Down-Heapify

Look at node i (initially the root).

• If and , all is well. (Why?)
• Similarly if i is a leaf. (Why?)
• Otherwise, swap i and the smaller of its children.
• Start again on the child that changed (i.e., move i down).

We know that the only node that may violate the heap property is a child of the new i. (Why?)

Kind of like bubblesort or insertion sort in a tree. The root value trickles down until it stops.

Running Time? (Maximum number of comparisons and swaps.)