How do you make a max-heap in Java?

Java's PriorityQueue is a min-heap by default — it orders by natural ordering and hands you the smallest element. To get a max-heap, you reverse the comparator so the largest element compares as "first."

// Cleanest for Comparable types:
PriorityQueue<Integer> maxHeap = new PriorityQueue<>(Comparator.reverseOrder());

maxHeap.addAll(List.of(3, 1, 4, 1, 5));
maxHeap.peek();   // 5  -- largest at the head
maxHeap.poll();   // 5

The three idioms

• Comparator.reverseOrder() — the idiomatic, type-safe choice for any Comparable.
• Lambda (a, b) -> b - a — works for int, but risks overflow when b - a exceeds Integer.MAX_VALUE. Prefer Integer.compare(b, a), which is overflow-safe.
• Key extractor reversed — for objects: Comparator.comparingInt(Task::priority).reversed().

// Max-heap of tasks by priority, overflow-safe:
PriorityQueue<Task> q =
    new PriorityQueue<>(Comparator.comparingInt(Task::priority).reversed());

// Common bug -- do NOT do this for arbitrary ints:
PriorityQueue<Integer> buggy = new PriorityQueue<>((a, b) -> b - a);  // overflow!

Why there's no built-in max-heap

There's no separate MaxPriorityQueue class because a comparator fully parameterizes the ordering — min and max are the same structure with an inverted compare. This generalizes: any "extract the most important" rule (longest job, highest score, closest point) is just a custom comparator over a min-heap.