. // // LANGUAGE DETAILS // Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic // lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or // overflow throw RangeError. // // EXAMPLE // Expected return: 6. // Run: node example.js // Tests for this exact source artifact run before publication. The accompanying source // archive includes unit cases, runtime results, and source hashes. function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); } function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; } function alg_add(a,b) { return alg_checked(a+b); } function alg_sub(a,b) { return alg_checked(a-b); } function alg_mul(a,b) { return alg_checked(a*b); } function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; } function gcd(a, b) { alg_require(Number.isInteger(a) && a >= -2147483648 && a <= 2147483647); alg_require(Number.isInteger(b) && b >= -2147483648 && b <= 2147483647); alg_require(((a >= 0) && (b >= 0))); let remainder = 0; while ((b != 0)) { remainder = (a % b); a = b; b = remainder; } return a; } let a = 48; let b = 18; let result = gcd(a, b); console.log(result); |