b) Using Fig. 7.1 in page 147 (page 172 in the third edition) of the book as the model, illustrate the operation of PARTITION on the array A = {3, 10, 8, 5, 12,9,6, 13, 4, 2,7}

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Answer 2b

i pj
(a)
2 8713 5 6 4
p,i j
(b)
28713 564
p.i
(c)
7|1
3 |5|64
p.i
(d)
8.
1|356 4
pi
(e)
2 178 3 564
P
(f)
1
38|75| 64
(g)
2 |1|387|564
i
(h)
2 138756 4
i
(i)
2 13 47 56 8
Figure 7.1 The operation of PARTITION Oon a sample aray. Array entry A[r] becomes the pivot
element x. Lightly shaded aray elements are all in the first partition with values no greater than x.
Heavily shaded elements are in the second partition with values greater than x. The unshaded el-
ements have not yet been put in one of the first two partitions, and the final white element is the
pivot x. (a) The initial array and variable settings. None of the elements have been placed in either
of the firsttwo partitions. (b) The value 2 is “swapped with itself" and put in the partition of smaller
val ues. (c)-(d) The values 8 and 7 are added to the partition of larger values. (e) The values 1 and 8
are swapped, and the smaller partition grows. () The values 3 and 7 are swapped, and the smaller
partition grows. (g)-(h) The larger partition grows to include 5 and 6, and the loop terminates. (i) In
lines 7-8, the pivot element is swapped so that it lies between the two partitions.
Transcribed Image Text:i pj (a) 2 8713 5 6 4 p,i j (b) 28713 564 p.i (c) 7|1 3 |5|64 p.i (d) 8. 1|356 4 pi (e) 2 178 3 564 P (f) 1 38|75| 64 (g) 2 |1|387|564 i (h) 2 138756 4 i (i) 2 13 47 56 8 Figure 7.1 The operation of PARTITION Oon a sample aray. Array entry A[r] becomes the pivot element x. Lightly shaded aray elements are all in the first partition with values no greater than x. Heavily shaded elements are in the second partition with values greater than x. The unshaded el- ements have not yet been put in one of the first two partitions, and the final white element is the pivot x. (a) The initial array and variable settings. None of the elements have been placed in either of the firsttwo partitions. (b) The value 2 is “swapped with itself" and put in the partition of smaller val ues. (c)-(d) The values 8 and 7 are added to the partition of larger values. (e) The values 1 and 8 are swapped, and the smaller partition grows. () The values 3 and 7 are swapped, and the smaller partition grows. (g)-(h) The larger partition grows to include 5 and 6, and the loop terminates. (i) In lines 7-8, the pivot element is swapped so that it lies between the two partitions.
2) X
With the help of an example, explain the following:
i)
Algorithm.
ii) Input and output for an algorithm.
iii) Running time of an algorithm.
b) Using Fig. 7.1 in page 147 (page 172 in the third edition) of the book as the model, illustrate the
operation of PARTITION on the array A =
{3,10,8,5, 12,9,6, 13,4, 2,7}
Transcribed Image Text:2) X With the help of an example, explain the following: i) Algorithm. ii) Input and output for an algorithm. iii) Running time of an algorithm. b) Using Fig. 7.1 in page 147 (page 172 in the third edition) of the book as the model, illustrate the operation of PARTITION on the array A = {3,10,8,5, 12,9,6, 13,4, 2,7}
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