1 Problem 1 (15 points) For each part below, say whether the statement is true or false. If true, give a brief (one or two sentences) explanation; if false, give a counterexample. Part 1 (3 points) The minimum element of a max-heap is always a leaf . Part 2 (3 points) The second smallest element of a max-heap is always a leaf . Part 3 (4 points) The second and third largest elements of a max-heap are always the twchildren of the root Part 4 (5 points) The sum of the heights of all nodes in an n-node heap is (n)