Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

idea is to iteratively remove the smallest element from the front of one of the two
lists and add it to the end of the output sequence, S, until one of the two input lists
is empty, at which point we copy the remainder of the other list to S. We show an
example execution of this version of algorithm merge in Figure 11.6.
Code Fragment 11.2: Algorithm merge for merging
two sorted sequences implemented as linked lists.
The Running Time for Merging
We analyze the running time of the merge algorithm by making some simple
observations. Let n 1 and n 2 be the number of elements of S 1 and S 2 , respectively.
Algorithm merge has three while loops. Independent of whether we are analyzing
the array-based version or the list-based version, the operations performed inside
each loop take O(1) time each. The key observation is that during each iteration of
one of the loops, one element is copied or moved from either S1 or S 2 into S (and
that element is considered no further). Since no insertions are performed into S 1
or S 2 , this observation implies that the overall number of iterations of the three
n 2 ).
loops is n 1 +n 2 . Thus, the running time of algorithm merge is 0(n 1 +
Figure 11.6: Example of an execution of the
algorithm merge shown in Code Fragment 11.2.
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