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In the realm of binary trees, a child swap transformation is defined as selecting any node and exchanging its left and right subtrees. Two binary trees are considered mirror equivalent if one can be transformed into the other through zero or more such child swap transformations.
Given the roots of two binary trees, root1 and root2, determine whether they are mirror equivalent. Return true if the trees can be made identical through any sequence of child swap transformations, or false otherwise.
Understanding Mirror Equivalence:
This concept is fundamental in tree comparison algorithms where rotational symmetry matters, such as in isomorphism detection, tree canonicalization, and equivalence testing under symmetric operations.
root1 = [1,2,3,4,5,6,null,null,null,7,8]
root2 = [1,3,2,null,6,4,5,null,null,null,null,8,7]trueThe trees are mirror equivalent. By applying child swap transformations at nodes with values 1, 3, and 5 in the first tree, we can obtain exactly the second tree. At node 1, we swap children 2 and 3. At node 3 (now on the left), we swap to bring 6 to its new position. At node 5, we swap 7 and 8.
root1 = []
root2 = []trueBoth trees are empty, which makes them trivially mirror equivalent. No transformations are needed.
root1 = []
root2 = [1]falseAn empty tree cannot be transformed into a non-empty tree through child swap operations. The structural difference is fundamental and cannot be resolved.
Constraints