Start to impl AddBatch efficient algorithm Case A

In case that the tree is empty, build the full tree from bottom to top
(from all the leaf to the root).

addbatch_test.go

@@ -0,0 +1,51 @@
+package arbo
+
+import (
+	"fmt"
+	"math/big"
+	"testing"
+	"time"
+
+	qt "github.com/frankban/quicktest"
+	"github.com/iden3/go-merkletree/db/memory"
+)
+
+func TestAddBatchCaseA(t *testing.T) {
+	c := qt.New(t)
+
+	nLeafs := 1024
+
+	tree, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon)
+	c.Assert(err, qt.IsNil)
+	defer tree.db.Close()
+
+	start := time.Now()
+	for i := 0; i < nLeafs; i++ {
+		k := BigIntToBytes(big.NewInt(int64(i)))
+		v := BigIntToBytes(big.NewInt(int64(i * 2)))
+		if err := tree.Add(k, v); err != nil {
+			t.Fatal(err)
+		}
+	}
+	fmt.Println(time.Since(start))
+
+	tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon)
+	c.Assert(err, qt.IsNil)
+	defer tree2.db.Close()
+
+	var keys, values [][]byte
+	for i := 0; i < nLeafs; i++ {
+		k := BigIntToBytes(big.NewInt(int64(i)))
+		v := BigIntToBytes(big.NewInt(int64(i * 2)))
+		keys = append(keys, k)
+		values = append(values, v)
+	}
+	start = time.Now()
+	indexes, err := tree2.AddBatchOpt(keys, values)
+	c.Assert(err, qt.IsNil)
+	fmt.Println(time.Since(start))
+	c.Check(len(indexes), qt.Equals, 0)
+
+	// check that both trees roots are equal
+	c.Check(tree2.Root(), qt.DeepEquals, tree.Root())
+}