Do the following problems:

1. Page 132,  6.2-1
Using Figure 6.2 as a model, illustrate the operation of MAX-HEAPIFY(A, 3) on the array
A={27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0}.
2. Page 135,  6.3-1
Using Figure 6.3 as a model, illustrate the operation of BUILD-MAX-HEAP on the array
A={5, 3, 17, 10, 84, 19, 6, 22, 9}.
3. Page 136,  6.4-1
Using Figure 6.4 as a model, illustrate the operation of HEAPSORT on the array
A={5, 13, 2, 25, 7, 17, 20, 8, 4}.
4. Page 140,  6.5-1
Illustrate the operation of HEAP-EXTRACT-MAX on the heap
A={15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1}.
5. Page 140,  6.5-2
Illustrate the operation of MAX-HEAP-INSERT(A, 10) on the heap
A={15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1}.
Use the heap of Figure 6,5 as a model for the HEAP-INCREASE-KEY call.
6. Page 140,  6.5-7
The operation HEAP-DELETE(A, i) deletes the item in node i from heap A.
Give an implementation of HEAP-DELETE that runs in O(lgn) time for an n-element max-heap.
7. Page 148,  7.1-1
Using Figure 7.1 as a model, illustrate the operation of PARTITION on the array
A={13, 19, 9, 5, 12, 8, 7, 4, 11, 2, 6, 21}.
8. Page 170,  8.2-1
Using Figure 8.2 as a model, illustrate the operation of COUNTING-SORT on the array
A={6, 0, 2, 0, 1, 3, 4, 6, 1, 3, 2}.
9. Page 170,  8.2-3
Suppose that the for loop header in line 9 of the COUNTING-SORT procedure is rewritten as
9    for j <-- 1 to length[A]
Show that the algorithm still works properly.  Is modified algorithm stable?
10. Page 173,  8.3-1
Using Figure 8.3 as a model, illustrate the operation of RADIX-SORT on the following list of English words:
COW, DOG, SEA, RUG, ROW, MOB, BOX, TAB, BAR, EAR, TAR, DIG, BIG, TEA, NOW, FOX.