Segment 16.8 introduced you to an iterative

merge sort. This project continues that discussion by providing more details

about the merge steps.

a. If n is a power of 2, as it is in Figure

16-3, you would merge pairs of individual entries, starting at the beginning of

the array. Then you would return to the beginning of the array and merge pairs

of two-entry subarrays. Finally, you would merge one pair of four-entry

subarrays. Notice that the subarrays in each pair of subarrays contain the same

number of entries. In general, n might not be a power of 2. After merging a

certain number of

Segment 16.8 introduced you to an iterative

merge sort. This project continues that discussion by providing more details

about the merge steps.

a. If n is a power of 2, as it is in Figure

16-3, you would merge pairs of individual entries, starting at the beginning of

the array. Then you would return to the beginning of the array and merge pairs

of two-entry subarrays. Finally, you would merge one pair of four-entry

subarrays. Notice that the subarrays in each pair of subarrays contain the same

number of entries. In general, n might not be a power of 2. After merging a

certain number of pairs of subarrays, you might have too few entries left to

make up a complete pair of subarrays. In Figure 16-12a (on the next page),

after merging pairs of single entries, one entry is left over. You then merge

one pair of two-entry subarrays, and merge the leftover two-entry subarray with

the leftover single entry. Parts b and c of Figure 16-12 show two other

possibilities.

Special cases in an iterative merge sort

after merging one-entry subarrays

Implement an iterative merge sort. Use the

algorithm merge that was given in Segment 16.3. A private method that uses

merge to merge the pairs of subarrays is useful. After the method completes its

task, you can handle the leftovers that we just described.

b. Merging two subarrays requires an

additional temporary array. Although you need to use this extra space, you can

save much of the time that our earlier merge algorithm spends in copying

entries from the temporary array back to the original array. If a is the

original array and t is the temporary array, you first merge subarrays of a

into the array t. Instead of copying t back to a and continuing the merge, you

determine subarrays of t and merge them into a. If you can do this an even

number of times, no additional copying is necessary. Make these changes to the

iterative merge sort that you wrote in Part a.

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