2 4 7 9 3 8 6 1 1 3 6 8 7 2 2 7 9 4 4 9 3 8 3 8 6 1 1

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   2  4  7  9 3  8  6  1       1  3  6  8  2     2  7 9  4       4  9 3  8      3  8 6  1      1  6 7     7 2     2   9 4    4 3     3 8     8 6     6 1     1 7  2  9  4   3  8  6  1       1  2  3  4  6  7  8  9
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©  2004 Goodrich, Tamassia Merge Sort 15 Execution Example (cont.) Merge  7  2   9  4      2  4  7  9 3  8  6  1       1  3  6  8  2     2  7 9  4       4  9 3  8      3  8 6  1      1  6 7     7 2     2   9 4    4 3     3 8     8 6     6 1     1 7  2  9  4   3  8  6  1       1  2  3  4  6  7  8  9
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©  2004 Goodrich, Tamassia Merge Sort 16 Analysis of Merge-Sort The height  h  of the merge-sort tree is  O (log n )   at each recursive call we divide in half the sequence,  The overall amount or work done at the nodes of depth  i is  O ( n )   we partition and merge  2 i  sequences of size  n / 2 i   we make  2 i + 1  recursive calls Thus, the total running time of merge-sort is  O ( n log n ) depth #seqs size 0 1 n 1 2 n / 2 i 2 i n / 2 i
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©  2004 Goodrich, Tamassia Merge Sort 17 Summary of Sorting Algorithms Algorithm Time Notes selection-sort O ( n 2 )  slow  in-place  for small data sets (< 1K) insertion-sort O ( n 2 )  slow  in-place  for small data sets (< 1K) heap-sort O ( n log n )  fast  in-place  for large data sets (1K — 1M) merge-sort O ( n log n )  fast  sequential data access  for huge data sets (> 1M)
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