Identifier
Identifier
Values
=>
Cc0010;cc-rep
[.,[.,.]]=>1 [[.,.],.]=>0 [.,[.,[.,.]]]=>2 [.,[[.,.],.]]=>1 [[.,.],[.,.]]=>1 [[.,[.,.]],.]=>1 [[[.,.],.],.]=>0 [.,[.,[.,[.,.]]]]=>3 [.,[.,[[.,.],.]]]=>2 [.,[[.,.],[.,.]]]=>2 [.,[[.,[.,.]],.]]=>2 [.,[[[.,.],.],.]]=>1 [[.,.],[.,[.,.]]]=>2 [[.,.],[[.,.],.]]=>1 [[.,[.,.]],[.,.]]=>2 [[[.,.],.],[.,.]]=>1 [[.,[.,[.,.]]],.]=>2 [[.,[[.,.],.]],.]=>1 [[[.,.],[.,.]],.]=>1 [[[.,[.,.]],.],.]=>1 [[[[.,.],.],.],.]=>0 [.,[.,[.,[.,[.,.]]]]]=>4 [.,[.,[.,[[.,.],.]]]]=>3 [.,[.,[[.,.],[.,.]]]]=>3 [.,[.,[[.,[.,.]],.]]]=>3 [.,[.,[[[.,.],.],.]]]=>2 [.,[[.,.],[.,[.,.]]]]=>3 [.,[[.,.],[[.,.],.]]]=>2 [.,[[.,[.,.]],[.,.]]]=>3 [.,[[[.,.],.],[.,.]]]=>2 [.,[[.,[.,[.,.]]],.]]=>3 [.,[[.,[[.,.],.]],.]]=>2 [.,[[[.,.],[.,.]],.]]=>2 [.,[[[.,[.,.]],.],.]]=>2 [.,[[[[.,.],.],.],.]]=>1 [[.,.],[.,[.,[.,.]]]]=>3 [[.,.],[.,[[.,.],.]]]=>2 [[.,.],[[.,.],[.,.]]]=>2 [[.,.],[[.,[.,.]],.]]=>2 [[.,.],[[[.,.],.],.]]=>1 [[.,[.,.]],[.,[.,.]]]=>3 [[.,[.,.]],[[.,.],.]]=>2 [[[.,.],.],[.,[.,.]]]=>2 [[[.,.],.],[[.,.],.]]=>1 [[.,[.,[.,.]]],[.,.]]=>3 [[.,[[.,.],.]],[.,.]]=>2 [[[.,.],[.,.]],[.,.]]=>2 [[[.,[.,.]],.],[.,.]]=>2 [[[[.,.],.],.],[.,.]]=>1 [[.,[.,[.,[.,.]]]],.]=>3 [[.,[.,[[.,.],.]]],.]=>2 [[.,[[.,.],[.,.]]],.]=>2 [[.,[[.,[.,.]],.]],.]=>2 [[.,[[[.,.],.],.]],.]=>1 [[[.,.],[.,[.,.]]],.]=>2 [[[.,.],[[.,.],.]],.]=>1 [[[.,[.,.]],[.,.]],.]=>2 [[[[.,.],.],[.,.]],.]=>1 [[[.,[.,[.,.]]],.],.]=>2 [[[.,[[.,.],.]],.],.]=>1 [[[[.,.],[.,.]],.],.]=>1 [[[[.,[.,.]],.],.],.]=>1 [[[[[.,.],.],.],.],.]=>0 [.,[.,[.,[.,[.,[.,.]]]]]]=>5 [.,[.,[.,[.,[[.,.],.]]]]]=>4 [.,[.,[.,[[.,.],[.,.]]]]]=>4 [.,[.,[.,[[.,[.,.]],.]]]]=>4 [.,[.,[.,[[[.,.],.],.]]]]=>3 [.,[.,[[.,.],[.,[.,.]]]]]=>4 [.,[.,[[.,.],[[.,.],.]]]]=>3 [.,[.,[[.,[.,.]],[.,.]]]]=>4 [.,[.,[[[.,.],.],[.,.]]]]=>3 [.,[.,[[.,[.,[.,.]]],.]]]=>4 [.,[.,[[.,[[.,.],.]],.]]]=>3 [.,[.,[[[.,.],[.,.]],.]]]=>3 [.,[.,[[[.,[.,.]],.],.]]]=>3 [.,[.,[[[[.,.],.],.],.]]]=>2 [.,[[.,.],[.,[.,[.,.]]]]]=>4 [.,[[.,.],[.,[[.,.],.]]]]=>3 [.,[[.,.],[[.,.],[.,.]]]]=>3 [.,[[.,.],[[.,[.,.]],.]]]=>3 [.,[[.,.],[[[.,.],.],.]]]=>2 [.,[[.,[.,.]],[.,[.,.]]]]=>4 [.,[[.,[.,.]],[[.,.],.]]]=>3 [.,[[[.,.],.],[.,[.,.]]]]=>3 [.,[[[.,.],.],[[.,.],.]]]=>2 [.,[[.,[.,[.,.]]],[.,.]]]=>4 [.,[[.,[[.,.],.]],[.,.]]]=>3 [.,[[[.,.],[.,.]],[.,.]]]=>3 [.,[[[.,[.,.]],.],[.,.]]]=>3 [.,[[[[.,.],.],.],[.,.]]]=>2 [.,[[.,[.,[.,[.,.]]]],.]]=>4 [.,[[.,[.,[[.,.],.]]],.]]=>3 [.,[[.,[[.,.],[.,.]]],.]]=>3 [.,[[.,[[.,[.,.]],.]],.]]=>3 [.,[[.,[[[.,.],.],.]],.]]=>2 [.,[[[.,.],[.,[.,.]]],.]]=>3 [.,[[[.,.],[[.,.],.]],.]]=>2 [.,[[[.,[.,.]],[.,.]],.]]=>3 [.,[[[[.,.],.],[.,.]],.]]=>2 [.,[[[.,[.,[.,.]]],.],.]]=>3 [.,[[[.,[[.,.],.]],.],.]]=>2 [.,[[[[.,.],[.,.]],.],.]]=>2 [.,[[[[.,[.,.]],.],.],.]]=>2 [.,[[[[[.,.],.],.],.],.]]=>1 [[.,.],[.,[.,[.,[.,.]]]]]=>4 [[.,.],[.,[.,[[.,.],.]]]]=>3 [[.,.],[.,[[.,.],[.,.]]]]=>3 [[.,.],[.,[[.,[.,.]],.]]]=>3 [[.,.],[.,[[[.,.],.],.]]]=>2 [[.,.],[[.,.],[.,[.,.]]]]=>3 [[.,.],[[.,.],[[.,.],.]]]=>2 [[.,.],[[.,[.,.]],[.,.]]]=>3 [[.,.],[[[.,.],.],[.,.]]]=>2 [[.,.],[[.,[.,[.,.]]],.]]=>3 [[.,.],[[.,[[.,.],.]],.]]=>2 [[.,.],[[[.,.],[.,.]],.]]=>2 [[.,.],[[[.,[.,.]],.],.]]=>2 [[.,.],[[[[.,.],.],.],.]]=>1 [[.,[.,.]],[.,[.,[.,.]]]]=>4 [[.,[.,.]],[.,[[.,.],.]]]=>3 [[.,[.,.]],[[.,.],[.,.]]]=>3 [[.,[.,.]],[[.,[.,.]],.]]=>3 [[.,[.,.]],[[[.,.],.],.]]=>2 [[[.,.],.],[.,[.,[.,.]]]]=>3 [[[.,.],.],[.,[[.,.],.]]]=>2 [[[.,.],.],[[.,.],[.,.]]]=>2 [[[.,.],.],[[.,[.,.]],.]]=>2 [[[.,.],.],[[[.,.],.],.]]=>1 [[.,[.,[.,.]]],[.,[.,.]]]=>4 [[.,[.,[.,.]]],[[.,.],.]]=>3 [[.,[[.,.],.]],[.,[.,.]]]=>3 [[.,[[.,.],.]],[[.,.],.]]=>2 [[[.,.],[.,.]],[.,[.,.]]]=>3 [[[.,.],[.,.]],[[.,.],.]]=>2 [[[.,[.,.]],.],[.,[.,.]]]=>3 [[[.,[.,.]],.],[[.,.],.]]=>2 [[[[.,.],.],.],[.,[.,.]]]=>2 [[[[.,.],.],.],[[.,.],.]]=>1 [[.,[.,[.,[.,.]]]],[.,.]]=>4 [[.,[.,[[.,.],.]]],[.,.]]=>3 [[.,[[.,.],[.,.]]],[.,.]]=>3 [[.,[[.,[.,.]],.]],[.,.]]=>3 [[.,[[[.,.],.],.]],[.,.]]=>2 [[[.,.],[.,[.,.]]],[.,.]]=>3 [[[.,.],[[.,.],.]],[.,.]]=>2 [[[.,[.,.]],[.,.]],[.,.]]=>3 [[[[.,.],.],[.,.]],[.,.]]=>2 [[[.,[.,[.,.]]],.],[.,.]]=>3 [[[.,[[.,.],.]],.],[.,.]]=>2 [[[[.,.],[.,.]],.],[.,.]]=>2 [[[[.,[.,.]],.],.],[.,.]]=>2 [[[[[.,.],.],.],.],[.,.]]=>1 [[.,[.,[.,[.,[.,.]]]]],.]=>4 [[.,[.,[.,[[.,.],.]]]],.]=>3 [[.,[.,[[.,.],[.,.]]]],.]=>3 [[.,[.,[[.,[.,.]],.]]],.]=>3 [[.,[.,[[[.,.],.],.]]],.]=>2 [[.,[[.,.],[.,[.,.]]]],.]=>3 [[.,[[.,.],[[.,.],.]]],.]=>2 [[.,[[.,[.,.]],[.,.]]],.]=>3 [[.,[[[.,.],.],[.,.]]],.]=>2 [[.,[[.,[.,[.,.]]],.]],.]=>3 [[.,[[.,[[.,.],.]],.]],.]=>2 [[.,[[[.,.],[.,.]],.]],.]=>2 [[.,[[[.,[.,.]],.],.]],.]=>2 [[.,[[[[.,.],.],.],.]],.]=>1 [[[.,.],[.,[.,[.,.]]]],.]=>3 [[[.,.],[.,[[.,.],.]]],.]=>2 [[[.,.],[[.,.],[.,.]]],.]=>2 [[[.,.],[[.,[.,.]],.]],.]=>2 [[[.,.],[[[.,.],.],.]],.]=>1 [[[.,[.,.]],[.,[.,.]]],.]=>3 [[[.,[.,.]],[[.,.],.]],.]=>2 [[[[.,.],.],[.,[.,.]]],.]=>2 [[[[.,.],.],[[.,.],.]],.]=>1 [[[.,[.,[.,.]]],[.,.]],.]=>3 [[[.,[[.,.],.]],[.,.]],.]=>2 [[[[.,.],[.,.]],[.,.]],.]=>2 [[[[.,[.,.]],.],[.,.]],.]=>2 [[[[[.,.],.],.],[.,.]],.]=>1 [[[.,[.,[.,[.,.]]]],.],.]=>3 [[[.,[.,[[.,.],.]]],.],.]=>2 [[[.,[[.,.],[.,.]]],.],.]=>2 [[[.,[[.,[.,.]],.]],.],.]=>2 [[[.,[[[.,.],.],.]],.],.]=>1 [[[[.,.],[.,[.,.]]],.],.]=>2 [[[[.,.],[[.,.],.]],.],.]=>1 [[[[.,[.,.]],[.,.]],.],.]=>2 [[[[[.,.],.],[.,.]],.],.]=>1 [[[[.,[.,[.,.]]],.],.],.]=>2 [[[[.,[[.,.],.]],.],.],.]=>1 [[[[[.,.],[.,.]],.],.],.]=>1 [[[[[.,[.,.]],.],.],.],.]=>1 [[[[[[.,.],.],.],.],.],.]=>0
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Description
The number of left oriented leafs of a binary tree except the first one.
In other other words, this is the sum of canopee vector of the tree.
The canopee of a non empty binary tree T with n internal nodes is the list l of 0 and 1 of length n-1 obtained by going along the leaves of T from left to right except the two extremal ones, writing 0 if the leaf is a right leaf and 1 if the leaf is a left leaf.
This is also the number of nodes having a right child. Indeed each of said right children will give exactly one left oriented leaf.
Code
def statistic(bt):
    return sum(bt.canopee())
Created
Jun 13, 2013 at 10:02 by Viviane Pons
Updated
Oct 17, 2015 at 10:48 by Christian Stump