Problem $3.(30$ points$)$ Assume that q refers to a heap$-$based priority queue which stores its

elements using an array. Answer each of the following problems.

$($a$)(10$ points$)$ Let $[1,2,4,5,6,7,$ null$]$ denote the array that q uses. Explain how this

array changes when q$.$add$(3)$ is executed. Briefly justify your answer.

$($b$)(10$ points$)$ Let $[1,2,4,5,6,7,$ null$]$ denote the array that q uses. Explain how this

array changes when q$.$removeMin$()$ is executed. Briefly justify your answer.

$($c$)(10$ points$)$ Let $[1,2,4,5,6,7,$ null$]$ denote the array that q uses. Explain how this array changes when q$.$add$(0)$ and then q$.$removeMin$()$ are executed. Briefly justify your answer.