const std = @import("std.zig");
const assert = std.debug.assert;
const testing = std.testing;
const Order = std.math.Order;
pub fn Treap(comptime Key: type, comptime compareFn: anytype) type {
return struct {
const Self = @This();
fn compare(a: Key, b: Key) Order {
return compareFn(a, b);
}
root: ?*Node = null,
prng: Prng = .{},
const Prng = struct {
xorshift: usize = 0,
fn random(self: *Prng, seed: usize) usize {
if (self.xorshift == 0) {
self.xorshift = seed;
}
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;
}
};
pub const Node = struct {
key: Key,
priority: usize,
parent: ?*Node,
children: [2]?*Node,
};
pub fn getMin(self: Self) ?*Node {
var node = self.root;
while (node) |current| {
node = current.children[0] orelse break;
}
return node;
}
pub fn getMax(self: Self) ?*Node {
var node = self.root;
while (node) |current| {
node = current.children[1] orelse break;
}
return node;
}
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 },
};
}
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 },
};
}
pub const Entry = struct {
key: Key,
treap: *Self,
node: ?*Node,
context: union(enum) {
inserted_under: ?*Node,
removed,
},
pub fn set(self: *Entry, new_node: ?*Node) void {
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| {
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;
while (node) |current| {
const order = compare(key, current.key);
if (order == .eq) break;
parent_ref.* = current;
node = current.children[@boolToInt(order == .gt)];
}
return node;
}
fn insert(self: *Self, key: Key, parent: ?*Node, node: *Node) void {
node.key = key;
node.priority = self.prng.random(@ptrToInt(node));
node.parent = parent;
node.children = [_]?*Node{ null, null };
const link = if (parent) |p| &p.children[@boolToInt(compare(key, p.key) == .gt)] else &self.root;
assert(link.* == null);
link.* = node;
while (node.parent) |p| {
if (p.priority <= node.priority) break;
const is_right = p.children[1] == node;
assert(p.children[@boolToInt(is_right)] == node);
const rotate_right = !is_right;
self.rotate(p, rotate_right);
}
}
fn replace(self: *Self, old: *Node, new: *Node) void {
new.key = old.key;
new.priority = old.priority;
new.parent = old.parent;
new.children = old.children;
const link = if (old.parent) |p| &p.children[@boolToInt(p.children[1] == old)] else &self.root;
assert(link.* == old);
link.* = new;
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 {
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);
});
}
const link = if (node.parent) |p| &p.children[@boolToInt(p.children[1] == node)] else &self.root;
assert(link.* == node);
link.* = null;
node.key = undefined;
node.priority = 0;
node.parent = null;
node.children = [_]?*Node{ null, null };
}
fn rotate(self: *Self, node: *Node, right: bool) void {
const parent = node.parent;
const target = node.children[@boolToInt(!right)] orelse unreachable;
const adjacent = target.children[@boolToInt(right)];
target.children[@boolToInt(right)] = node;
node.children[@boolToInt(!right)] = adjacent;
node.parent = target;
target.parent = parent;
if (adjacent) |adj| adj.parent = node;
const link = if (parent) |p| &p.children[@boolToInt(p.children[1] == node)] else &self.root;
assert(link.* == node);
link.* = target;
}
};
}
fn SliceIterRandomOrder(comptime T: type) type {
return struct {
rng: std.rand.Random,
slice: []T,
index: usize = undefined,
offset: usize = undefined,
co_prime: usize,
const Self = @This();
pub fn init(slice: []T, rng: std.rand.Random) Self {
return Self{
.rng = rng,
.slice = slice,
.co_prime = blk: {
if (slice.len == 0) break :blk 0;
var prime = slice.len / 2;
while (prime < slice.len) : (prime += 1) {
var gcd = [_]usize{ prime, slice.len };
while (gcd[1] != 0) {
const temp = gcd;
gcd = [_]usize{ temp[1], temp[0] % temp[1] };
}
if (gcd[0] == 1) break;
}
break :blk prime;
},
};
}
pub fn reset(self: *Self) void {
self.index = 0;
self.offset = self.rng.int(usize);
}
pub fn next(self: *Self) ?*T {
if (self.index >= self.slice.len) return null;
defer self.index += 1;
return &self.slice[((self.index *% self.co_prime) +% self.offset) % self.slice.len];
}
};
}
const TestTreap = Treap(u64, std.math.order);
const TestNode = TestTreap.Node;
test "std.Treap: insert, find, replace, remove" {
var treap = TestTreap{};
var nodes: [10]TestNode = undefined;
var prng = std.rand.DefaultPrng.init(0xdeadbeef);
var iter = SliceIterRandomOrder(TestNode).init(&nodes, prng.random());
iter.reset();
while (iter.next()) |node| {
const key = prng.random().int(u64);
var entry = treap.getEntryFor(key);
try testing.expectEqual(entry.key, key);
try testing.expectEqual(entry.node, null);
entry.set(node);
try testing.expectEqual(node.key, key);
try testing.expectEqual(entry.key, key);
try testing.expectEqual(entry.node, node);
}
iter.reset();
while (iter.next()) |node| {
const key = node.key;
var entry = treap.getEntryFor(node.key);
try testing.expectEqual(entry.key, key);
try testing.expectEqual(entry.node, node);
try testing.expectEqual(entry.node, treap.getEntryForExisting(node).node);
}
iter.reset();
while (iter.next()) |node| {
const key = node.key;
var entry = treap.getEntryForExisting(node);
try testing.expectEqual(entry.key, key);
try testing.expectEqual(entry.node, node);
var stub_node: TestNode = undefined;
entry.set(&stub_node);
try testing.expectEqual(entry.node, &stub_node);
try testing.expectEqual(entry.node, treap.getEntryFor(key).node);
try testing.expectEqual(entry.node, treap.getEntryForExisting(&stub_node).node);
entry.set(node);
try testing.expectEqual(entry.node, node);
try testing.expectEqual(entry.node, treap.getEntryFor(key).node);
try testing.expectEqual(entry.node, treap.getEntryForExisting(node).node);
}
iter.reset();
while (iter.next()) |node| {
const key = node.key;
var entry = treap.getEntryForExisting(node);
try testing.expectEqual(entry.key, key);
try testing.expectEqual(entry.node, node);
entry.set(null);
try testing.expectEqual(entry.node, null);
try testing.expectEqual(entry.node, treap.getEntryFor(key).node);
entry.set(node);
try testing.expectEqual(entry.node, node);
try testing.expectEqual(entry.node, treap.getEntryFor(key).node);
try testing.expectEqual(entry.node, treap.getEntryForExisting(node).node);
entry.set(null);
try testing.expectEqual(entry.node, null);
try testing.expectEqual(entry.node, treap.getEntryFor(key).node);
}
}