    const std = @import("std.zig");
    const Allocator = std.mem.Allocator;
    const assert = std.debug.assert;
    const Order = std.math.Order;
    const testing = std.testing;
    const expect = testing.expect;
    const expectEqual = testing.expectEqual;
    const expectError = testing.expectError;

    /// Priority queue for storing generic data. Initialize with `init`.
    /// Provide `compareFn` that returns `Order.lt` when its second
    /// argument should get popped before its third argument,
    /// `Order.eq` if the arguments are of equal priority, or `Order.gt`
    /// if the third argument should be popped first.
    /// For example, to make `pop` return the smallest number, provide
    /// `fn lessThan(context: void, a: T, b: T) Order { _ = context; return std.math.order(a, b); }`
    pub fn PriorityQueue(comptime T: type, comptime Context: type, comptime compareFn: fn (context: Context, a: T, b: T) Order) type {
        return struct {
            const Self = @This();

            items: []T,
            len: usize,
            allocator: Allocator,
            context: Context,

            /// Initialize and return a priority queue.
            pub fn init(allocator: Allocator, context: Context) Self {
                return Self{
                    .items = &[_]T{},
                    .len = 0,
                    .allocator = allocator,
                    .context = context,
                };
            }

            /// Free memory used by the queue.
            pub fn deinit(self: Self) void {
                self.allocator.free(self.items);
            }

            /// Insert a new element, maintaining priority.
            pub fn add(self: *Self, elem: T) !void {
                try self.ensureUnusedCapacity(1);
                addUnchecked(self, elem);
            }

            fn addUnchecked(self: *Self, elem: T) void {
                self.items[self.len] = elem;
                siftUp(self, self.len);
                self.len += 1;
            }

            fn siftUp(self: *Self, start_index: usize) void {
                var child_index = start_index;
                while (child_index > 0) {
                    var parent_index = ((child_index - 1) >> 1);
                    const child = self.items[child_index];
                    const parent = self.items[parent_index];

                    if (compareFn(self.context, child, parent) != .lt) break;

                    self.items[parent_index] = child;
                    self.items[child_index] = parent;
                    child_index = parent_index;
                }
            }

            /// Add each element in `items` to the queue.
            pub fn addSlice(self: *Self, items: []const T) !void {
                try self.ensureUnusedCapacity(items.len);
                for (items) |e| {
                    self.addUnchecked(e);
                }
            }

            /// Look at the highest priority element in the queue. Returns
            /// `null` if empty.
            pub fn peek(self: *Self) ?T {
                return if (self.len > 0) self.items[0] else null;
            }

            /// Pop the highest priority element from the queue. Returns
            /// `null` if empty.
            pub fn removeOrNull(self: *Self) ?T {
                return if (self.len > 0) self.remove() else null;
            }

            /// Remove and return the highest priority element from the
            /// queue.
            pub fn remove(self: *Self) T {
                return self.removeIndex(0);
            }

            /// Remove and return element at index. Indices are in the
            /// same order as iterator, which is not necessarily priority
            /// order.
            pub fn removeIndex(self: *Self, index: usize) T {
                assert(self.len > index);
                const last = self.items[self.len - 1];
                const item = self.items[index];
                self.items[index] = last;
                self.len -= 1;

                if (index == 0) {
                    siftDown(self, index);
                } else {
                    const parent_index = ((index - 1) >> 1);
                    const parent = self.items[parent_index];
                    if (compareFn(self.context, last, parent) == .gt) {
                        siftDown(self, index);
                    } else {
                        siftUp(self, index);
                    }
                }

                return item;
            }

            /// Return the number of elements remaining in the priority
            /// queue.
            pub fn count(self: Self) usize {
                return self.len;
            }

            /// Return the number of elements that can be added to the
            /// queue before more memory is allocated.
            pub fn capacity(self: Self) usize {
                return self.items.len;
            }

            fn siftDown(self: *Self, start_index: usize) void {
                var index = start_index;
                const half = self.len >> 1;
                while (true) {
                    var left_index = (index << 1) + 1;
                    var right_index = left_index + 1;
                    var left = if (left_index < self.len) self.items[left_index] else null;
                    var right = if (right_index < self.len) self.items[right_index] else null;

                    var smallest_index = index;
                    var smallest = self.items[index];

                    if (left) |e| {
                        if (compareFn(self.context, e, smallest) == .lt) {
                            smallest_index = left_index;
                            smallest = e;
                        }
                    }

                    if (right) |e| {
                        if (compareFn(self.context, e, smallest) == .lt) {
                            smallest_index = right_index;
                            smallest = e;
                        }
                    }

                    if (smallest_index == index) return;

                    self.items[smallest_index] = self.items[index];
                    self.items[index] = smallest;
                    index = smallest_index;

                    if (index >= half) return;
                }
            }

            /// PriorityQueue takes ownership of the passed in slice. The slice must have been
            /// allocated with `allocator`.
            /// Deinitialize with `deinit`.
            pub fn fromOwnedSlice(allocator: Allocator, items: []T, context: Context) Self {
                var queue = Self{
                    .items = items,
                    .len = items.len,
                    .allocator = allocator,
                    .context = context,
                };

                if (queue.len <= 1) return queue;

                const half = (queue.len >> 1) - 1;
                var i: usize = 0;
                while (i <= half) : (i += 1) {
                    queue.siftDown(half - i);
                }
                return queue;
            }

            /// Ensure that the queue can fit at least `new_capacity` items.
            pub fn ensureTotalCapacity(self: *Self, new_capacity: usize) !void {
                var better_capacity = self.capacity();
                if (better_capacity >= new_capacity) return;
                while (true) {
                    better_capacity += better_capacity / 2 + 8;
                    if (better_capacity >= new_capacity) break;
                }
                self.items = try self.allocator.realloc(self.items, better_capacity);
            }

            /// Ensure that the queue can fit at least `additional_count` **more** item.
            pub fn ensureUnusedCapacity(self: *Self, additional_count: usize) !void {
                return self.ensureTotalCapacity(self.len + additional_count);
            }

            /// Reduce allocated capacity to `new_len`.
            pub fn shrinkAndFree(self: *Self, new_len: usize) void {
                assert(new_len <= self.items.len);

                // Cannot shrink to smaller than the current queue size without invalidating the heap property

                assert(new_len >= self.len);

                self.items = self.allocator.realloc(self.items[0..], new_len) catch |e| switch (e) {
                    error.OutOfMemory => { // no problem, capacity is still correct then.

                        self.items.len = new_len;
                        return;
                    },
                };
            }

            pub fn update(self: *Self, elem: T, new_elem: T) !void {
                const update_index = blk: {
                    for (self.items) |item, idx| {
                        if (compareFn(self.context, item, elem).compare(.eq)) break :blk idx;
                    }
                    return error.ElementNotFound;
                };
                const old_elem: T = self.items[update_index];
                self.items[update_index] = new_elem;
                switch (compareFn(self.context, new_elem, old_elem)) {
                    .lt => siftUp(self, update_index),
                    .gt => siftDown(self, update_index),
                    .eq => {}, // Nothing to do as the items have equal priority

                }
            }

            pub const Iterator = struct {
                queue: *PriorityQueue(T, Context, compareFn),
                count: usize,

                pub fn next(it: *Iterator) ?T {
                    if (it.count >= it.queue.len) return null;
                    const out = it.count;
                    it.count += 1;
                    return it.queue.items[out];
                }

                pub fn reset(it: *Iterator) void {
                    it.count = 0;
                }
            };

            /// Return an iterator that walks the queue without consuming
            /// it. Invalidated if the heap is modified.
            pub fn iterator(self: *Self) Iterator {
                return Iterator{
                    .queue = self,
                    .count = 0,
                };
            }

            fn dump(self: *Self) void {
                const print = std.debug.print;
                print("{{ ", .{});
                print("items: ", .{});
                for (self.items) |e, i| {
                    if (i >= self.len) break;
                    print("{}, ", .{e});
                }
                print("array: ", .{});
                for (self.items) |e| {
                    print("{}, ", .{e});
                }
                print("len: {} ", .{self.len});
                print("capacity: {}", .{self.capacity()});
                print(" }}\n", .{});
            }
        };
    }

    fn lessThan(context: void, a: u32, b: u32) Order {
        _ = context;
        return std.math.order(a, b);
    }

    fn greaterThan(context: void, a: u32, b: u32) Order {
        return lessThan(context, a, b).invert();
    }

    const PQlt = PriorityQueue(u32, void, lessThan);
    const PQgt = PriorityQueue(u32, void, greaterThan);

    test "std.PriorityQueue: add and remove min heap" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(54);
        try queue.add(12);
        try queue.add(7);
        try queue.add(23);
        try queue.add(25);
        try queue.add(13);
        try expectEqual(@as(u32, 7), queue.remove());
        try expectEqual(@as(u32, 12), queue.remove());
        try expectEqual(@as(u32, 13), queue.remove());
        try expectEqual(@as(u32, 23), queue.remove());
        try expectEqual(@as(u32, 25), queue.remove());
        try expectEqual(@as(u32, 54), queue.remove());
    }

    test "std.PriorityQueue: add and remove same min heap" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(1);
        try queue.add(1);
        try queue.add(2);
        try queue.add(2);
        try queue.add(1);
        try queue.add(1);
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 2), queue.remove());
    }

    test "std.PriorityQueue: removeOrNull on empty" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try expect(queue.removeOrNull() == null);
    }

    test "std.PriorityQueue: edge case 3 elements" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(9);
        try queue.add(3);
        try queue.add(2);
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 3), queue.remove());
        try expectEqual(@as(u32, 9), queue.remove());
    }

    test "std.PriorityQueue: peek" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try expect(queue.peek() == null);
        try queue.add(9);
        try queue.add(3);
        try queue.add(2);
        try expectEqual(@as(u32, 2), queue.peek().?);
        try expectEqual(@as(u32, 2), queue.peek().?);
    }

    test "std.PriorityQueue: sift up with odd indices" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();
        const items = [_]u32{ 15, 7, 21, 14, 13, 22, 12, 6, 7, 25, 5, 24, 11, 16, 15, 24, 2, 1 };
        for (items) |e| {
            try queue.add(e);
        }

        const sorted_items = [_]u32{ 1, 2, 5, 6, 7, 7, 11, 12, 13, 14, 15, 15, 16, 21, 22, 24, 24, 25 };
        for (sorted_items) |e| {
            try expectEqual(e, queue.remove());
        }
    }

    test "std.PriorityQueue: addSlice" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();
        const items = [_]u32{ 15, 7, 21, 14, 13, 22, 12, 6, 7, 25, 5, 24, 11, 16, 15, 24, 2, 1 };
        try queue.addSlice(items[0..]);

        const sorted_items = [_]u32{ 1, 2, 5, 6, 7, 7, 11, 12, 13, 14, 15, 15, 16, 21, 22, 24, 24, 25 };
        for (sorted_items) |e| {
            try expectEqual(e, queue.remove());
        }
    }

    test "std.PriorityQueue: fromOwnedSlice trivial case 0" {
        const items = [0]u32{};
        const queue_items = try testing.allocator.dupe(u32, &items);
        var queue = PQlt.fromOwnedSlice(testing.allocator, queue_items[0..], {});
        defer queue.deinit();
        try expectEqual(@as(usize, 0), queue.len);
        try expect(queue.removeOrNull() == null);
    }

    test "std.PriorityQueue: fromOwnedSlice trivial case 1" {
        const items = [1]u32{1};
        const queue_items = try testing.allocator.dupe(u32, &items);
        var queue = PQlt.fromOwnedSlice(testing.allocator, queue_items[0..], {});
        defer queue.deinit();

        try expectEqual(@as(usize, 1), queue.len);
        try expectEqual(items[0], queue.remove());
        try expect(queue.removeOrNull() == null);
    }

    test "std.PriorityQueue: fromOwnedSlice" {
        const items = [_]u32{ 15, 7, 21, 14, 13, 22, 12, 6, 7, 25, 5, 24, 11, 16, 15, 24, 2, 1 };
        const heap_items = try testing.allocator.dupe(u32, items[0..]);
        var queue = PQlt.fromOwnedSlice(testing.allocator, heap_items[0..], {});
        defer queue.deinit();

        const sorted_items = [_]u32{ 1, 2, 5, 6, 7, 7, 11, 12, 13, 14, 15, 15, 16, 21, 22, 24, 24, 25 };
        for (sorted_items) |e| {
            try expectEqual(e, queue.remove());
        }
    }

    test "std.PriorityQueue: add and remove max heap" {
        var queue = PQgt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(54);
        try queue.add(12);
        try queue.add(7);
        try queue.add(23);
        try queue.add(25);
        try queue.add(13);
        try expectEqual(@as(u32, 54), queue.remove());
        try expectEqual(@as(u32, 25), queue.remove());
        try expectEqual(@as(u32, 23), queue.remove());
        try expectEqual(@as(u32, 13), queue.remove());
        try expectEqual(@as(u32, 12), queue.remove());
        try expectEqual(@as(u32, 7), queue.remove());
    }

    test "std.PriorityQueue: add and remove same max heap" {
        var queue = PQgt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(1);
        try queue.add(1);
        try queue.add(2);
        try queue.add(2);
        try queue.add(1);
        try queue.add(1);
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
    }

    test "std.PriorityQueue: iterator" {
        var queue = PQlt.init(testing.allocator, {});
        var map = std.AutoHashMap(u32, void).init(testing.allocator);
        defer {
            queue.deinit();
            map.deinit();
        }

        const items = [_]u32{ 54, 12, 7, 23, 25, 13 };
        for (items) |e| {
            _ = try queue.add(e);
            try map.put(e, {});
        }

        var it = queue.iterator();
        while (it.next()) |e| {
            _ = map.remove(e);
        }

        try expectEqual(@as(usize, 0), map.count());
    }

    test "std.PriorityQueue: remove at index" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        const items = [_]u32{ 2, 1, 8, 9, 3, 4, 5 };
        for (items) |e| {
            _ = try queue.add(e);
        }

        var it = queue.iterator();
        var idx: usize = 0;
        const two_idx = while (it.next()) |elem| {
            if (elem == 2)
                break idx;
            idx += 1;
        } else unreachable;
        var sorted_items = [_]u32{ 1, 3, 4, 5, 8, 9 };
        try expectEqual(queue.removeIndex(two_idx), 2);

        var i: usize = 0;
        while (queue.removeOrNull()) |n| : (i += 1) {
            try expectEqual(n, sorted_items[i]);
        }
        try expectEqual(queue.removeOrNull(), null);
    }

    test "std.PriorityQueue: iterator while empty" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        var it = queue.iterator();

        try expectEqual(it.next(), null);
    }

    test "std.PriorityQueue: shrinkAndFree" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.ensureTotalCapacity(4);
        try expect(queue.capacity() >= 4);

        try queue.add(1);
        try queue.add(2);
        try queue.add(3);
        try expect(queue.capacity() >= 4);
        try expectEqual(@as(usize, 3), queue.len);

        queue.shrinkAndFree(3);
        try expectEqual(@as(usize, 3), queue.capacity());
        try expectEqual(@as(usize, 3), queue.len);

        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 3), queue.remove());
        try expect(queue.removeOrNull() == null);
    }

    test "std.PriorityQueue: update min heap" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(55);
        try queue.add(44);
        try queue.add(11);
        try queue.update(55, 5);
        try queue.update(44, 4);
        try queue.update(11, 1);
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 4), queue.remove());
        try expectEqual(@as(u32, 5), queue.remove());
    }

    test "std.PriorityQueue: update same min heap" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(1);
        try queue.add(1);
        try queue.add(2);
        try queue.add(2);
        try queue.update(1, 5);
        try queue.update(2, 4);
        try expectEqual(@as(u32, 1), queue.remove());
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 4), queue.remove());
        try expectEqual(@as(u32, 5), queue.remove());
    }

    test "std.PriorityQueue: update max heap" {
        var queue = PQgt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(55);
        try queue.add(44);
        try queue.add(11);
        try queue.update(55, 5);
        try queue.update(44, 1);
        try queue.update(11, 4);
        try expectEqual(@as(u32, 5), queue.remove());
        try expectEqual(@as(u32, 4), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
    }

    test "std.PriorityQueue: update same max heap" {
        var queue = PQgt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.add(1);
        try queue.add(1);
        try queue.add(2);
        try queue.add(2);
        try queue.update(1, 5);
        try queue.update(2, 4);
        try expectEqual(@as(u32, 5), queue.remove());
        try expectEqual(@as(u32, 4), queue.remove());
        try expectEqual(@as(u32, 2), queue.remove());
        try expectEqual(@as(u32, 1), queue.remove());
    }

    test "std.PriorityQueue: siftUp in remove" {
        var queue = PQlt.init(testing.allocator, {});
        defer queue.deinit();

        try queue.addSlice(&.{ 0, 1, 100, 2, 3, 101, 102, 4, 5, 6, 7, 103, 104, 105, 106, 8 });

        _ = queue.removeIndex(std.mem.indexOfScalar(u32, queue.items[0..queue.len], 102).?);

        const sorted_items = [_]u32{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 100, 101, 103, 104, 105, 106 };
        for (sorted_items) |e| {
            try expectEqual(e, queue.remove());
        }
    }

    fn contextLessThan(context: []const u32, a: usize, b: usize) Order {
        return std.math.order(context[a], context[b]);
    }

    const CPQlt = PriorityQueue(usize, []const u32, contextLessThan);

    test "std.PriorityQueue: add and remove min heap with contextful comparator" {
        const context = [_]u32{ 5, 3, 4, 2, 2, 8, 0 };

        var queue = CPQlt.init(testing.allocator, context[0..]);
        defer queue.deinit();

        try queue.add(0);
        try queue.add(1);
        try queue.add(2);
        try queue.add(3);
        try queue.add(4);
        try queue.add(5);
        try queue.add(6);
        try expectEqual(@as(usize, 6), queue.remove());
        try expectEqual(@as(usize, 4), queue.remove());
        try expectEqual(@as(usize, 3), queue.remove());
        try expectEqual(@as(usize, 1), queue.remove());
        try expectEqual(@as(usize, 2), queue.remove());
        try expectEqual(@as(usize, 0), queue.remove());
        try expectEqual(@as(usize, 5), queue.remove());
    }