Immutable binary tree.
Tree[A] = Leaf(value) | Branch(value, left, right)
Every node holds a value. map applies a function to all values,
preserving structure. Tree is a Functor but not a Monad.
Examples:
>>> from funstruct.collections.tree import Tree, Leaf, Branch
>>> from funstruct.collections.cons import Cons, Nil
>>> t = Branch(1, Leaf(2), Leaf(3))
>>> t.map(lambda x: x * 10)
Branch(10, Leaf(20), Leaf(30))
>>> t.size
3
>>> t.depth
1
>>> big = Branch(1, Branch(2, Leaf(3), Leaf(4)), Leaf(5))
>>> big.map(str)
Branch('1', Branch('2', Leaf('3'), Leaf('4')), Leaf('5'))
>>> big.to_list()
Cons(3, Cons(2, Cons(4, Cons(1, Cons(5, Nil())))))
>>> big.depth
2
fold — reduce the tree:
>>> t.fold(lambda v: v, lambda v, l, r: v + l + r)
6
Tree
Bases: DataType, Generic[A]
Binary tree where every node holds a value.
Source code in funstruct/collections/tree/__init__.py
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90 | class Tree(DataType, Generic[A]):
"""Binary tree where every node holds a value."""
@property
@abstractmethod
def size(self) -> int: ...
@property
@abstractmethod
def depth(self) -> int: ...
@abstractmethod
def fold(
self,
on_leaf: Callable[[A], C],
on_branch: Callable[[A, C, C], C],
) -> C: ...
@abstractmethod
def to_list(self) -> CList[A]: ...
@abstractmethod
def fold_right(self, acc: B, f: Callable[[A, B], B]) -> B: ...
def fold_left(self, acc: B, f: Callable[[B, A], B]) -> B:
items: list = []
self.fold_right(None, lambda a, _: items.append(a))
for item in items:
acc = f(acc, item)
return acc
def length(self) -> int:
return self.fold_right(0, lambda _, acc: acc + 1)
def is_empty(self) -> bool:
return False
@abstractmethod
def traverse(self, f: Callable, pure_fn: Callable) -> object: ...
def sequence(self, pure_fn: Callable) -> object:
return self.traverse(lambda x: x, pure_fn)
|
Leaf
dataclass
Bases: Tree[A]
Terminal node holding a single value.
Source code in funstruct/collections/tree/__init__.py
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131 | @dataclass(frozen=True, eq=False)
class Leaf(Tree[A]):
"""Terminal node holding a single value."""
value: A
@property
def size(self) -> int:
return 1
@property
def depth(self) -> int:
return 0
def fold(
self,
on_leaf: Callable[[A], C],
on_branch: Callable[[A, C, C], C],
) -> C:
return on_leaf(self.value)
def fold_right(self, acc: B, f: Callable[[A, B], B]) -> B:
return f(self.value, acc)
def traverse(self, f: Callable, pure_fn: Callable) -> object:
return f(self.value).map(Leaf)
def to_list(self) -> CList[A]:
return Cons.pure(self.value)
def __eq__(self, other: object) -> bool:
match other:
case Leaf(v):
return self.value == v
case _:
return False
def __repr__(self) -> str:
return f"Leaf({repr(self.value)})"
|
Branch
dataclass
Bases: Tree[A]
Internal node with a value and two children.
Source code in funstruct/collections/tree/__init__.py
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186 | @dataclass(frozen=True, eq=False)
class Branch(Tree[A]):
"""Internal node with a value and two children."""
value: A
left: Tree[A]
right: Tree[A]
@property
def size(self) -> int:
return 1 + self.left.size + self.right.size
@property
def depth(self) -> int:
return 1 + max(self.left.depth, self.right.depth)
def fold(
self,
on_leaf: Callable[[A], C],
on_branch: Callable[[A, C, C], C],
) -> C:
return on_branch(
self.value,
self.left.fold(on_leaf, on_branch),
self.right.fold(on_leaf, on_branch),
)
def fold_right(self, acc: B, f: Callable[[A, B], B]) -> B:
acc = self.right.fold_right(acc, f)
acc = f(self.value, acc)
acc = self.left.fold_right(acc, f)
return acc
def traverse(self, f: Callable, pure_fn: Callable) -> object:
fv = f(self.value)
fl = self.left.traverse(f, pure_fn)
fr = self.right.traverse(f, pure_fn)
return (
pure_fn(lambda v: lambda l: lambda r: Branch(v, l, r)).ap(fv).ap(fl).ap(fr)
)
def to_list(self) -> CList[A]:
return self.left.to_list() + Cons(self.value, self.right.to_list())
def __eq__(self, other: object) -> bool:
match other:
case Branch(v, l, r):
return self.value == v and self.left == l and self.right == r
case _:
return False
def __repr__(self) -> str:
return f"Branch({repr(self.value)}, {repr(self.left)}, {repr(self.right)})"
|