pub fn Treap(comptime Key: type, comptime compareFn: anytype) typepub fn Treap(comptime Key: type, comptime compareFn: anytype) type {
return struct {
const Self = @This();
// Allow for compareFn to be fn (anytype, anytype) anytype
// which allows the convenient use of std.math.order.
fn compare(a: Key, b: Key) Order {
return compareFn(a, b);
}
root: ?*Node = null,
prng: Prng = .{},
/// A customized pseudo random number generator for the treap.
/// This just helps reducing the memory size of the treap itself
/// as std.Random.DefaultPrng requires larger state (while producing better entropy for randomness to be fair).
const Prng = struct {
xorshift: usize = 0,
fn random(self: *Prng, seed: usize) usize {
// Lazily seed the prng state
if (self.xorshift == 0) {
self.xorshift = seed;
}
// Since we're using usize, decide the shifts by the integer's bit width.
const shifts = switch (@bitSizeOf(usize)) {
64 => .{ 13, 7, 17 },
32 => .{ 13, 17, 5 },
16 => .{ 7, 9, 8 },
else => @compileError("platform not supported"),
};
self.xorshift ^= self.xorshift >> shifts[0];
self.xorshift ^= self.xorshift << shifts[1];
self.xorshift ^= self.xorshift >> shifts[2];
assert(self.xorshift != 0);
return self.xorshift;
}
};
/// A Node represents an item or point in the treap with a uniquely associated key.
pub const Node = struct {
key: Key,
priority: usize,
parent: ?*Node,
children: [2]?*Node,
pub fn next(node: *Node) ?*Node {
return nextOnDirection(node, 1);
}
pub fn prev(node: *Node) ?*Node {
return nextOnDirection(node, 0);
}
};
fn extremeInSubtreeOnDirection(node: *Node, direction: u1) *Node {
var cur = node;
while (cur.children[direction]) |next| cur = next;
return cur;
}
fn nextOnDirection(node: *Node, direction: u1) ?*Node {
if (node.children[direction]) |child| {
return extremeInSubtreeOnDirection(child, direction ^ 1);
}
var cur = node;
// Traversing upward until we find `parent` to `cur` is NOT on
// `direction`, or equivalently, `cur` to `parent` IS on
// `direction` thus `parent` is the next.
while (true) {
if (cur.parent) |parent| {
// If `parent -> node` is NOT on `direction`, then
// `node -> parent` IS on `direction`
if (parent.children[direction] != cur) return parent;
cur = parent;
} else {
return null;
}
}
}
/// Returns the smallest Node by key in the treap if there is one.
/// Use `getEntryForExisting()` to replace/remove this Node from the treap.
pub fn getMin(self: Self) ?*Node {
if (self.root) |root| return extremeInSubtreeOnDirection(root, 0);
return null;
}
/// Returns the largest Node by key in the treap if there is one.
/// Use `getEntryForExisting()` to replace/remove this Node from the treap.
pub fn getMax(self: Self) ?*Node {
if (self.root) |root| return extremeInSubtreeOnDirection(root, 1);
return null;
}
/// Lookup the Entry for the given key in the treap.
/// The Entry act's as a slot in the treap to insert/replace/remove the node associated with the key.
pub fn getEntryFor(self: *Self, key: Key) Entry {
var parent: ?*Node = undefined;
const node = self.find(key, &parent);
return Entry{
.key = key,
.treap = self,
.node = node,
.context = .{ .inserted_under = parent },
};
}
/// Get an entry for a Node that currently exists in the treap.
/// It is undefined behavior if the Node is not currently inserted in the treap.
/// The Entry act's as a slot in the treap to insert/replace/remove the node associated with the key.
pub fn getEntryForExisting(self: *Self, node: *Node) Entry {
assert(node.priority != 0);
return Entry{
.key = node.key,
.treap = self,
.node = node,
.context = .{ .inserted_under = node.parent },
};
}
/// An Entry represents a slot in the treap associated with a given key.
pub const Entry = struct {
/// The associated key for this entry.
key: Key,
/// A reference to the treap this entry is apart of.
treap: *Self,
/// The current node at this entry.
node: ?*Node,
/// The current state of the entry.
context: union(enum) {
/// A find() was called for this entry and the position in the treap is known.
inserted_under: ?*Node,
/// The entry's node was removed from the treap and a lookup must occur again for modification.
removed,
},
/// Update's the Node at this Entry in the treap with the new node (null for deleting). `new_node`
/// can have `undefind` content because the value will be initialized internally.
pub fn set(self: *Entry, new_node: ?*Node) void {
// Update the entry's node reference after updating the treap below.
defer self.node = new_node;
if (self.node) |old| {
if (new_node) |new| {
self.treap.replace(old, new);
return;
}
self.treap.remove(old);
self.context = .removed;
return;
}
if (new_node) |new| {
// A previous treap.remove() could have rebalanced the nodes
// so when inserting after a removal, we have to re-lookup the parent again.
// This lookup shouldn't find a node because we're yet to insert it..
var parent: ?*Node = undefined;
switch (self.context) {
.inserted_under => |p| parent = p,
.removed => assert(self.treap.find(self.key, &parent) == null),
}
self.treap.insert(self.key, parent, new);
self.context = .{ .inserted_under = parent };
}
}
};
fn find(self: Self, key: Key, parent_ref: *?*Node) ?*Node {
var node = self.root;
parent_ref.* = null;
// basic binary search while tracking the parent.
while (node) |current| {
const order = compare(key, current.key);
if (order == .eq) break;
parent_ref.* = current;
node = current.children[@intFromBool(order == .gt)];
}
return node;
}
fn insert(self: *Self, key: Key, parent: ?*Node, node: *Node) void {
// generate a random priority & prepare the node to be inserted into the tree
node.key = key;
node.priority = self.prng.random(@intFromPtr(node));
node.parent = parent;
node.children = [_]?*Node{ null, null };
// point the parent at the new node
const link = if (parent) |p| &p.children[@intFromBool(compare(key, p.key) == .gt)] else &self.root;
assert(link.* == null);
link.* = node;
// rotate the node up into the tree to balance it according to its priority
while (node.parent) |p| {
if (p.priority <= node.priority) break;
const is_right = p.children[1] == node;
assert(p.children[@intFromBool(is_right)] == node);
const rotate_right = !is_right;
self.rotate(p, rotate_right);
}
}
fn replace(self: *Self, old: *Node, new: *Node) void {
// copy over the values from the old node
new.key = old.key;
new.priority = old.priority;
new.parent = old.parent;
new.children = old.children;
// point the parent at the new node
const link = if (old.parent) |p| &p.children[@intFromBool(p.children[1] == old)] else &self.root;
assert(link.* == old);
link.* = new;
// point the children's parent at the new node
for (old.children) |child_node| {
const child = child_node orelse continue;
assert(child.parent == old);
child.parent = new;
}
}
fn remove(self: *Self, node: *Node) void {
// rotate the node down to be a leaf of the tree for removal, respecting priorities.
while (node.children[0] orelse node.children[1]) |_| {
self.rotate(node, rotate_right: {
const right = node.children[1] orelse break :rotate_right true;
const left = node.children[0] orelse break :rotate_right false;
break :rotate_right (left.priority < right.priority);
});
}
// node is a now a leaf; remove by nulling out the parent's reference to it.
const link = if (node.parent) |p| &p.children[@intFromBool(p.children[1] == node)] else &self.root;
assert(link.* == node);
link.* = null;
// clean up after ourselves
node.priority = 0;
node.parent = null;
node.children = [_]?*Node{ null, null };
}
fn rotate(self: *Self, node: *Node, right: bool) void {
// if right, converts the following:
// parent -> (node (target YY adjacent) XX)
// parent -> (target YY (node adjacent XX))
//
// if left (!right), converts the following:
// parent -> (node (target YY adjacent) XX)
// parent -> (target YY (node adjacent XX))
const parent = node.parent;
const target = node.children[@intFromBool(!right)] orelse unreachable;
const adjacent = target.children[@intFromBool(right)];
// rotate the children
target.children[@intFromBool(right)] = node;
node.children[@intFromBool(!right)] = adjacent;
// rotate the parents
node.parent = target;
target.parent = parent;
if (adjacent) |adj| adj.parent = node;
// fix the parent link
const link = if (parent) |p| &p.children[@intFromBool(p.children[1] == node)] else &self.root;
assert(link.* == node);
link.* = target;
}
/// Usage example:
/// var iter = treap.inorderIterator();
/// while (iter.next()) |node| {
/// ...
/// }
pub const InorderIterator = struct {
current: ?*Node,
pub fn next(it: *InorderIterator) ?*Node {
const current = it.current;
it.current = if (current) |cur|
cur.next()
else
null;
return current;
}
};
pub fn inorderIterator(self: *Self) InorderIterator {
return .{ .current = self.getMin() };
}
};
}