This question is about the heap. $(20\%)$

a$.$ Suppose array S$=[10,12,1,14,6,5,8,15,3,9,7,4,11,13,2].$ Show the result of

a max$-$heap after heapifying the array S $.$

b$.$ Suppose $20$ is inserted to the result of $($a$).$ Show the result of the max$-$heap after

insertion.

c$.$ Suppose the root of the max$-$heap in $($b$)$ is removed twice. Show the result after each

deletion.

Note: If your final answer is correct, you will obtain full scores. If your final answer

is incorrect, you can obtain partial scores from the intermediate steps.