I have just begun working on a MOOC on algorithms offered by Stanford. Since this course gives us the liberty to choose a programming language, there isn’t any code discussed in those lectures. I plan to convert any algorithm discussed in those lectures into Python code. Since Merge Sort was the first algorithm discussed, I’m starting with that.

Merge Sort is supposedly a good introduction to divide and conquer algorithms, greatly improving upon selection, insertion and bubble sort techniques, especially when input size increases.

**Pseudocode:**

**— Recursively sort the first half of the input array.**

**— Recursively sort the second half of the input array.**

**— Merge two sorted sub-lists into one list.**

C = output [length = n]

A = 1st sorted array [n/2]

B = 2nd sorted array [n/2]

i = 0 or 1 (depending on the programming language)

j = 0 or 1 (depending on the programming language)

*for k = 1 to n*

*if A(i) < B(j)*

* C(k) = A(i)*

* i = i + 1*

*else if A(i) > B(j)*

* C(k) = B(j)*

* j = j + 1*

Note: the pseudocode for the merge operation ignores the end cases.

Visualizing the algorithm can be done in 2 stages — first, the recursive splitting of the arrays, 2 each 2 at a time, and second, the merge operation.

Here’s the Python code to merge sort an array.

We can divide a list in half **log _{2} **

*times where*

**n****is the length of the list. The second process is the**

*n***merge**. Each item in the list will eventually be processed and placed on the sorted list. So the merge operation which results in a list of size

**requires**

*n***operations. The result of this analysis is that**

*n***log**

_{2}*splits, each of which costs*

**n****n**for a total of

**nlog**operations.

_{2}*n***Other Algorithms:**

Karatsuba Integer Multiplication Algorithm

Quick Sort Python Code

You must use a floor function in line 26, otherwise is gives an error.

TypeError: slice indices must be integers or None or have an

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or simply: len(x)//2

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die

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You should not be using the “a.remove(a[0])” and “b.remove(b[0])”. Removing from the head of a list is O(n) and you are doing it n times so it is quadratic.

Maybe something like:

would be better?

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I believe it doesn’t matter …. you are using/ creating a variable i_a and i_b and doing an increment everytime same as .remove[0] done by the author (constant time).

But In one case your algorithm takes more time than the authors …

Your while loop runs longer when one of a or b is done sorting first …

Proof:

because if all elements in a are sorted first (len(a) == i_a)

Author: His algorithm takes the remaining elements in b and puts them in c in one single attempt

Yours: Keeps running till len(b) ==i_b

and vice versa in case you finish sorting b before a

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fast head pops?

https://docs.python.org/3/library/collections.html#collections.deque

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pretty neat

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