- FindStat

Identifier
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00019: Binary trees —right rotate⟶ Binary trees
Images
=>
            
              Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
            

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[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
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[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
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[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
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[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
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[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]=>[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]]
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[[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],[.,.]]]]
[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],[.,.]]]]]
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[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[[[[.,[[.,[[.,.],.]],.]],.],.],[.,.]]
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[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
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[[.,[.,[.,[[.,.],.]]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[[.,[.,.]],.],.],.]]=>[.,[[.,[.,.]],[[[[.,[.,.]],.],.],.]]]
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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
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 $C$.