Note:you must use your own heap and sort algorithms not use BUILT IN ONE in the programming language $($JAVA$).$ your question in three parts which connect to each other.

Part A$-$Design two algorithms in pseudocode: one for the insert operation and the other for the removeMin operation, both for a Heap implemented on an array $H.$

Part B$-$Use Java programming language, implement the Heap ADT on an array, including the following operations: insert, removeMin, min, size and isEmpty. Use the insert and removeMin algorithms of part A$.$

Part C$-$Design the Heap$-$Sort algorithm in pseudocode, which uses the Heap ADT of Part B$.$ Your algorithm should sort an

array of integers in increasing order.