6.006 Intro to Algorithms
Recitation 08
March 2, 2011
Merge Sort
The merge sort algorithm deals with the problem of sorting a list of
n
elements. It is able to sort
a list of
n
elements in
O
(
n
log
n
)
runtime, which is considerably faster than insertion sort, which
takes
O
(
n
2
)
. Merge sort uses a divide and conquer method:
1. If the length of the list is 1, the list is sorted. Return the list
2. Otherwise, split the list in two (roughly) equal halves and then recursively merge sort the
two halves
3. Merge the two sorted halves into one sorted list
The merge operation takes two sorted lists and an iterator at the head of each list. At each step,
we compare the elements at the iterators with each other. We take the smaller element, add it to our
merged list, and then advance the iterator associated with that smaller element. We repeat this step
until every element in the two sorted halves has been added to the merged list, forming a single
large sorted list. The runtime of the merge operation is
O
(
n
)
where
n
is the number of elements
we are merging.
Solving Recurrences
We can use merge sort as an example of how to solve recurrences. Recall back to peak ﬁnding
where we solved recurrences by showing them in the form of “Runtime of original problem” =
“Runtime of reduced problem” + “Time taken to reduce problem”, and then solved them using the
dot dot dot method. We are going to formalize this a little more.
The form of the recurrences that we’ll be dealing with look like:
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 Spring '11
 byrns
 Math

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