Identifier
Mp00050: to binary tree: right brother = right childBinary trees
Mp00016: left-right symmetry
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
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[[[[],[],[[[],[]]]]]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] [[[[],[],[[[[]]]]]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] [[[[],[[]],[],[],[]]]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]] [[[[],[[]],[],[[]]]]]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] [[[[],[[]],[[]],[]]]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] [[[[],[[]],[[],[]]]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] [[[[],[[]],[[[]]]]]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] [[[[],[[],[]],[],[]]]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]] [[[[],[[[]]],[],[]]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] [[[[],[[],[]],[[]]]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] [[[[],[[[]]],[[]]]]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] [[[[],[[],[],[]],[]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]] [[[[],[[],[[]]],[]]]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] [[[[],[[[]],[]],[]]]]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] [[[[],[[[],[]]],[]]]]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] [[[[],[[[[]]]],[]]]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] [[[[],[[],[],[],[]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]] [[[[],[[],[],[[]]]]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] [[[[],[[],[[]],[]]]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] [[[[],[[],[[],[]]]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] [[[[],[[],[[[]]]]]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] [[[[],[[[]],[],[]]]]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] [[[[],[[[]],[[]]]]]]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] [[[[],[[[],[]],[]]]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] [[[[],[[[[]]],[]]]]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] [[[[],[[[],[],[]]]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] [[[[],[[[],[[]]]]]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] [[[[],[[[[]],[]]]]]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] [[[[],[[[[],[]]]]]]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] [[[[],[[[[[]]]]]]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] [[[[[]],[],[],[],[]]]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]] [[[[[]],[],[],[[]]]]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] [[[[[]],[],[[]],[]]]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] [[[[[]],[],[[],[]]]]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] [[[[[]],[],[[[]]]]]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] [[[[[]],[[]],[],[]]]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] [[[[[]],[[]],[[]]]]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] [[[[[]],[[],[]],[]]]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] [[[[[]],[[[]]],[]]]]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] [[[[[]],[[],[],[]]]]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] [[[[[]],[[],[[]]]]]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] [[[[[]],[[[]],[]]]]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] [[[[[]],[[[],[]]]]]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] [[[[[]],[[[[]]]]]]]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] [[[[[],[]],[],[],[]]]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]] [[[[[[]]],[],[],[]]]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] [[[[[],[]],[],[[]]]]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] [[[[[[]]],[],[[]]]]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] [[[[[],[]],[[]],[]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] [[[[[[]]],[[]],[]]]]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] [[[[[],[]],[[],[]]]]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] [[[[[],[]],[[[]]]]]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] [[[[[[]]],[[],[]]]]]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] [[[[[[]]],[[[]]]]]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] [[[[[],[],[]],[],[]]]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]] [[[[[],[[]]],[],[]]]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] [[[[[[]],[]],[],[]]]]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] [[[[[[],[]]],[],[]]]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] [[[[[[[]]]],[],[]]]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] [[[[[],[],[]],[[]]]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] [[[[[],[[]]],[[]]]]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] [[[[[[]],[]],[[]]]]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] [[[[[[],[]]],[[]]]]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] [[[[[[[]]]],[[]]]]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] [[[[[],[],[],[]],[]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]] [[[[[],[],[[]]],[]]]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] [[[[[],[[]],[]],[]]]]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] [[[[[],[[],[]]],[]]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] [[[[[],[[[]]]],[]]]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] [[[[[[]],[],[]],[]]]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] [[[[[[]],[[]]],[]]]]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] [[[[[[],[]],[]],[]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] [[[[[[[]]],[]],[]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [[[[[[],[],[]]],[]]]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] [[[[[[],[[]]]],[]]]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] [[[[[[[]],[]]],[]]]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] [[[[[[[],[]]]],[]]]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] [[[[[[[[]]]]],[]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] [[[[[],[],[],[],[]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]] [[[[[],[],[],[[]]]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] [[[[[],[],[[]],[]]]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] [[[[[],[],[[],[]]]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] [[[[[],[],[[[]]]]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] [[[[[],[[]],[],[]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] [[[[[],[[]],[[]]]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] [[[[[],[[],[]],[]]]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] [[[[[],[[[]]],[]]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] [[[[[],[[],[],[]]]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] [[[[[],[[],[[]]]]]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] [[[[[],[[[]],[]]]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] [[[[[],[[[],[]]]]]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] [[[[[],[[[[]]]]]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] [[[[[[]],[],[],[]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] [[[[[[]],[],[[]]]]]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] [[[[[[]],[[]],[]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] [[[[[[]],[[],[]]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] [[[[[[]],[[[]]]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] [[[[[[],[]],[],[]]]]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] [[[[[[[]]],[],[]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] [[[[[[],[]],[[]]]]]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] [[[[[[[]]],[[]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] [[[[[[],[],[]],[]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] [[[[[[],[[]]],[]]]]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] [[[[[[[]],[]],[]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] [[[[[[[],[]]],[]]]]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] [[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] [[[[[[],[],[],[]]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] [[[[[[],[],[[]]]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] [[[[[[],[[]],[]]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] [[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] [[[[[[],[[[]]]]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] [[[[[[[]],[],[]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] [[[[[[[]],[[]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] [[[[[[[],[]],[]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] [[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] [[[[[[[],[],[]]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] [[[[[[[],[[]]]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] [[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [[[[[[[[],[]]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[[[[[],[]],[]],[]],[]],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [[[[[[[],[]],[]],[]],[]],[]],[]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
Map
to binary tree: right brother = right child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.