A binary heap is a complete binary tree with a simple ordering between parents and children. Two properties define it, and both must always hold.
The shape property says the tree is complete. Every level is full except possibly the last, which fills left to right. That compact shape lets it live in a plain array with no pointers.
The heap property is a parent-child rule. In a max-heap, every parent is at least as large as its children, so the largest value sits at the root. A min-heap flips it, keeping the smallest at the root. The rule only relates parents to their own children, not siblings, so a heap is far weaker than a sorted order. That weakness makes reading the top O(1) while keeping inserts cheap.
Rewriting in plainer words…
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A binary heap is a complete binary tree where each parent is ordered against its own children, and two properties have to hold at all times.
The shape property says the tree is complete, so every level is full except maybe the last, and the last level fills from left to right.
Because the shape has no gaps, the whole tree fits in a plain array with no parent or child pointers.
The heap property says that in a max-heap every parent is at least as large as its children, so the biggest value sits at the root, and a min-heap flips that to keep the smallest on top.
That rule only compares a parent with its own children, never siblings, so a heap is much weaker than a sorted order.
That weakness is the trade-off. Reading the top is O(1) and inserts stay cheap, but you don't get sorted order or a fast lookup of any other value.
Weak answers to avoid
Names the ordering rule but skips completenessCompleteness is half the definition. It's what lets the heap live in an array and keeps the height near log n. Name both properties.
Calls a heap sorted or treats it like a BSTOrder only runs from parent to child. Siblings and left versus right have no rule, so an in-order walk isn't sorted. Say it's weaker than sorted, and that's why it's cheap.
Says complete but describes a full or perfect treeComplete means every level is full except the last, which fills left to right. A perfect tree needs every level full, which only some sizes allow.
Interview lens
Likely follow-ups, what you can say, and the weak answers to avoid.
