(Solved): (a) What is the worst-case time complexity of build-heap on \( n \) elements? (b) What is the wors ...

(a) What is the worst-case time complexity of build-heap on \( n \) elements? (b) What is the worst-case time complexity of extract-max on a max-heap with \( n \) elements? (c) What is the worst-case time complexity of insertion onto a max-heap with \( n \) elements? (d) What is the worst-case time complexity of increase-key onto a max-heap with \( n \) elements? (e) What is the worst-case time complexity of find-set in a disjoint set data structure, assuming we are using union by rank and find with path compression? (f) What is the worst-case time complexity of link in a disjoint set data structure, assuming we are using union by rank and find with path compression? (g) What is the worst-case time complexity of union in a disjoint set data structure, assuming we are using union by rank and find with path compression? (h) What is the worst-case time complexity of \( m \) operations of union, find, and make-set, including \( n \) make-set operations at the start?