algorithm: binomial coefficient (TheAlgorithms#539)

* feat: Add binomial coefficient implementation

* test: Add tests for binomial coefficient

* fix: Fix typing error in binomialcoefficient.go

* fix: Add linter fixes to BenchmarkBinomialCoefficient()

* fix: Fix import statement in binomialcoefficient_test.go

* fix: Fix return statement

* test: Add detailed unit tests for binomial coefficient

* fix: Replace all occurrences of C with Combinations

* fix: Move error variable outside Combinations function

* refactor: Add t.Run block

* refactor: Remove log statement

* refactor: Refactor unit tests

* fix: Change error variable name from error to err

math/binomialcoefficient.go

@@ -0,0 +1,33 @@
+// binomialcoefficient.go
+// description: Returns C(n, k)
+// details:
+// a binomial coefficient C(n,k) gives number ways
+// in which k objects can be chosen from n objects.
+// wikipedia: https://en.wikipedia.org/wiki/Binomial_coefficient
+// author: Akshay Dubey (https://github.com/itsAkshayDubey)
+// see binomialcoefficient_test.go
+
+package math
+
+import (
+	"errors"
+)
+
+var ErrPosArgsOnly error = errors.New("arguments must be positive")
+
+// C is Binomial Coefficient function
+// This function returns C(n, k) for given n and k
+func Combinations(n int, k int) (int, error) {
+	if n < 0 || k < 0 {
+		return -1, ErrPosArgsOnly
+	}
+	if k > (n - k) {
+		k = n - k
+	}
+	res := 1
+	for i := 0; i < k; i++ {
+		res *= (n - i)
+		res /= (i + 1)
+	}
+	return res, nil
+}

math/binomialcoefficient_test.go

@@ -0,0 +1,42 @@
+// binomialcoefficient_test.go
+// description: Returns C(n, k)
+// author: Akshay Dubey (https://github.com/itsAkshayDubey)
+// see binomialcoefficient.go
+
+package math_test
+
+import (
+	"testing"
+
+	"github.com/TheAlgorithms/Go/math"
+)
+
+func TestCombinations(t *testing.T) {
+	var tests = []struct {
+		name          string
+		n             int
+		k             int
+		expectedValue int
+		expectedError error
+	}{
+		{"n = 5, k = 2", 5, 2, 10, nil},
+		{"n = 7, k = 4", 7, 4, 35, nil},
+		{"n = 0, k = 0", 0, 0, 1, nil},
+		{"n = -1, k = 1", -1, 1, -1, math.ErrPosArgsOnly},
+		{"n = 1, k = -1", 1, -1, -1, math.ErrPosArgsOnly},
+		{"n = -1, k = -1", -1, -1, -1, math.ErrPosArgsOnly},
+	}
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			result, err := math.Combinations(test.n, test.k)
+			if result != test.expectedValue || test.expectedError != err {
+				t.Errorf("expected error: %s, got: %s; expected value: %v, got: %v", test.expectedError, err, test.expectedValue, result)
+			}
+		})
+	}
+}
+func BenchmarkCombinations(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		_, _ = math.Combinations(65536, 65536)
+	}
+}