Problem 1 a) Illustrate the execution of the heap-sort algorithm on the following input sequence: (5,8, 19,7, 13, 26, 42, 21, 29, 18). Show the contents of both the heap and the sequence at each step of the algorithm. ) Illustrate the execution of the bottom-up construction of a heap on the following sequence (5,8, 19,7, 13, 26, 42,21,29, 18, 10, 12, 33,34,43)