Commits on Apr 29, 2024

1. fix: P2D …

   The previous implementation could give an incorrect result when the
   first node was not a root node.
   
   Example:
   
   P2D 0 2 2
   
   correctly returns:
   
   0 1 0    0 2 1
   
   However
   
   P2D 1 1
   
   returns
   
   1 0    0 1
   
   Therefore, it says that no permutation is necessary to have the
   depth-first traversal.
   
   The reason is that, in the matrix `(-1+d)↑⍤0 1⊢⌽z`, a zero can either
   mean the index of a node or an element used to fill the empty positions.
   
   In the last example, `(-1+d)↑⍤0 1⊢⌽z` is:
   
   1 0  <- path of the node is 1 0
   1 0  <- path of the node is 1
   
   Grade Up says that rows of this matrix are already sorted.
   
   A quick fix is just to add one to the matrix z. Therefore,
   we have instead `(-1+d)↑⍤0 1⊢⌽1+z)` which is in our example:
   
   2 1
   2 0
   
   And we have the expected result:
   
   >> P2D 1 1
   
   1 0     1 0
   
   Notes:
   - There are no issue when the first node is a root node.
   - There is no issue when `⎕IO` is equal to 1. Actually, the value we
     need to add to z is `1 - ⎕IO`, if we wanted a solution that works
     for any value of `⎕IO`.

   

   axiles committed Apr 29, 2024
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