Trees

Min Insert appends a value at the end of the array, then bubbles it up until the parent is smaller.

Extract Min removes the root, moves the last value into position, and sifts it down to restore order.

Heapify builds a valid min heap bottom-up from an arbitrary array in linear time.

Compare Min/Max shows the same input reorganized so the smallest value sits at the root of a min heap while the largest value sits at the root of a max heap.