edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
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[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>7 [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>6 [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>6 [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>5 [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>8 [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>7 [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>6 [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>7 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>6 [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>11 [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>10 [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>9 [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>10 [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>9 [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>9 [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>8 [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>8 [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>7 [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>10 [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>9 [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>8 [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>9 [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>8 [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>9 [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>8 [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>7 [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>8 [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>7 [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>7 [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>6 [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>7 [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>6 [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>8 [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>7 [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>6 [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>7 [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>6 [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>10 [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>9 [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>8 [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>9 [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>8 [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>8 [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>7 [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>7 [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>6 [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>9 [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>8 [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>7 [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>8
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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Description
The depth or height of a binary tree.
The depth (or height) of a binary tree is the maximal depth (or height) of one of its vertices.
The height of a vertex is the number of edges on the longest path between that node and a leaf. The depth of a vertex is the number of edges from the vertex to the root.
See [1] and [2] for this terminology.
The depth (or height) of a tree $T$ can be recursively defined: $\operatorname{depth}(T) = 0$ if $T$ is empty and
$$\operatorname{depth}(T) = 1 + max(\operatorname{depth}(L),\operatorname{depth}(R))$$
if $T$ is nonempty with left and right subtrees $L$ and $R$, respectively.
The upper and lower bounds on the depth of a binary tree $T$ of size $n$ are $log_2(n) \leq \operatorname{depth}(T) \leq n$.
References
[1] wikipedia:Tree (data_structure)
[2] Depth and height of tree
Code
def statistic(t):
    return t.depth()
Created
Mar 25, 2013 at 11:09 by Viviane Pons
Updated
Jan 17, 2018 at 23:05 by Martin Rubey