Java:Implement the binary heap $($min$-$heap$)$

a$)$ Write functions to implement Parent$($i$),$ LeftChild$($i$)$ and RightChild$($i$).$

b$)$ Write a constructor to create an empty heap with a given maxSize.

c$)$ Implement SiftUp$($i$).$

d$)$ Implement Insert$($p$).$

e$)$ Test your code by creating the heap given in the slides, $(16,10,14,9,7,1,4,2,8,3).$

f$)$ If you change the order of the numbers that are entered, do you get the same tree?

g$)$ If the answer to part $f$ is no$,$ explain why it doesn't matter.

h$)$ Implement SiftDown$($i$).$

i$)$ Implement ExtractMax$().$

j$)$ Implement Remove$($i$).$

k$)$ Write tests for all the functions.