Identifier
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
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Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2Cc0010;cc-rep-3Cc0010;cc-rep-4
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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 $B$.