Introduction to Algorithms No.5

Hello. Long time not to see. I enjoyed summer vacation...

This is the merge-sort algorithm:

https://github.com/uriha421/introduction_to_algorithms/blob/master/I_Foundations/merge_sort.c


Merge-sort is one of divide-and-conquer algorithms. It may be important to understand the concept. Let me explain it.
Divide means cutting a problem into some small ones. Conquer means solving the divided problems. Then we combine the divided problems and we solve the entire problem. In merge-sort, divide is:
<1 2 8 7 6 3 5 4>   --->   <1 2 8 7> <6 3 5 4>
 Conquer is:
<1 2 8 7> <6 3 5 4>   --->   <1 2 7 8> <3 4 5 6>
Combine is:
<1 2 7 8> <3 4 5 6>   --->   <1 2 3 4 5 6 7 8>
Now let T(n) be the running time of sorting a n-size array. Then, we have the following recursion:
T(n) = c, (if n = 1), 2T(n/2) + O(n), (if n > 1).
(2T(n/2) is the running time of conquer. O(n) is the running time of combine here.)

In conclusion, we can get a recursion from a divide-conquer algorithm. And we can calculate the running time.


Thank you. See you tomorrow.
 

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