Difference between revisions of "TADM2E 1.5"
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Revision as of 18:13, 11 September 2014
<p>First-fit algorithm counterexample:</p> <p> <math>S = \{1, 2, 3\}</math> <br/> <math>T = 5</math> </p>
<p>Best-fit algorithm counterexample:</p> <p> <math>S = \{1, 2, 3\}</math> <br/> <math>T = 5</math> </p>
<p>Largest to smallest algorithm counterexample:</p> <p> <math>S = \{4, 3, 2\}</math> <br/> <math>T = 5</math> </p>
<p>Another counterexample:</p> If <math>t=11</math>, the solution would be the subset <math>\{2, 9\}</math> or <math>\{1, 10\}</math> which none of the algorithms found.
Using first-fit algorithm (left to right)
Item added | Subset of <math>S</math> | Sum |
---|---|---|
1 | <math>\{1\}</math> | 1 < 11 |
2 | <math>\{1, 2\}</math> | 3 < 11 |
5 | <math>\{1, 2, 5\}</math> | 8 < 11 |
9 | <math>\{1, 2, 5, 9\}</math> | 17 > 11 |
Using best-fit algorithm (smallest to largest)
Item added | Subset of <math>S</math> | Sum |
---|---|---|
1 | <math>\{1\}</math> | 1 < 11 |
2 | <math>\{1, 2\}</math> | 3 < 11 |
5 | <math>\{1, 2, 5\}</math> | 8 < 11 |
9 | <math>\{1, 2, 5, 9\}</math> | 17 > 11 |
Using largest to smallest
Item added | Subset of <math>S</math> | Sum |
---|---|---|
10 | <math>\{10\}</math> | 10 < 11 |
9 | <math>\{9, 10\}</math> | 19 > 11 |