rb.zig

// SPDX-License-Identifier: MIT
// Copyright (c) 2015-2020 Zig Contributors
// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
// The MIT license requires this copyright notice to be included in all copies
// and substantial portions of the software.
const std = @import("std");
const assert = std.debug.assert;
const testing = std.testing;
const Order = std.math.Order;

const Color = enum(u1) {
    Black,
    Red,
};
const Red = Color.Red;
const Black = Color.Black;

const ReplaceError = error{NotEqual};
const SortError = error{NotUnique}; // The new comparison function results in duplicates.

/// Insert this into your struct that you want to add to a red-black tree.
/// Do not use a pointer. Turn the *rb.Node results of the functions in rb
/// (after resolving optionals) to your structure using @fieldParentPtr(). Example:
///
/// const Number = struct {
///     node: rb.Node,
///     value: i32,
/// };
/// fn number(node: *rb.Node) Number {
///     return @fieldParentPtr(Number, "node", node);
/// }
pub const Node = struct {
    left: ?*Node,
    right: ?*Node,

    /// parent | color
    parent_and_color: usize,

    pub fn next(constnode: *Node) ?*Node {
        var node = constnode;

        if (node.right) |right| {
            var n = right;
            while (n.left) |left|
                n = left;
            return n;
        }

        while (true) {
            var parent = node.getParent();
            if (parent) |p| {
                if (node != p.right)
                    return p;
                node = p;
            } else
                return null;
        }
    }

    pub fn prev(constnode: *Node) ?*Node {
        var node = constnode;

        if (node.left) |left| {
            var n = left;
            while (n.right) |right|
                n = right;
            return n;
        }

        while (true) {
            var parent = node.getParent();
            if (parent) |p| {
                if (node != p.left)
                    return p;
                node = p;
            } else
                return null;
        }
    }

    pub fn isRoot(node: *Node) bool {
        return node.getParent() == null;
    }

    fn isRed(node: *Node) bool {
        return node.getColor() == Red;
    }

    fn isBlack(node: *Node) bool {
        return node.getColor() == Black;
    }

    fn setParent(node: *Node, parent: ?*Node) void {
        node.parent_and_color = @ptrToInt(parent) | (node.parent_and_color & 1);
    }

    fn getParent(node: *Node) ?*Node {
        const mask: usize = 1;
        comptime {
            assert(@alignOf(*Node) >= 2);
        }
        const maybe_ptr = node.parent_and_color & ~mask;
        return if (maybe_ptr == 0) null else @intToPtr(*Node, maybe_ptr);
    }

    fn setColor(node: *Node, color: Color) void {
        const mask: usize = 1;
        node.parent_and_color = (node.parent_and_color & ~mask) | @enumToInt(color);
    }

    fn getColor(node: *Node) Color {
        return @intToEnum(Color, @intCast(u1, node.parent_and_color & 1));
    }

    fn setChild(node: *Node, child: ?*Node, is_left: bool) void {
        if (is_left) {
            node.left = child;
        } else {
            node.right = child;
        }
    }

    fn getFirst(nodeconst: *Node) *Node {
        var node = nodeconst;
        while (node.left) |left| {
            node = left;
        }
        return node;
    }

    fn getLast(nodeconst: *Node) *Node {
        var node = nodeconst;
        while (node.right) |right| {
            node = right;
        }
        return node;
    }
};

pub const Tree = struct {
    root: ?*Node,
    compareFn: fn (*Node, *Node, *Tree) Order,

    /// Re-sorts a tree with a new compare function
    pub fn sort(tree: *Tree, newCompareFn: fn (*Node, *Node, *Tree) Order) SortError!void {
        var newTree = Tree.init(newCompareFn);
        var node: *Node = undefined;
        while (true) {
            node = tree.first() orelse break;
            tree.remove(node);
            if (newTree.insert(node) != null) {
                return error.NotUnique; // EEXISTS
            }
        }
        tree.* = newTree;
    }

    /// If you have a need for a version that caches this, please file a bug.
    pub fn first(tree: *Tree) ?*Node {
        var node: *Node = tree.root orelse return null;

        while (node.left) |left| {
            node = left;
        }

        return node;
    }

    pub fn last(tree: *Tree) ?*Node {
        var node: *Node = tree.root orelse return null;

        while (node.right) |right| {
            node = right;
        }

        return node;
    }

    /// Duplicate keys are not allowed. The item with the same key already in the
    /// tree will be returned, and the item will not be inserted.
    pub fn insert(tree: *Tree, node_const: *Node) ?*Node {
        var node = node_const;
        var maybe_key: ?*Node = undefined;
        var maybe_parent: ?*Node = undefined;
        var is_left: bool = undefined;

        maybe_key = doLookup(node, tree, &maybe_parent, &is_left);
        if (maybe_key) |key| {
            return key;
        }

        node.left = null;
        node.right = null;
        node.setColor(Red);
        node.setParent(maybe_parent);

        if (maybe_parent) |parent| {
            parent.setChild(node, is_left);
        } else {
            tree.root = node;
        }

        while (node.getParent()) |*parent| {
            if (parent.*.isBlack())
                break;
            // the root is always black
            var grandpa = parent.*.getParent() orelse unreachable;

            if (parent.* == grandpa.left) {
                var maybe_uncle = grandpa.right;

                if (maybe_uncle) |uncle| {
                    if (uncle.isBlack())
                        break;

                    parent.*.setColor(Black);
                    uncle.setColor(Black);
                    grandpa.setColor(Red);
                    node = grandpa;
                } else {
                    if (node == parent.*.right) {
                        rotateLeft(parent.*, tree);
                        node = parent.*;
                        parent.* = node.getParent().?; // Just rotated
                    }
                    parent.*.setColor(Black);
                    grandpa.setColor(Red);
                    rotateRight(grandpa, tree);
                }
            } else {
                var maybe_uncle = grandpa.left;

                if (maybe_uncle) |uncle| {
                    if (uncle.isBlack())
                        break;

                    parent.*.setColor(Black);
                    uncle.setColor(Black);
                    grandpa.setColor(Red);
                    node = grandpa;
                } else {
                    if (node == parent.*.left) {
                        rotateRight(parent.*, tree);
                        node = parent.*;
                        parent.* = node.getParent().?; // Just rotated
                    }
                    parent.*.setColor(Black);
                    grandpa.setColor(Red);
                    rotateLeft(grandpa, tree);
                }
            }
        }
        // This was an insert, there is at least one node.
        tree.root.?.setColor(Black);
        return null;
    }

    /// lookup searches for the value of key, using binary search. It will
    /// return a pointer to the node if it is there, otherwise it will return null.
    /// Complexity guaranteed O(log n), where n is the number of nodes book-kept
    /// by tree.
    pub fn lookup(tree: *Tree, key: *Node) ?*Node {
        var parent: ?*Node = undefined;
        var is_left: bool = undefined;
        return doLookup(key, tree, &parent, &is_left);
    }

    /// If node is not part of tree, behavior is undefined.
    pub fn remove(tree: *Tree, nodeconst: *Node) void {
        var node = nodeconst;
        // as this has the same value as node, it is unsafe to access node after newnode
        var newnode: ?*Node = nodeconst;
        var maybe_parent: ?*Node = node.getParent();
        var color: Color = undefined;
        var next: *Node = undefined;

        // This clause is to avoid optionals
        if (node.left == null and node.right == null) {
            if (maybe_parent) |parent| {
                parent.setChild(null, parent.left == node);
            } else
                tree.root = null;
            color = node.getColor();
            newnode = null;
        } else {
            if (node.left == null) {
                next = node.right.?; // Not both null as per above
            } else if (node.right == null) {
                next = node.left.?; // Not both null as per above
            } else
                next = node.right.?.getFirst(); // Just checked for null above

            if (maybe_parent) |parent| {
                parent.setChild(next, parent.left == node);
            } else
                tree.root = next;

            if (node.left != null and node.right != null) {
                const left = node.left.?;
                const right = node.right.?;

                color = next.getColor();
                next.setColor(node.getColor());

                next.left = left;
                left.setParent(next);

                if (next != right) {
                    var parent = next.getParent().?; // Was traversed via child node (right/left)
                    next.setParent(node.getParent());

                    newnode = next.right;
                    parent.left = node;

                    next.right = right;
                    right.setParent(next);
                } else {
                    next.setParent(maybe_parent);
                    maybe_parent = next;
                    newnode = next.right;
                }
            } else {
                color = node.getColor();
                newnode = next;
            }
        }

        if (newnode) |n|
            n.setParent(maybe_parent);

        if (color == Red)
            return;
        if (newnode) |n| {
            n.setColor(Black);
            return;
        }

        while (node == tree.root) {
            // If not root, there must be parent
            var parent = maybe_parent.?;
            if (node == parent.left) {
                var sibling = parent.right.?; // Same number of black nodes.

                if (sibling.isRed()) {
                    sibling.setColor(Black);
                    parent.setColor(Red);
                    rotateLeft(parent, tree);
                    sibling = parent.right.?; // Just rotated
                }
                if ((if (sibling.left) |n| n.isBlack() else true) and
                    (if (sibling.right) |n| n.isBlack() else true))
                {
                    sibling.setColor(Red);
                    node = parent;
                    maybe_parent = parent.getParent();
                    continue;
                }
                if (if (sibling.right) |n| n.isBlack() else true) {
                    sibling.left.?.setColor(Black); // Same number of black nodes.
                    sibling.setColor(Red);
                    rotateRight(sibling, tree);
                    sibling = parent.right.?; // Just rotated
                }
                sibling.setColor(parent.getColor());
                parent.setColor(Black);
                sibling.right.?.setColor(Black); // Same number of black nodes.
                rotateLeft(parent, tree);
                newnode = tree.root;
                break;
            } else {
                var sibling = parent.left.?; // Same number of black nodes.

                if (sibling.isRed()) {
                    sibling.setColor(Black);
                    parent.setColor(Red);
                    rotateRight(parent, tree);
                    sibling = parent.left.?; // Just rotated
                }
                if ((if (sibling.left) |n| n.isBlack() else true) and
                    (if (sibling.right) |n| n.isBlack() else true))
                {
                    sibling.setColor(Red);
                    node = parent;
                    maybe_parent = parent.getParent();
                    continue;
                }
                if (if (sibling.left) |n| n.isBlack() else true) {
                    sibling.right.?.setColor(Black); // Same number of black nodes
                    sibling.setColor(Red);
                    rotateLeft(sibling, tree);
                    sibling = parent.left.?; // Just rotated
                }
                sibling.setColor(parent.getColor());
                parent.setColor(Black);
                sibling.left.?.setColor(Black); // Same number of black nodes
                rotateRight(parent, tree);
                newnode = tree.root;
                break;
            }

            if (node.isRed())
                break;
        }

        if (newnode) |n|
            n.setColor(Black);
    }

    /// This is a shortcut to avoid removing and re-inserting an item with the same key.
    pub fn replace(tree: *Tree, old: *Node, newconst: *Node) !void {
        var new = newconst;

        // I assume this can get optimized out if the caller already knows.
        if (tree.compareFn(old, new, tree) != .eq) return ReplaceError.NotEqual;

        if (old.getParent()) |parent| {
            parent.setChild(new, parent.left == old);
        } else
            tree.root = new;

        if (old.left) |left|
            left.setParent(new);
        if (old.right) |right|
            right.setParent(new);

        new.* = old.*;
    }

    pub fn init(f: fn (*Node, *Node, *Tree) Order) Tree {
        return Tree{
            .root = null,
            .compareFn = f,
        };
    }
};

fn rotateLeft(node: *Node, tree: *Tree) void {
    var p: *Node = node;
    var q: *Node = node.right orelse unreachable;
    var parent: *Node = undefined;

    if (!p.isRoot()) {
        parent = p.getParent().?;
        if (parent.left == p) {
            parent.left = q;
        } else {
            parent.right = q;
        }
        q.setParent(parent);
    } else {
        tree.root = q;
        q.setParent(null);
    }
    p.setParent(q);

    p.right = q.left;
    if (p.right) |right| {
        right.setParent(p);
    }
    q.left = p;
}

fn rotateRight(node: *Node, tree: *Tree) void {
    var p: *Node = node;
    var q: *Node = node.left orelse unreachable;
    var parent: *Node = undefined;

    if (!p.isRoot()) {
        parent = p.getParent().?;
        if (parent.left == p) {
            parent.left = q;
        } else {
            parent.right = q;
        }
        q.setParent(parent);
    } else {
        tree.root = q;
        q.setParent(null);
    }
    p.setParent(q);

    p.left = q.right;
    if (p.left) |left| {
        left.setParent(p);
    }
    q.right = p;
}

fn doLookup(key: *Node, tree: *Tree, pparent: *?*Node, is_left: *bool) ?*Node {
    var maybe_node: ?*Node = tree.root;

    pparent.* = null;
    is_left.* = false;

    while (maybe_node) |node| {
        const res = tree.compareFn(node, key, tree);
        if (res == .eq) {
            return node;
        }
        pparent.* = node;
        switch (res) {
            .gt => {
                is_left.* = true;
                maybe_node = node.left;
            },
            .lt => {
                is_left.* = false;
                maybe_node = node.right;
            },
            .eq => unreachable, // handled above
        }
    }
    return null;
}

const testNumber = struct {
    node: Node,
    value: usize,
};

fn testGetNumber(node: *Node) *testNumber {
    return @fieldParentPtr(testNumber, "node", node);
}

fn testCompare(l: *Node, r: *Node, contextIgnored: *Tree) Order {
    var left = testGetNumber(l);
    var right = testGetNumber(r);

    if (left.value < right.value) {
        return .lt;
    } else if (left.value == right.value) {
        return .eq;
    } else if (left.value > right.value) {
        return .gt;
    }
    unreachable;
}

fn testCompareReverse(l: *Node, r: *Node, contextIgnored: *Tree) Order {
    return testCompare(r, l, contextIgnored);
}

test "rb" {
    if (@import("builtin").arch == .aarch64) {
        // TODO https://github.com/ziglang/zig/issues/3288
        return error.SkipZigTest;
    }

    var tree = Tree.init(testCompare);
    var ns: [10]testNumber = undefined;
    ns[0].value = 42;
    ns[1].value = 41;
    ns[2].value = 40;
    ns[3].value = 39;
    ns[4].value = 38;
    ns[5].value = 39;
    ns[6].value = 3453;
    ns[7].value = 32345;
    ns[8].value = 392345;
    ns[9].value = 4;

    var dup: testNumber = undefined;
    dup.value = 32345;

    _ = tree.insert(&ns[1].node);
    _ = tree.insert(&ns[2].node);
    _ = tree.insert(&ns[3].node);
    _ = tree.insert(&ns[4].node);
    _ = tree.insert(&ns[5].node);
    _ = tree.insert(&ns[6].node);
    _ = tree.insert(&ns[7].node);
    _ = tree.insert(&ns[8].node);
    _ = tree.insert(&ns[9].node);
    tree.remove(&ns[3].node);
    testing.expect(tree.insert(&dup.node) == &ns[7].node);
    try tree.replace(&ns[7].node, &dup.node);

    var num: *testNumber = undefined;
    num = testGetNumber(tree.first().?);
    while (num.node.next() != null) {
        testing.expect(testGetNumber(num.node.next().?).value > num.value);
        num = testGetNumber(num.node.next().?);
    }
}

test "inserting and looking up" {
    var tree = Tree.init(testCompare);
    var number: testNumber = undefined;
    number.value = 1000;
    _ = tree.insert(&number.node);
    var dup: testNumber = undefined;
    //Assert that tuples with identical value fields finds the same pointer
    dup.value = 1000;
    assert(tree.lookup(&dup.node) == &number.node);
    //Assert that tuples with identical values do not clobber when inserted.
    _ = tree.insert(&dup.node);
    assert(tree.lookup(&dup.node) == &number.node);
    assert(tree.lookup(&number.node) != &dup.node);
    assert(testGetNumber(tree.lookup(&dup.node).?).value == testGetNumber(&dup.node).value);
    //Assert that if looking for a non-existing value, return null.
    var non_existing_value: testNumber = undefined;
    non_existing_value.value = 1234;
    assert(tree.lookup(&non_existing_value.node) == null);
}

test "multiple inserts, followed by calling first and last" {
    if (@import("builtin").arch == .aarch64) {
        // TODO https://github.com/ziglang/zig/issues/3288
        return error.SkipZigTest;
    }
    var tree = Tree.init(testCompare);
    var zeroth: testNumber = undefined;
    zeroth.value = 0;
    var first: testNumber = undefined;
    first.value = 1;
    var second: testNumber = undefined;
    second.value = 2;
    var third: testNumber = undefined;
    third.value = 3;
    _ = tree.insert(&zeroth.node);
    _ = tree.insert(&first.node);
    _ = tree.insert(&second.node);
    _ = tree.insert(&third.node);
    assert(testGetNumber(tree.first().?).value == 0);
    assert(testGetNumber(tree.last().?).value == 3);
    var lookupNode: testNumber = undefined;
    lookupNode.value = 3;
    assert(tree.lookup(&lookupNode.node) == &third.node);
    tree.sort(testCompareReverse) catch unreachable;
    assert(testGetNumber(tree.first().?).value == 3);
    assert(testGetNumber(tree.last().?).value == 0);
    assert(tree.lookup(&lookupNode.node) == &third.node);
}