Problem 2. (25 points) a. Construct a heap for the list 1, 8, 6, 5, 3, 7, 4 by the bottom-up algorithm. b. Construct a heap for the list 1, 8,

6, 5, 3, 7, 4 by successive key insertions (top-down algorithm). c. Is it always true that the bottom-up and top-down algorithms yield the same heap for the same input?