It depends on what traversals are given. If one of the traversal methods is Inorder then the tree can be constructed, otherwise not.
Therefore, following combination can uniquely identify a tree.
Inorder and Preorder.
Inorder and Postorder.
Inorder and Level-order.
And following do not.
Postorder and Preorder.
Preorder and Level-order.
Postorder and Level-order.
For example, Preorder, Level-order and Postorder traversals are same for the trees given in above diagram.
Preorder Traversal = AB
Postorder Traversal = BA
Level-Order Traversal = AB
So, even if three of them (Pre, Post and Level) are given, the tree can not be constructed.
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