add method factorial with tree

Signed-off-by: deemak <[email protected]>

pkg/combinatorics/factorial.go

@@ -17,3 +17,42 @@ func FactorialInt(n int64) int64 {
 func FactorialString(n int64) string {
 	return Factorial(n).String()
 }
+
+/*FactorialTree *big.Int*/
+func FactorialTree(n int64) *big.Int {
+	if n < 0 {
+		return big.NewInt(0)
+	}
+	if n == 0 {
+		return big.NewInt(1)
+	}
+	if n == 1 || n == 2 {
+		return big.NewInt(n)
+	}
+	return factorialTreeExecute(big.NewInt(2), big.NewInt(n))
+}
+
+/*FactorialTree string*/
+func FactorialTreeString(n int64) string {
+	return FactorialTree(n).String()
+
+}
+func factorialTreeExecute(n, m *big.Int) *big.Int {
+	if n.CmpAbs(m) == 1 {
+		return big.NewInt(1)
+	}
+	if n.CmpAbs(m) == 0 {
+		return n
+	}
+	var temp, tempR big.Int
+	if temp.Sub(m, n).CmpAbs(big.NewInt(1)) == 0 {
+		return tempR.Mul(n, m)
+	}
+	var mod, modR, modr, result big.Int
+	mod.Add(n, m)
+	modR.Quo(&mod, big.NewInt(2))
+	resLeft := factorialTreeExecute(n, &modR)
+	modr.Add(&modR, big.NewInt(1))
+	resRight := factorialTreeExecute(&modr, m)
+	return result.Mul(resLeft, resRight)
+}

pkg/combinatorics/factorial_test.go

@@ -1,6 +1,8 @@
 package combinatorics
 
 import (
+	"math/big"
+	"reflect"
 	"testing"
 )
 
@@ -14,11 +16,11 @@ func TestFactorial(t *testing.T) {
 		want int64
 	}{
 		{
-			name: "Factorial 4! = 24",
+			name: "Factorial 10! = 24",
 			args: args{
-				n: 399168,
+				n: 10,
 			},
-			want: 24,
+			want: 3628800,
 		},
 	}
 	for _, tt := range tests {
@@ -29,3 +31,55 @@ func TestFactorial(t *testing.T) {
 		})
 	}
 }
+
+func TestFactorialTree(t *testing.T) {
+	type args struct {
+		n int64
+	}
+	tests := []struct {
+		name string
+		args args
+		want *big.Int
+	}{
+		{
+			name: "1000000!",
+			args: args{
+				n: 1000000,
+			},
+			want: big.NewInt(3628800),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := FactorialTree(tt.args.n); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("FactorialTree() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestFactorialTreeString(t *testing.T) {
+	type args struct {
+		n int64
+	}
+	tests := []struct {
+		name string
+		args args
+		want string
+	}{
+		{
+			name: "1000000!",
+			args: args{
+				n: 1000000,
+			},
+			want: ``,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := FactorialTreeString(tt.args.n); got != tt.want {
+				t.Errorf("FactorialTreeString() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}