Identifier
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2Cc0021;cc-rep-3
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[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[],[],[],[[]]] [[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[]],[[]],[[]],[[],[[]]]] [.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[[[[],[[],[],[],[],[]]]]] [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[[[[[]]]],[],[],[],[],[]] [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[[[[[[[]]]]]],[],[],[]] [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[[[[[[[]]]]]],[[]],[]] [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[[[[[[[]]]]]]],[[]]] [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[[],[],[],[],[],[],[],[],[[]],[]] [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[[[]],[],[],[],[],[[]],[]] [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[[[],[],[],[],[],[],[],[],[],[]]] [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]],[[]],[[]]] [[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[[[]],[[]],[]],[[[]],[]]] [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[[[[]],[]],[]],[[[]],[]]] [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[[[]],[]],[[[]],[[]],[]]] [[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[[]],[[[]],[[]],[[]],[]]] [[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[[]],[[[[]],[]],[[]],[]]] [.,[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]=>[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.],.]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[[[[[[]],[]],[]],[[]],[]]] [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]],[[]],[[]],[[]]] [[[.,[[.,.],.]],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[[[]],[[]],[[]],[]],[[[]],[]]] [[[.,[[.,.],.]],[.,[[.,.],[[.,[[.,.],.]],.]]]],.]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[[[[[]],[]],[[]],[]],[[[]],[]]] [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[[[]],[[[]],[]],[]],[[[]],[]]] [[[.,[[.,.],.]],[.,[[.,[[.,.],[[.,.],.]]],.]]],.]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[[[[[]],[[]],[]],[]],[[[]],[]]] [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[[[]],[[]],[]],[[[]],[[]],[]]] 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[[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[[]],[[[]],[[[]],[]],[[]],[]]] [[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[[]],[[[[]],[[]],[]],[[]],[]]] [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[],[],[[[[[[[]]]]]]]] [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[[[],[[]]],[[]],[[],[[]]]] [[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]]],[[],[[]],[[],[[]]]]] 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[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[],[],[],[[[]]]] [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[[],[],[[],[],[],[],[],[]]] [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[],[[]],[],[]] [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[[],[[]],[],[],[],[],[],[],[]] [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[],[],[[]],[],[]] [[[[[.,.],[.,.]],.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>[[],[[]],[[]],[[[],[[]]]]] [.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]=>[[[],[],[[]],[[],[[]]]]] [[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.]=>[[],[[]],[[],[[],[]]],[]] [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[[],[[[],[],[],[],[]],[]]] [.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>[[[[]],[[]],[[],[[]]]]] [[[[[[.,.],.],.],.],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[]]]],[[[[[]]]]]] [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[],[]],[[[[[[]]]]]]] [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[[[[[[[[],[]]]]]]],[]] [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[[[[[[[[]]]]]]]],[[]]] [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]=>[[[],[[[]]],[],[],[],[]]] [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[[[],[],[],[],[],[]],[],[]] [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[[[],[],[],[],[],[[]]],[]] [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[],[[[[[[[]]]]]]],[]] [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]=>[[[[[[[]]]]],[[]]],[]] [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[[[[[[[[[[[]]]]]]]]]],[]] [[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[]],[[[[[[]],[]]]]]] [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[],[[[[[[]]]]]]]] [.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[[[[[[[[],[]]]]]],[]]] [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]=>[[[[[[]]]]],[],[[],[]]] [[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[[[[[[[]]]]],[],[]],[]] [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[[[[[[[[]]]]]],[]],[]] [[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[[[[[[[[]]]]]],[],[]],[]] [[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[[[[[[[[[]]]]]]],[]],[]] [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[[[],[],[],[],[]],[],[[]]] [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[[],[[[[[[]]]]],[],[]]] [[.,[[.,.],[.,.]]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[[.,.],[[.,.],.]],[[.,.],[.,.]]],.]=>[[],[[],[]],[[],[[]]],[]] [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[[],[],[[],[],[],[],[],[],[]]] [.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[],[[[[[[]]]]]],[]]] [.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[[[],[[]],[[],[[]]]]]] [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[[[[[[[[]]]]]]],[[]],[]] [[[[[[[.,.],.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[],[[[]],[[[[[]]]]]]] [[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[[[[[[]]]]]],[[],[]]] [.,[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]=>[[[],[[],[]],[[],[[]]]]]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
Map
left rotate
Description
Return the result of left rotation applied to a binary tree.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
  • if $x$ is the right child of $y$, $x$ becomes the last child of $y$.