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234
15.
Solutions to Exercises
k
=
2:
2,2,3,4,5,5,7
k
=
1:
~,3,4,5,5,
7
~
2,2,3,4,5,5,7
~
2,2,3,4,5,5,7
This required a total of 6
+
5
+
4
+
3
+
2
+
1
=
(6)P)
=
21 comparisons.
(b) Here's the merge sort.
Step 2:
7;
2;
2;
5;
3;
5;
4;
Step 3:
2,7;
2,5;
3,5;
4
Step 3:
2,2,5,7;
3,4,5
Step 3:
2,2,3,4,5,5,7
Merging two lists of length 1 to one of length 2 requires 1
+
11
=
1 comparison. Thus, the initial
merging of seven lists of length 1 to three of length 2 and one of length 1 required 1
+ 1 + 1
=
3
comparisons. The merging of three lists of length 2 and one of length 1 to one list of length 4
and another of length 3 required (2
+
2  1)
+
(2
+
1  1)
=
5 comparisons. The final merging
required 4
+
3  1
=
6 comparisons. The total is 3
+
5
+
6
=
14 comparisons.
(a) Here's the bubble sort:
k
=
7:
10,11,15,3,18,14,7,1
k
=
6:
10,11,3,15,14,7,1,18
~
10,11,15,3,18,14,7,1
~
10,11,3,15,14,7,1,18
~
10,11,15,3,18,14,7,1
~
10,3,11,15,14,7,1,18
~
10,11,3,15,18,14,7,1
~
10,3,11,15,14,7,1,18
~
10,11,3,15,18,14,7,1
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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