diff --git a/src/contraction_tree.cpp b/src/contraction_tree.cpp
index edef8c20..6282a819 100644
--- a/src/contraction_tree.cpp
+++ b/src/contraction_tree.cpp
@@ -8,141 +8,140 @@ using namespace std;
 #else
 
 namespace cytnx {
-  void ContractionTree::build_default_contraction_tree() {
-    this->reset_contraction_order();
-    
- 
-    cytnx_error_msg(this->base_nodes.size() < 2, 
-    "[ERROR] Need at least 2 tensors for contraction","\n");
-  
-
-    std::shared_ptr<Node> left = this->base_nodes[0];
-    std::shared_ptr<Node> right;
-    
-    this->nodes_container.reserve(this->base_nodes.size());
-    
-    for (cytnx_uint64 i = 1; i < this->base_nodes.size(); i++) {
-        right = this->base_nodes[i];
-        
-        auto new_node = std::make_shared<Node>(left, right);
-        
-        this->nodes_container.push_back(new_node);
-        left = new_node;
-    }
+void ContractionTree::build_default_contraction_tree() {
+  this->reset_contraction_order();
 
-    if (!nodes_container.empty()) {
-        auto root = nodes_container.back();
-        std::cout << "Setting root pointers from " << root->name << std::endl;
-        root->set_root_ptrs();
-    }
+  cytnx_error_msg(this->base_nodes.size() < 2, "[ERROR] Need at least 2 tensors for contraction",
+                  "\n");
+
+  std::shared_ptr<Node> left = this->base_nodes[0];
+  std::shared_ptr<Node> right;
+
+  this->nodes_container.reserve(this->base_nodes.size());
+
+  for (cytnx_uint64 i = 1; i < this->base_nodes.size(); i++) {
+    right = this->base_nodes[i];
+
+    auto new_node = std::make_shared<Node>(left, right);
+
+    this->nodes_container.push_back(new_node);
+    left = new_node;
   }
-  void ContractionTree::build_contraction_tree_by_tokens(
-    const std::map<std::string, cytnx_uint64> &name2pos, const std::vector<std::string> &tokens) {
-    this->reset_contraction_order();
-    cytnx_error_msg(this->base_nodes.size() < 2,
-                    "[ERROR][ContractionTree][build_contraction_order_by_tokens] contraction tree "
-                    "should contain >=2 tensors in order to build contraction order.%s",
-                    "\n");
-    cytnx_error_msg(
-      tokens.size() == 0,
-      "[ERROR][ContractionTree][build_contraction_order_by_tokens] cannot have empty tokens.%s",
-      "\n");
-
-    stack<std::shared_ptr<Node>> stk;
-    std::shared_ptr<Node> left, right;
-    stack<char> operators;
-    char topc;
-    size_t pos = 0;
-    std::string tok;
-
-    // evaluate each token, and construct the Contraction Tree.
-    this->nodes_container.reserve(
-      this->base_nodes.size());  // reserve a contiguous memeory address to prevent re-allocate that
-                                 // change address.
-    for (cytnx_uint64 i = 0; i < tokens.size(); i++) {
-      tok = str_strip(tokens[i]);  // remove space.
-      // cout << tokens[i] << "|" << tok << "|" << endl;
-      if (tok.length() == 0) continue;
-      // cout << tok << "|";
-      if (tok == "(") {
-        operators.push(tok.c_str()[0]);
-        // cout << "put(" << endl;
-      } else if (tok == ")") {
-        // cout << "put)-->";
-        if (!operators.empty()) {
-          topc = operators.top();
-          while ((topc != '(')) {
-            operators.pop();
-            right = stk.top();
-            stk.pop();
-            left = stk.top();
-            stk.pop();
-            auto new_node = std::make_shared<Node>(left, right);
-            this->nodes_container.push_back(new_node);
-            stk.push(this->nodes_container.back());
-            if (!operators.empty())
-              topc = operators.top();
-            else
-              break;
-          }
-        }
-        // cout << endl;
-        operators.pop();  // discard the '('
-      } else if (tok == ",") {
-        // cout << "put,-->";
-        if (!operators.empty()) {
-          topc = operators.top();
-          while ((topc != '(') && (topc != ')')) {
-            operators.pop();
-            right = stk.top();
-            stk.pop();
-            left = stk.top();
-            stk.pop();
-            auto new_node = std::make_shared<Node>(left, right);
-            this->nodes_container.push_back(new_node);
-            stk.push(this->nodes_container.back());
-            if (!operators.empty())
-              topc = operators.top();
-            else
-              break;
-          }
+
+  if (!nodes_container.empty()) {
+    auto root = nodes_container.back();
+    std::cout << "Setting root pointers from " << root->name << std::endl;
+    root->set_root_ptrs();
+  }
+}
+
+void ContractionTree::build_contraction_tree_by_tokens(
+  const std::map<std::string, cytnx_uint64> &name2pos, const std::vector<std::string> &tokens) {
+  this->reset_contraction_order();
+  cytnx_error_msg(this->base_nodes.size() < 2,
+                  "[ERROR][ContractionTree][build_contraction_order_by_tokens] contraction tree "
+                  "should contain >=2 tensors in order to build contraction order.%s",
+                  "\n");
+  cytnx_error_msg(
+    tokens.size() == 0,
+    "[ERROR][ContractionTree][build_contraction_order_by_tokens] cannot have empty tokens.%s",
+    "\n");
+
+  stack<std::shared_ptr<Node>> stk;
+  std::shared_ptr<Node> left, right;
+  stack<char> operators;
+  char topc;
+  size_t pos = 0;
+  std::string tok;
+
+  // evaluate each token, and construct the Contraction Tree.
+  this->nodes_container.reserve(
+    this->base_nodes.size());  // reserve a contiguous memeory address to prevent re-allocate that
+                               // change address.
+  for (cytnx_uint64 i = 0; i < tokens.size(); i++) {
+    tok = str_strip(tokens[i]);  // remove space.
+    // cout << tokens[i] << "|" << tok << "|" << endl;
+    if (tok.length() == 0) continue;
+    // cout << tok << "|";
+    if (tok == "(") {
+      operators.push(tok.c_str()[0]);
+      // cout << "put(" << endl;
+    } else if (tok == ")") {
+      // cout << "put)-->";
+      if (!operators.empty()) {
+        topc = operators.top();
+        while ((topc != '(')) {
+          operators.pop();
+          right = stk.top();
+          stk.pop();
+          left = stk.top();
+          stk.pop();
+          auto new_node = std::make_shared<Node>(left, right);
+          this->nodes_container.push_back(new_node);
+          stk.push(this->nodes_container.back());
+          if (!operators.empty())
+            topc = operators.top();
+          else
+            break;
         }
-        // cout << endl;
-        operators.push(',');
-      } else {
-        cytnx_uint64 idx;
-        try {
-          idx = name2pos.at(tok);
-        } catch (std::out_of_range) {
-          cytnx_error_msg(true,
-                          "[ERROR][ContractionTree][build_contraction_order_by_token] tokens "
-                          "contain invalid TN name: %s ,which is not previously defined. \n",
-                          tok.c_str());
+      }
+      // cout << endl;
+      operators.pop();  // discard the '('
+    } else if (tok == ",") {
+      // cout << "put,-->";
+      if (!operators.empty()) {
+        topc = operators.top();
+        while ((topc != '(') && (topc != ')')) {
+          operators.pop();
+          right = stk.top();
+          stk.pop();
+          left = stk.top();
+          stk.pop();
+          auto new_node = std::make_shared<Node>(left, right);
+          this->nodes_container.push_back(new_node);
+          stk.push(this->nodes_container.back());
+          if (!operators.empty())
+            topc = operators.top();
+          else
+            break;
         }
-        stk.push(this->base_nodes[idx]);
       }
-
-    }  // for each token
-
-    while (!operators.empty()) {
-      operators.pop();
-      right = stk.top();
-      stk.pop();
-      left = stk.top();
-      stk.pop();
-      // this->nodes_container.back().name = right->name +  left->name;
-      auto new_node = std::make_shared<Node>(left, right);
-      this->nodes_container.push_back(new_node);
-      stk.push(this->nodes_container.back());
-    }
-    /*
-    cout << "============" << endl;
-    for(int i=0;i<this->nodes_container.size();i++){
-        cout << this->nodes_container[i].name << endl;
+      // cout << endl;
+      operators.push(',');
+    } else {
+      cytnx_uint64 idx;
+      try {
+        idx = name2pos.at(tok);
+      } catch (std::out_of_range) {
+        cytnx_error_msg(true,
+                        "[ERROR][ContractionTree][build_contraction_order_by_token] tokens "
+                        "contain invalid TN name: %s ,which is not previously defined. \n",
+                        tok.c_str());
+      }
+      stk.push(this->base_nodes[idx]);
     }
-    cout << "============" << endl;
-    */
+
+  }  // for each token
+
+  while (!operators.empty()) {
+    operators.pop();
+    right = stk.top();
+    stk.pop();
+    left = stk.top();
+    stk.pop();
+    // this->nodes_container.back().name = right->name +  left->name;
+    auto new_node = std::make_shared<Node>(left, right);
+    this->nodes_container.push_back(new_node);
+    stk.push(this->nodes_container.back());
+  }
+  /*
+  cout << "============" << endl;
+  for(int i=0;i<this->nodes_container.size();i++){
+      cout << this->nodes_container[i].name << endl;
   }
+  cout << "============" << endl;
+  */
+}
 
 }  // namespace cytnx
 #endif