feat: nth Fibonacci number using formula (TheAlgorithms#450)

Co-authored-by: Rak Laptudirm <[email protected]> Co-authored-by: github-action <${GITHUB_ACTOR}@users.noreply.github.com>
pengchant · Dec 5, 2021 · 3766420 · 3766420
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diff --git a/README.md b/README.md
@@ -287,7 +287,8 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.
 
 ##### Functions:
 
-1. [`Matrix`](./math/fibonacci/fibonacci.go#L11):  Matrix This function calculates the n-th fibonacci number using the matrix method. [See](https://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form)
+1. [`Formula`](./math/fibonacci/fibonacci.go#L42):  Formula This function calculates the n-th fibonacci number using the [formula](https://en.wikipedia.org/wiki/Fibonacci_number#Relation_to_the_golden_ratio) Attention! Tests for large values fall due to rounding error of floating point numbers, works well, only on small numbers
+2. [`Matrix`](./math/fibonacci/fibonacci.go#L15):  Matrix This function calculates the n-th fibonacci number using the matrix method. [See](https://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form)
 
 ---
 </details><details>

diff --git a/math/fibonacci/fibonacci.go b/math/fibonacci/fibonacci.go
@@ -7,6 +7,10 @@
 
 package fibonacci
 
+import (
+	"math"
+)
+
 // Matrix This function calculates the n-th fibonacci number using the matrix method. [See](https://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form)
 func Matrix(n uint) uint {
 	a, b := 1, 1
@@ -32,3 +36,12 @@ func Matrix(n uint) uint {
 	}
 	return uint(rc)
 }
+
+// Formula This function calculates the n-th fibonacci number using the [formula](https://en.wikipedia.org/wiki/Fibonacci_number#Relation_to_the_golden_ratio)
+// Attention! Tests for large values fall due to rounding error of floating point numbers, works well, only on small numbers
+func Formula(n uint) uint {
+	sqrt5 := math.Sqrt(5)
+	phi := (sqrt5 + 1) / 2
+	powPhi := math.Pow(phi, float64(n))
+	return uint(powPhi/sqrt5 + 0.5)
+}
diff --git a/math/fibonacci/fibonacci_test.go b/math/fibonacci/fibonacci_test.go
@@ -53,6 +53,17 @@ func TestNthFibonacci(t *testing.T) {
 	}
 }
 
+func TestFormula(t *testing.T) {
+	tests := getTests()
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			if got := Formula(test.n); test.n <= 10 && got != test.want {
+				t.Errorf("Return value = %v, want %v", got, test.want)
+			}
+		})
+	}
+}
+
 func BenchmarkNthFibonacci(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		dynamic.NthFibonacci(90)
@@ -64,3 +75,9 @@ func BenchmarkMatrix(b *testing.B) {
 		Matrix(90)
 	}
 }
+
+func BenchmarkFormula(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Formula(90)
+	}
+}