In a min-heap, what property must be maintained after every insertion?

In a min-heap, the defining property is that every parent node must be less than or equal to its child nodes. This ensures that the smallest element is always located at the root of the heap, which is a crucial characteristic of a min-heap structure.

When an element is inserted into a min-heap, it is typically placed at the end of the heap to maintain the complete tree property. After the insertion, the heap property must be restored. This is done through a process called "bubble up" or "percolate up," where the newly inserted element is compared with its parent node. If it is smaller than the parent, they are swapped, and this process continues until the heap property is maintained and the newly inserted element is in the correct position.

The requirement that the parent node be less than or equal to its child nodes is what distinguishes a min-heap from other types of heaps. In contrast, a max-heap would require that the parent node be greater than or equal to its child nodes.

Other options such as requiring the child nodes to be equal or maintaining a balanced tree are not characteristics of a min-heap. A min-heap does not have equal child nodes, and it does not need to maintain