Princeton Algorithms: Part 1 [Final Exam Part I]

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Explanation：

The correct answer is: 48 29 18 24

Here is the array to be searched after each compare:

     12 18 24 29 40 41 45 48 49 65 70 73 77 84 91 
48:  12 18 24 29 40 41 45  -  -  -  -  -  -  -  - 
29:  12 18 24  -  -  -  -  -  -  -  -  -  -  -  - 
18:   -  - 24  -  -  -  -  -  -  -  -  -  -  -  - 
24:   -  -  -  -  -  -  -  -  -  -  -  -  -  -  -

Explanation:

The theoretical order-of-growth is N ^ (52/15) = 3.47

The empirical order-of-growth is N ^ (log_2 ratio)

                                  log_2
        N   seconds     ratio     ratio
---------------------------------------
       32     0.000         -         -
       64     0.003         -         -
      128     0.026      8.67      3.12
      256     0.281     10.81      3.43
      512     3.173     11.29      3.50
     1024    35.897     11.31      3.50
     2048   391.666     10.91      3.45
     4096  4336.940     11.07      3.47

Explanation:

The answer is : N log N

The i loop iterates lg N times; the j loop iterates N times.

Explanation:

The correct answer is: 0 1 3 5 2 4 6

 0: Original input
 1: Selection sort after 12 iterations
 3: Mergesort (top-down) just before the last call to merge()
 5: Heapsort after heap construction phase
 2: Insertion sort after 16 iterations
 4: Quicksort (standard, no shuffle) after first partitioning step
 6: Sorted