diff --git a/colossalai/auto_parallel/tensor_shard/deprecated/cost_graph.py b/colossalai/auto_parallel/tensor_shard/deprecated/cost_graph.py
index 239d02115..50220bca6 100644
--- a/colossalai/auto_parallel/tensor_shard/deprecated/cost_graph.py
+++ b/colossalai/auto_parallel/tensor_shard/deprecated/cost_graph.py
@@ -1,6 +1,8 @@
-from typing import List
 import math
+from typing import List
+
 from torch.fx.node import Node
+
 from .constants import INFINITY_COST
 
 
@@ -9,7 +11,7 @@ class CostGraph:
     A graph data structure to simplify the edge cost graph. It has two main functions:
     1. To feed the quadratic resharding costs into solver, we need to linearize it. We build edge_cost in
     CostGraph, and it stored every combinations of strategies for a src-dst node pair in an 1D list.
-    2. To reduce the searching space, we merge computationally-trivial operators, such as 
+    2. To reduce the searching space, we merge computationally-trivial operators, such as
     element-wise operators, transpose, and reduction, into their following nodes. The merging infomation will
     be given by the StrategiesVector depending on the type of target node and following nodes.
 
@@ -75,14 +77,14 @@ class CostGraph:
     def merge_node(self, src_node, dst_node):
         '''
         To merge dst_node into src_node, we need to do it in following steps:
-        
+
         1. For each strategy in dst_node, we need to pick an appropriate strategy
-        of src_node to merge, it is important because the logical resharding costs 
-        between the parents node of src_node and merged node depend on the src_node 
+        of src_node to merge, it is important because the logical resharding costs
+        between the parents node of src_node and merged node depend on the src_node
         strategies dispatching. For example, for the graph 0->1->2, after merging node 1
         into node 2, edge_costs[(node 0, node 2)][(0, 0)] = edge_costs[(node 0, node 1)][(0, x)]
         x represents the picking strategy of node 1 merged into node 2 strategy 0.
-        
+
         2. We need to accumulate the extra costs introduced by merging nodes, the extra costs
         contains two parts, one is resharding costs between src_node strategy and dst_node strategy,
         another is the origin extra costs in src_node strategy.