Data Str & Algorithm HW Solutions 51

Data Str & Algorithm HW Solutions 51 - 51 Best...

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51 Best case: 2 compares. Avgcase:16/6=22/3compares . Worst case: 3 compares. (b) Doing a similar approach of building a decision tree for 5 numbers is somewhat overwhelming since there are 120 permutations. A pretty good algorithm can be had be building on Sort3 from part (a). Use Sort3 to sort the f rst 3 numbers. Then, add the 4th number in 2 comparisons by checking the middle of the f rst 3, and then checking the 1st or 3rd as appropriate. The last number can be added using at most 3 comparisons by checking the 2nd of the f rst 4 numbers, then (at worst) the 3rd and 4th. Thus, the total number of comparisons is at most 8. The best case is 6, the average case is 7 4/15 (2 2/3 for the f rst 3 numbers, exactly 2 for the 4th number and 2 3/5 for the 5th number). It is possible to do this in 7 comparisons, worst case. Seek Knuth, Volume 3. (c) Call the algorithm from part (b) Sort5. Use it to sort the f rst 5 num- bers in at most 8 comparisons. Now, add in the sixth number by f
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