Add extended gcd (TheAlgorithms#307)

Co-authored-by: Christian Clauss <[email protected]>
Co-authored-by: Andrii Siriak <[email protected]>

math/gcd/extendedgcd.go

@@ -0,0 +1,12 @@
+package gcd
+
+// ExtendedRecursive finds and returns gcd(a, b), x, y satisfying a*x + b*y = gcd(a, b).
+func ExtendedRecursive(a, b int64) (int64, int64, int64) {
+	if b > 0 {
+		d, y, x := ExtendedRecursive(b, a%b)
+		y -= (a / b) * x
+		return d, x, y
+	}
+
+	return a, 1, 0
+}

math/gcd/extendedgcd_test.go

@@ -0,0 +1,57 @@
+package gcd
+
+import "testing"
+
+type testExtendedFunction func(int64, int64) (int64, int64, int64)
+
+var testCasesExtended = []struct {
+	name string
+	a    int64
+	b    int64
+	gcd  int64
+	x    int64
+	y    int64
+}{
+	{"gcd of 10 and 0", 10, 0, 10, 1, 0},
+	{"gcd of 98 and 56", 98, 56, 14, -1, 2},
+	{"gcd of 0 and 10", 0, 10, 10, 0, 1},
+}
+
+func TemplateTestExtendedGCD(t *testing.T, f testExtendedFunction) {
+	for _, tc := range testCasesExtended {
+		t.Run(tc.name, func(t *testing.T) {
+			actualGcd, actualX, actualY := f(tc.a, tc.b)
+			if actualGcd != tc.gcd {
+				t.Errorf("Expected GCD of %d and %d to be: %v, but got: %d", tc.a, tc.b, tc.gcd, actualGcd)
+			}
+			if actualX != tc.x {
+				t.Errorf("Expected x satisfying %d * x + %d * y = gcd to be: %v, but got: %d", tc.a, tc.b, tc.x, actualX)
+			}
+			if actualY != tc.y {
+				t.Errorf("Expected y satisfying %d * x + %d * y = gcd to be: %v, but got: %d", tc.a, tc.b, tc.y, actualY)
+			}
+		})
+	}
+}
+
+func TestExtendedGCDRecursive(t *testing.T) {
+	TemplateTestExtendedGCD(t, ExtendedRecursive)
+}
+
+func TestExtendedGCDIterative(t *testing.T) {
+	TemplateTestExtendedGCD(t, ExtendedIterative)
+}
+
+func TemplateBenchmarkExtendedGCD(b *testing.B, f testExtendedFunction) {
+	for i := 0; i < b.N; i++ {
+		f(98, 56)
+	}
+}
+
+func BenchmarkExtendedGCDRecursive(b *testing.B) {
+	TemplateBenchmarkExtendedGCD(b, ExtendedRecursive)
+}
+
+func BenchmarkExtendedGCDIterative(b *testing.B) {
+	TemplateBenchmarkExtendedGCD(b, ExtendedIterative)
+}

math/gcd/extendedgcditerative.go

@@ -0,0 +1,13 @@
+package gcd
+
+// ExtendedIterative finds and returns gcd(a, b), x, y satisfying a*x + b*y = gcd(a, b).
+func ExtendedIterative(a, b int64) (int64, int64, int64) {
+	var u, y, v, x int64 = 1, 1, 0, 0
+	for a > 0 {
+		var q int64 = b / a
+		x, u = u, x-q*u
+		y, v = v, y-q*v
+		b, a = a, b-q*a
+	}
+	return b, x, y
+}