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After inserting or lowering a key in a minimum-oriented binary heap, compare it with its parent in a rooted tree. Exchange them while the moving key is smaller, then continue at its new index. Stop at the root of a tree or when the heap order is satisfied. This repair assumes the rest of the binary heap was valid before the insertion or key decrease.

A treap is a binary search tree ordered by keys and simultaneously a binary heap ordered by priorities. Independent random priorities give logarithmic expected search depth. An implicit treap uses subtree sizes to address sequence positions instead of storing explicit keys.