Identifier
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00019: Binary trees —right rotate⟶ Binary trees
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0010;cc-rep-2Cc0010;cc-rep-3
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[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.] [[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.] [[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.] [[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.] [[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.] [[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.] [[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.] [[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.] 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[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] [[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.] [[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] [[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.] [[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.] [[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] [[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] [[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] [[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.] [[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.] [[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.] [[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.] [[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] [[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.] [[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] [[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.] [[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] [[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.] [[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] [[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] [[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] [[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] [[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.] [[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] [[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] [[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] [[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] [[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.] [[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] [[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] [[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] [[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.] [[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.] [[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] [[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] [[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] [[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.] [[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] [[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] [[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] [[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] [[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] [[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] [[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] [[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] [[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] [[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] [[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] [[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] [[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
right rotate
Description
Return the result of right rotation applied to a binary tree.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.