knerr cs21 notes...

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WEEK10: recursion
 F: merge sort

Here are some interesting merge sort links:


 - merge sort uses a divide-and-conquer method to sort a list:

    given a list, split it in two (if the size of the list > 1)
    sort each of the two halves of the list
    merge the two sorted halves back into the original list

 - this is easy to express using recursion:

def mergeSort(L):
  n = len(L)
  if n > 1:
    L1 = L[0:n/2]
    L2 = L[n/2:]

 - that last step assumes we have a function called merge that
   merges the two sorted lists back into one big sorted list


 - copy /home/jk/inclass/ and add the mergeSort function

 - run and see how long mergeSort takes for N=5000,10000,20000
   (you may want to comment our selectionSort and insertionSort
    for the N=20000 run)

Here's what I get:

         N =  5000       10000       20000
   L.sort     0.0053     0.0114      0.0102
selection     7.1494     14.5595     51.2008
insertion     11.7596    19.9309     77.8990
    merge     0.1288     0.1150      0.2420

 So merge sort is much better than selection or insertion, but
 not as good as the default .sort() method.

 - how does mergeSort's time depend on N, the size of the list?
 - how many "steps" does mergeSort take to finish it's work?

 Each level of recursion requires copying all N values from the
 halved sub-lists back to the bigger original list. So that's
 N copies * how many levels of recursion. Each level of recursion
 requires splitting a given list into two smaller lists. So "how many 
 levels of recursion" is really just "how many times can we split
 the list in two?", which we already know is log(base2)N.

 So mergeSort's time  =  N * logN, which is better than NxN.

 See /home/jk/inclass/ for a graphical comparison
 of NlogN vs logN vs linear vs quadratic.