Weak heap

A weak heap is a sub-form of a heap data structure. It is a relaxed heap satisfying the following three conditions:

1. every key in the right subtree of a node is greater than the key stored in the node itself,
2. the root has no left child
3. leaves are only found on the last two levels of the tree.

It's form supports finding the minimum value in it with $O(1)$ worst-case time.

It is also useful for insert and delete-min or delete and decrease , with a worst-case time of $O(\log n)$.