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@@ -0,0 +1,678 @@
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+/*
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+package avl implements an AVL tree.
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+
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+The implementation is non-intrusive, and non-recursive.
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+*/
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+package container_avl
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+
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+import "base:intrinsics"
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+import "base:runtime"
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+import "core:slice"
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+
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+_ :: intrinsics
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+_ :: runtime
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+
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+// Originally based on the CC0 implementation by Eric Biggers
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+// See: https://github.com/ebiggers/avl_tree/
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+
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+// Direction specifies the traversal direction for a tree iterator.
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+Direction :: enum i8 {
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+ // Backward is the in-order backwards direction.
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+ Backward = -1,
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+ // Forward is the in-order forwards direction.
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+ Forward = 1,
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+}
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+
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+// Ordering specifies order when inserting/finding values into the tree.
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+Ordering :: slice.Ordering
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+
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+// Tree is an AVL tree.
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+Tree :: struct($Value: typeid) {
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+ // user_data is a parameter that will be passed to the on_remove
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+ // callback.
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+ user_data: rawptr,
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+ // on_remove is an optional callback that can be called immediately
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+ // after a node is removed from the tree.
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+ on_remove: proc(value: Value, user_data: rawptr),
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+
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+ _root: ^Node(Value),
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+ _node_allocator: runtime.Allocator,
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+ _cmp_fn: proc(a, b: Value) -> Ordering,
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+ _size: int,
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+}
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+
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+// Node is an AVL tree node.
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+//
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+// WARNING: It is unsafe to mutate value if the node is part of a tree
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+// if doing so will alter the Node's sort position relative to other
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+// elements in the tree.
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+Node :: struct($Value: typeid) {
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+ value: Value,
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+
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+ _parent: ^Node(Value),
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+ _left: ^Node(Value),
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+ _right: ^Node(Value),
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+ _balance: i8,
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+}
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+
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+// Iterator is a tree iterator.
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+//
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+// WARNING: It is unsafe to modify the tree while iterating, except via
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+// the iterator_remove method.
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+Iterator :: struct($Value: typeid) {
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+ _tree: ^Tree(Value),
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+ _cur: ^Node(Value),
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+ _next: ^Node(Value),
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+ _direction: Direction,
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+ _called_next: bool,
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+}
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+
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+// init initializes a tree.
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+init :: proc {
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+ init_ordered,
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+ init_cmp,
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+}
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+
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+// init_cmp initializes a tree.
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+init_cmp :: proc(
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+ t: ^$T/Tree($Value),
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+ cmp_fn: proc(a, b: Value) -> Ordering,
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+ node_allocator := context.allocator,
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+) {
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+ t._root = nil
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+ t._node_allocator = node_allocator
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+ t._cmp_fn = cmp_fn
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+ t._size = 0
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+}
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+
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+// init_ordered initializes a tree containing ordered items, with
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+// a comparison function that results in an ascending order sort.
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+init_ordered :: proc(
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+ t: ^$T/Tree($Value),
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+ node_allocator := context.allocator,
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+) where intrinsics.type_is_ordered_numeric(Value) {
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+ init_cmp(t, slice.cmp_proc(Value), node_allocator)
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+}
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+
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+// destroy de-initializes a tree.
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+destroy :: proc(t: ^$T/Tree($Value), call_on_remove: bool = true) {
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+ iter := iterator(t, Direction.Forward)
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+ for _ in iterator_next(&iter) {
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+ iterator_remove(&iter, call_on_remove)
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+ }
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+}
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+
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+// len returns the number of elements in the tree.
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+len :: proc "contextless" (t: ^$T/Tree($Value)) -> int {
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+ return t._size
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+}
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+
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+// first returns the first node in the tree (in-order) or nil iff
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+// the tree is empty.
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+first :: proc "contextless" (t: ^$T/Tree($Value)) -> ^Node(Value) {
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+ return tree_first_or_last_in_order(t, Direction.Backward)
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+}
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+
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+// last returns the last element in the tree (in-order) or nil iff
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+// the tree is empty.
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+last :: proc "contextless" (t: ^$T/Tree($Value)) -> ^Node(Value) {
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+ return tree_first_or_last_in_order(t, Direction.Forward)
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+}
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+
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+// find finds the value in the tree, and returns the corresponding
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+// node or nil iff the value is not present.
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+find :: proc(t: ^$T/Tree($Value), value: Value) -> ^Node(Value) {
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+ cur := t._root
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+ descend_loop: for cur != nil {
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+ switch t._cmp_fn(value, cur.value) {
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+ case .Less:
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+ cur = cur._left
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+ case .Greater:
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+ cur = cur._right
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+ case .Equal:
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+ break descend_loop
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+ }
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+ }
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+
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+ return cur
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+}
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+
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+// find_or_insert attempts to insert the value into the tree, and returns
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+// the node, a boolean indicating if the value was inserted, and the
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+// node allocator error if relevant. If the value is already
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+// present, the existing node is returned un-altered.
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+find_or_insert :: proc(
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+ t: ^$T/Tree($Value),
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+ value: Value,
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+) -> (
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+ n: ^Node(Value),
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+ inserted: bool,
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+ err: runtime.Allocator_Error,
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+) {
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+ n_ptr := &t._root
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+ for n_ptr^ != nil {
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+ n = n_ptr^
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+ switch t._cmp_fn(value, n.value) {
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+ case .Less:
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+ n_ptr = &n._left
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+ case .Greater:
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+ n_ptr = &n._right
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+ case .Equal:
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+ return
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+ }
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+ }
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+
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+ parent := n
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+ n = new(Node(Value), t._node_allocator) or_return
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+ n.value = value
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+ n._parent = parent
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+ n_ptr^ = n
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+ tree_rebalance_after_insert(t, n)
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+
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+ t._size += 1
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+ inserted = true
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+
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+ return
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+}
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+
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+// remove removes a node or value from the tree, and returns true iff the
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+// removal was successful. While the node's value will be left intact,
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+// the node itself will be freed via the tree's node allocator.
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+remove :: proc {
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+ remove_value,
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+ remove_node,
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+}
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+
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+// remove_value removes a value from the tree, and returns true iff the
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+// removal was successful. While the node's value will be left intact,
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+// the node itself will be freed via the tree's node allocator.
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+remove_value :: proc(t: ^$T/Tree($Value), value: Value, call_on_remove: bool = true) -> bool {
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+ n := find(t, value)
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+ if n == nil {
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+ return false
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+ }
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+ return remove_node(t, n, call_on_remove)
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+}
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+
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+// remove_node removes a node from the tree, and returns true iff the
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+// removal was successful. While the node's value will be left intact,
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+// the node itself will be freed via the tree's node allocator.
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+remove_node :: proc(t: ^$T/Tree($Value), node: ^Node(Value), call_on_remove: bool = true) -> bool {
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+ if node._parent == node || (node._parent == nil && t._root != node) {
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+ return false
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+ }
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+ defer {
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+ if call_on_remove && t.on_remove != nil {
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+ t.on_remove(node.value, t.user_data)
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+ }
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+ free(node, t._node_allocator)
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+ }
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+
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+ parent: ^Node(Value)
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+ left_deleted: bool
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+
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+ t._size -= 1
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+ if node._left != nil && node._right != nil {
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+ parent, left_deleted = tree_swap_with_successor(t, node)
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+ } else {
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+ child := node._left
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+ if child == nil {
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+ child = node._right
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+ }
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+ parent = node._parent
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+ if parent != nil {
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+ if node == parent._left {
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+ parent._left = child
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+ left_deleted = true
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+ } else {
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+ parent._right = child
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+ left_deleted = false
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+ }
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+ if child != nil {
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+ child._parent = parent
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+ }
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+ } else {
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+ if child != nil {
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+ child._parent = parent
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+ }
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+ t._root = child
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+ node_reset(node)
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+ return true
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+ }
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+ }
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+
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+ for {
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+ if left_deleted {
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+ parent = tree_handle_subtree_shrink(t, parent, +1, &left_deleted)
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+ } else {
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+ parent = tree_handle_subtree_shrink(t, parent, -1, &left_deleted)
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+ }
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+ if parent == nil {
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+ break
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+ }
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+ }
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+ node_reset(node)
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+
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+ return true
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+}
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+
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+// iterator returns a tree iterator in the specified direction.
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+iterator :: proc "contextless" (t: ^$T/Tree($Value), direction: Direction) -> Iterator(Value) {
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+ it: Iterator(Value)
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+ it._tree = transmute(^Tree(Value))t
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+ it._direction = direction
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+
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+ iterator_first(&it)
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+
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+ return it
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+}
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+
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+// iterator_from_pos returns a tree iterator in the specified direction,
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+// spanning the range [pos, last] (inclusive).
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+iterator_from_pos :: proc "contextless" (
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+ t: ^$T/Tree($Value),
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+ pos: ^Node(Value),
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+ direction: Direction,
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+) -> Iterator(Value) {
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+ it: Iterator(Value)
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+ it._tree = transmute(^Tree(Value))t
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+ it._direction = direction
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+ it._next = nil
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+ it._called_next = false
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+
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+ if it._cur = pos; pos != nil {
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+ it._next = node_next_or_prev_in_order(it._cur, it._direction)
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+ }
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+
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+ return it
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+}
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+
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+// iterator_get returns the node currently pointed to by the iterator,
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+// or nil iff the node has been removed, the tree is empty, or the end
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+// of the tree has been reached.
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+iterator_get :: proc "contextless" (it: ^$I/Iterator($Value)) -> ^Node(Value) {
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+ return it._cur
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+}
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+
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+// iterator_remove removes the node currently pointed to by the iterator,
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+// and returns true iff the removal was successful. Semantics are the
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+// same as the Tree remove.
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+iterator_remove :: proc(it: ^$I/Iterator($Value), call_on_remove: bool = true) -> bool {
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+ if it._cur == nil {
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+ return false
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+ }
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+
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+ ok := remove_node(it._tree, it._cur, call_on_remove)
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+ if ok {
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+ it._cur = nil
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+ }
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+
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+ return ok
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+}
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+
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+// iterator_next advances the iterator and returns the (node, true) or
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+// or (nil, false) iff the end of the tree has been reached.
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+//
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+// Note: The first call to iterator_next will return the first node instead
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+// of advancing the iterator.
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+iterator_next :: proc "contextless" (it: ^$I/Iterator($Value)) -> (^Node(Value), bool) {
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+ // This check is needed so that the first element gets returned from
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+ // a brand-new iterator, and so that the somewhat contrived case where
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+ // iterator_remove is called before the first call to iterator_next
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+ // returns the correct value.
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+ if !it._called_next {
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+ it._called_next = true
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+
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+ // There can be the contrived case where iterator_remove is
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+ // called before ever calling iterator_next, which needs to be
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+ // handled as an actual call to next.
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+ //
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+ // If this happens it._cur will be nil, so only return the
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+ // first value, if it._cur is valid.
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+ if it._cur != nil {
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+ return it._cur, true
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+ }
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+ }
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+
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+ if it._next == nil {
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+ return nil, false
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+ }
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+
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+ it._cur = it._next
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+ it._next = node_next_or_prev_in_order(it._cur, it._direction)
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+
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+ return it._cur, true
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+}
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+
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+@(private)
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+tree_first_or_last_in_order :: proc "contextless" (
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+ t: ^$T/Tree($Value),
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+ direction: Direction,
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+) -> ^Node(Value) {
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+ first, sign := t._root, i8(direction)
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+ if first != nil {
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+ for {
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+ tmp := node_get_child(first, +sign)
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+ if tmp == nil {
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+ break
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+ }
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+ first = tmp
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+ }
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+ }
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+
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+ return first
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+}
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+
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+@(private)
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+tree_replace_child :: proc "contextless" (
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+ t: ^$T/Tree($Value),
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+ parent, old_child, new_child: ^Node(Value),
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+) {
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+ if parent != nil {
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+ if old_child == parent._left {
|
|
|
|
+ parent._left = new_child
|
|
|
|
+ } else {
|
|
|
|
+ parent._right = new_child
|
|
|
|
+ }
|
|
|
|
+ } else {
|
|
|
|
+ t._root = new_child
|
|
|
|
+ }
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+tree_rotate :: proc "contextless" (t: ^$T/Tree($Value), a: ^Node(Value), sign: i8) {
|
|
|
|
+ b := node_get_child(a, -sign)
|
|
|
|
+ e := node_get_child(b, +sign)
|
|
|
|
+ p := a._parent
|
|
|
|
+
|
|
|
|
+ node_set_child(a, -sign, e)
|
|
|
|
+ a._parent = b
|
|
|
|
+
|
|
|
|
+ node_set_child(b, +sign, a)
|
|
|
|
+ b._parent = p
|
|
|
|
+
|
|
|
|
+ if e != nil {
|
|
|
|
+ e._parent = a
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ tree_replace_child(t, p, a, b)
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+tree_double_rotate :: proc "contextless" (
|
|
|
|
+ t: ^$T/Tree($Value),
|
|
|
|
+ b, a: ^Node(Value),
|
|
|
|
+ sign: i8,
|
|
|
|
+) -> ^Node(Value) {
|
|
|
|
+ e := node_get_child(b, +sign)
|
|
|
|
+ f := node_get_child(e, -sign)
|
|
|
|
+ g := node_get_child(e, +sign)
|
|
|
|
+ p := a._parent
|
|
|
|
+ e_bal := e._balance
|
|
|
|
+
|
|
|
|
+ node_set_child(a, -sign, g)
|
|
|
|
+ a_bal := -e_bal
|
|
|
|
+ if sign * e_bal >= 0 {
|
|
|
|
+ a_bal = 0
|
|
|
|
+ }
|
|
|
|
+ node_set_parent_balance(a, e, a_bal)
|
|
|
|
+
|
|
|
|
+ node_set_child(b, +sign, f)
|
|
|
|
+ b_bal := -e_bal
|
|
|
|
+ if sign * e_bal <= 0 {
|
|
|
|
+ b_bal = 0
|
|
|
|
+ }
|
|
|
|
+ node_set_parent_balance(b, e, b_bal)
|
|
|
|
+
|
|
|
|
+ node_set_child(e, +sign, a)
|
|
|
|
+ node_set_child(e, -sign, b)
|
|
|
|
+ node_set_parent_balance(e, p, 0)
|
|
|
|
+
|
|
|
|
+ if g != nil {
|
|
|
|
+ g._parent = a
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ if f != nil {
|
|
|
|
+ f._parent = b
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ tree_replace_child(t, p, a, e)
|
|
|
|
+
|
|
|
|
+ return e
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+tree_handle_subtree_growth :: proc "contextless" (
|
|
|
|
+ t: ^$T/Tree($Value),
|
|
|
|
+ node, parent: ^Node(Value),
|
|
|
|
+ sign: i8,
|
|
|
|
+) -> bool {
|
|
|
|
+ old_balance_factor := parent._balance
|
|
|
|
+ if old_balance_factor == 0 {
|
|
|
|
+ node_adjust_balance_factor(parent, sign)
|
|
|
|
+ return false
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ new_balance_factor := old_balance_factor + sign
|
|
|
|
+ if new_balance_factor == 0 {
|
|
|
|
+ node_adjust_balance_factor(parent, sign)
|
|
|
|
+ return true
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ if sign * node._balance > 0 {
|
|
|
|
+ tree_rotate(t, parent, -sign)
|
|
|
|
+ node_adjust_balance_factor(parent, -sign)
|
|
|
|
+ node_adjust_balance_factor(node, -sign)
|
|
|
|
+ } else {
|
|
|
|
+ tree_double_rotate(t, node, parent, -sign)
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ return true
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+tree_rebalance_after_insert :: proc "contextless" (t: ^$T/Tree($Value), inserted: ^Node(Value)) {
|
|
|
|
+ node, parent := inserted, inserted._parent
|
|
|
|
+ switch {
|
|
|
|
+ case parent == nil:
|
|
|
|
+ return
|
|
|
|
+ case node == parent._left:
|
|
|
|
+ node_adjust_balance_factor(parent, -1)
|
|
|
|
+ case:
|
|
|
|
+ node_adjust_balance_factor(parent, +1)
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ if parent._balance == 0 {
|
|
|
|
+ return
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ for done := false; !done; {
|
|
|
|
+ node = parent
|
|
|
|
+ if parent = node._parent; parent == nil {
|
|
|
|
+ return
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ if node == parent._left {
|
|
|
|
+ done = tree_handle_subtree_growth(t, node, parent, -1)
|
|
|
|
+ } else {
|
|
|
|
+ done = tree_handle_subtree_growth(t, node, parent, +1)
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+tree_swap_with_successor :: proc "contextless" (
|
|
|
|
+ t: ^$T/Tree($Value),
|
|
|
|
+ x: ^Node(Value),
|
|
|
|
+) -> (
|
|
|
|
+ ^Node(Value),
|
|
|
|
+ bool,
|
|
|
|
+) {
|
|
|
|
+ ret: ^Node(Value)
|
|
|
|
+ left_deleted: bool
|
|
|
|
+
|
|
|
|
+ y := x._right
|
|
|
|
+ if y._left == nil {
|
|
|
|
+ ret = y
|
|
|
|
+ } else {
|
|
|
|
+ q: ^Node(Value)
|
|
|
|
+
|
|
|
|
+ for {
|
|
|
|
+ q = y
|
|
|
|
+ if y = y._left; y._left == nil {
|
|
|
|
+ break
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ if q._left = y._right; q._left != nil {
|
|
|
|
+ q._left._parent = q
|
|
|
|
+ }
|
|
|
|
+ y._right = x._right
|
|
|
|
+ x._right._parent = y
|
|
|
|
+ ret = q
|
|
|
|
+ left_deleted = true
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ y._left = x._left
|
|
|
|
+ x._left._parent = y
|
|
|
|
+
|
|
|
|
+ y._parent = x._parent
|
|
|
|
+ y._balance = x._balance
|
|
|
|
+
|
|
|
|
+ tree_replace_child(t, x._parent, x, y)
|
|
|
|
+
|
|
|
|
+ return ret, left_deleted
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+tree_handle_subtree_shrink :: proc "contextless" (
|
|
|
|
+ t: ^$T/Tree($Value),
|
|
|
|
+ parent: ^Node(Value),
|
|
|
|
+ sign: i8,
|
|
|
|
+ left_deleted: ^bool,
|
|
|
|
+) -> ^Node(Value) {
|
|
|
|
+ old_balance_factor := parent._balance
|
|
|
|
+ if old_balance_factor == 0 {
|
|
|
|
+ node_adjust_balance_factor(parent, sign)
|
|
|
|
+ return nil
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ node: ^Node(Value)
|
|
|
|
+ new_balance_factor := old_balance_factor + sign
|
|
|
|
+ if new_balance_factor == 0 {
|
|
|
|
+ node_adjust_balance_factor(parent, sign)
|
|
|
|
+ node = parent
|
|
|
|
+ } else {
|
|
|
|
+ node = node_get_child(parent, sign)
|
|
|
|
+ if sign * node._balance >= 0 {
|
|
|
|
+ tree_rotate(t, parent, -sign)
|
|
|
|
+ if node._balance == 0 {
|
|
|
|
+ node_adjust_balance_factor(node, -sign)
|
|
|
|
+ return nil
|
|
|
|
+ }
|
|
|
|
+ node_adjust_balance_factor(parent, -sign)
|
|
|
|
+ node_adjust_balance_factor(node, -sign)
|
|
|
|
+ } else {
|
|
|
|
+ node = tree_double_rotate(t, node, parent, -sign)
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ parent := parent
|
|
|
|
+ if parent = node._parent; parent != nil {
|
|
|
|
+ left_deleted^ = node == parent._left
|
|
|
|
+ }
|
|
|
|
+ return parent
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+node_reset :: proc "contextless" (n: ^Node($Value)) {
|
|
|
|
+ // Mostly pointless as n will be deleted after this is called, but
|
|
|
|
+ // attempt to be able to catch cases of n not being in the tree.
|
|
|
|
+ n._parent = n
|
|
|
|
+ n._left = nil
|
|
|
|
+ n._right = nil
|
|
|
|
+ n._balance = 0
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+node_set_parent_balance :: #force_inline proc "contextless" (
|
|
|
|
+ n, parent: ^Node($Value),
|
|
|
|
+ balance: i8,
|
|
|
|
+) {
|
|
|
|
+ n._parent = parent
|
|
|
|
+ n._balance = balance
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+node_get_child :: #force_inline proc "contextless" (n: ^Node($Value), sign: i8) -> ^Node(Value) {
|
|
|
|
+ if sign < 0 {
|
|
|
|
+ return n._left
|
|
|
|
+ }
|
|
|
|
+ return n._right
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+node_next_or_prev_in_order :: proc "contextless" (
|
|
|
|
+ n: ^Node($Value),
|
|
|
|
+ direction: Direction,
|
|
|
|
+) -> ^Node(Value) {
|
|
|
|
+ next, tmp: ^Node(Value)
|
|
|
|
+ sign := i8(direction)
|
|
|
|
+
|
|
|
|
+ if next = node_get_child(n, +sign); next != nil {
|
|
|
|
+ for {
|
|
|
|
+ tmp = node_get_child(next, -sign)
|
|
|
|
+ if tmp == nil {
|
|
|
|
+ break
|
|
|
|
+ }
|
|
|
|
+ next = tmp
|
|
|
|
+ }
|
|
|
|
+ } else {
|
|
|
|
+ tmp, next = n, n._parent
|
|
|
|
+ for next != nil && tmp == node_get_child(next, +sign) {
|
|
|
|
+ tmp, next = next, next._parent
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+ return next
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+node_set_child :: #force_inline proc "contextless" (
|
|
|
|
+ n: ^Node($Value),
|
|
|
|
+ sign: i8,
|
|
|
|
+ child: ^Node(Value),
|
|
|
|
+) {
|
|
|
|
+ if sign < 0 {
|
|
|
|
+ n._left = child
|
|
|
|
+ } else {
|
|
|
|
+ n._right = child
|
|
|
|
+ }
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+node_adjust_balance_factor :: #force_inline proc "contextless" (n: ^Node($Value), amount: i8) {
|
|
|
|
+ n._balance += amount
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+@(private)
|
|
|
|
+iterator_first :: proc "contextless" (it: ^Iterator($Value)) {
|
|
|
|
+ // This is private because behavior when the user manually calls
|
|
|
|
+ // iterator_first followed by iterator_next is unintuitive, since
|
|
|
|
+ // the first call to iterator_next MUST return the first node
|
|
|
|
+ // instead of advancing so that `for node in iterator_next(&next)`
|
|
|
|
+ // works as expected.
|
|
|
|
+
|
|
|
|
+ switch it._direction {
|
|
|
|
+ case .Forward:
|
|
|
|
+ it._cur = tree_first_or_last_in_order(it._tree, .Backward)
|
|
|
|
+ case .Backward:
|
|
|
|
+ it._cur = tree_first_or_last_in_order(it._tree, .Forward)
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ it._next = nil
|
|
|
|
+ it._called_next = false
|
|
|
|
+
|
|
|
|
+ if it._cur != nil {
|
|
|
|
+ it._next = node_next_or_prev_in_order(it._cur, it._direction)
|
|
|
|
+ }
|
|
|
|
+}
|