edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
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[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>8 [[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>6 [[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>6 [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>7 [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>7 [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>6 [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>6 [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>7 [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>6 [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>6 [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>7 [.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]]=>11 [.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]]=>10 [.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]]=>8 [.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]]=>10 [.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]]=>9 [.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]]=>8 [.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]=>7 [.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]]=>10 [.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]]=>9 [.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]]=>7 [.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]]=>8 [.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]]=>7 [.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>7 [.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]]=>10 [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>8 [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>4 [[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]]=>5 [[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]=>6 [[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>6 [[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>5 [[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]=>5 [[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]=>6 [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>5 [[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]=>5 [[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.]=>11 [[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.]=>10 [[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.]=>10 [[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.]=>9 [[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.]=>9 [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.]=>8 [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>8 [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>7 [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>9 [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>7 [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>7 [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>8 [[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]]=>8 [[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]]=>6 [[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]]=>9 [[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]]=>6 [[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]]=>6 [[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]]=>7 [[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.]=>7 [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.]=>9 [[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.]=>10 [[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.]=>11 [[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.]=>11 [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>6 [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>7 [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>9 [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>8 [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>8 [[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]=>5 [[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]]=>6 [[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]=>9 [[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]]=>8 [[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]]=>8
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searching the database for the individual values of this statistic
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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 $log_2(n) \leq \operatorname{depth}(T) \leq n$.
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