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marcoonroad/mtrx-tree.hs

Last active August 31, 2017 18:43
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mtrx-tree.hs
-- para matrizes de rank 2 --
-- implementando-as como arvores --
data Tree a = Leaf | Node (Tree a) a (Tree a) deriving Eq
{-
| |
| A11 A12 A13 |
a = | |
| A21 A23 A23 |
| |
==========================================
A11 --------- A12 --------- A13 -- Leaf
| | |
| | |
A21 -- Leaf A22 -- Leaf A23 -- Leaf
| | |
Leaf Leaf Leaf
-}
ttranspose Leaf = Leaf
ttranspose (Node left value right) = Node (ttranspose right) value (ttranspose left)
{-
| |
| A11 A12 A13 |
a = | |
| A21 A23 A23 |
| |
==========================================
A11 ---------- A12 ---------- A13 -- Leaf
| | |
| | |
A21 -- Leaf A22 -- Leaf A23 -- Leaf
| | |
Leaf Leaf Leaf
------
||
||
ttranspose
||
||
\||/
\/
A11 ------ A21 -- Leaf
| |
| Leaf
|
|
a' = A12 ------ A22 -- Leaf
| |
| Leaf
|
|
A13 ------ A23 -- Leaf
| |
Leaf Leaf
-}
tjoin Leaf mtrx = mtrx
tjoin (Node left value right) mtrx = Node left value (tjoin right mtrx)
{-
A11 ------ A21 -- Leaf
| |
| Leaf
|
|
a' = A12 ------ A22 -- Leaf
| |
| Leaf
|
|
A13 ------ A23 -- Leaf
| |
Leaf Leaf
---------------------------------------
C11 -- Leaf
|
|
C12 -- Leaf
c' = |
|
C13 -- Leaf
|
Leaf
------
||
||
tjoin a'
||
||
\||/
\/
A11 ------ A21 ---------- C11 -- Leaf
| | |
| Leaf |
| |
| |
a'c' = A12 ------ A22 -- Leaf C12 -- Leaf
| | |
| Leaf |
| |
| |
A13 ------ A23 -- Leaf C13 -- Leaf
| | |
Leaf Leaf Leaf
-}
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