Final answer:
The running time of insert() and find() operations in a heap is primarily determined by the height of the heap, as adjustment operations are proportional to the height.
Step-by-step explanation:
The primary factor affecting the running time (t(n)) of the insert() and find() operations for a heap is the height of the heap. A heap is a special tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. The insert operation involves adding a new element to the heap and then performing an up-heap operation (also known as heapify up or bubble up) which at most takes as many steps as the height of the heap to ensure the heap property is maintained. Similarly, the find operation typically finds the maximum (in a max heap) or minimum (in a min heap) element, which is always at the root, but subsequent operations, such as delete or extract, may result in a down-heap operation (also known as heapify down or bubble down), which again is proportional to the height of the heap.