Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons required to find the maximum in the heap is _______.

In a balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in range [a, b]? Assume that the number of reported elements is k.

Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _____.

Consider the following $$New-order$$ strategy for traversing a binary tree:

$$\,\,\,\,\,\,\, \bullet \,\,\,\,\,$$ Visit the root;
$$\,\,\,\,\,\,\, \bullet \,\,\,\,\,$$ Visit the right subtree using $$New-order;$$
$$\,\,\,\,\,\,\, \bullet \,\,\,\,\,$$ Visit the left subtree using $$New-order;$$

The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 * 5 - 2 ^ 6 7 * 1 + - is given by: