Introduction to the algorithm 6-2 D fork Heap

Questions: The D-Fork Heap is similar to the two-fork heap, but each of its non-leaf nodes has d children;

1) How to represent a D-fork heap in an array?

2) What is the height of a d fork heap containing n elements?

3) The effective implementation of Extract-max in D fork Heap is given, and the time complexity is expressed by D and N.

4) The effective implementation of insert in D fork Heap is given, and the time complexity is expressed by D and N.

5) The effective implementation of Increase-key (A, I, K) is given. When K < A[i], it will touch an error, otherwise execute a[i] = k,

and update the corresponding D fork maximum heap, use D and N to indicate its time complexity.

3) The Heap-extract-max algorithm is suitable for the D-Fork heap, but the problem is the max-heapify algorithm.

Here you need to compare the processed nodes with all of its children. So the time to run should be θ(dlogDn).

4) The Max-heap-insert algorithm also applies to this. The worst-case run time is the height of the heap, or θ(logDn).

5) Heap-increase-key algorithm, run time is O (logDn)

Introduction to the algorithm 6-2 D fork Heap