A min-max-heap is like a binary heap, but it allows extracting both the minimum and maximum value efficiently. In particular, finding either the minimum or maximum element is O(1). A removal of either extremum, or an insertion, is O(log n).

It’s on crates.io, so add this to your Cargo.toml:

[dependencies]
min-max-heap = "1.3.0"

This crate supports Rust version 1.32.0 and later.

My reference for a min-max heap is here. Much of this code is also based on BinaryHeap from the standard library.