c-sorting-algorithms

📦 A collection of sorting algorithms written in C.

Algorithms
Why sorting algorithms?
Why C?
Parameters
- arr
- n
Time complexity
- Big O

Algorithms

Why sorting algorithms?

Most languages already have a sort method implemented in standard libraries, so why learn sorting algorithms?

Learning sorting algorithms teaches you algorithm design. You will learn how to use paradigms like divide and conquer, how to measure algorithm complexity and when to use different sorting algorithms to maximize efficiency.

Why C?

C is a low-level high-level language.

It's close enough to the metal that we still need to consider memory management. Being able to see how we manage memory in the algorithm makes it easier to calculate the running time.

At the same time, it's a high-level language, so the syntax is human readable.

Finally, a lot of languages are based on C, so the syntax will be familiar to many developers.

Parameters

The parameter names used throughout the algorithms

arr

Array to be sorted.

Note: Arrays in C are passed by reference

n

Number of elements in arr.

Time complexity

Time complexity is a way of measuring how long an algorithm takes to run.

It's important to consider how long an algorithm takes to run. A poorly written algorithm could take tens of thousands of times longer to finish than a well written algorithm.

But measuring the running time of an algorithm can be tricky.

We can't measure an algorithm absolutely (i.e. in milliseconds), because the amount of time it takes will vary between hardware and between runs. An algorithm could take 1200ms to complete on my machine, and 4000ms on a slow computer.

Instead, we measure the relative running time.

To do this, we count the number of operations performed in the algorithm.

The most common way to express time complexity is with big O notation.

Big O notation

Big O notation measures the relative time an algorithm takes to run given the worst case.

Big O only cares about the big operations.

Generally we only care about the rough running time, so constant actions aren't included in the calculation.

Here's a table to use as a reference when looking through the algorithms in this project:

Big-O	Name	Description
O(1)	constant	This is the best. The algorithm always takes the same amount of time, regardless of how much data there is. Example: looking up an element of an array by its index.
O(log n)	logarithmic	Pretty great. These kinds of algorithms halve the amount of data with each iteration. If you have 100 items, it takes about 7 steps to find the answer. With 1,000 items, it takes 10 steps. And 1,000,000 items only take 20 steps. This is super fast even for large amounts of data. Example: binary search.
O(n)	linear	Good performance. If you have 100 items, this does 100 units of work. Doubling the number of items makes the algorithm take exactly twice as long (200 units of work). Example: sequential search.
O(n log n)	"linearithmic"	Decent performance. This is slightly worse than linear but not too bad. Example: the fastest general-purpose sorting algorithms.
O(n^2)	quadratic	Kinda slow. If you have 100 items, this does 100^2 = 10,000 units of work. Doubling the number of items makes it four times slower (because 2 squared equals 4). Example: algorithms using nested loops, such as insertion sort.
O(n^3)	cubic	Poor performance. If you have 100 items, this does 100^3 = 1,000,000 units of work. Doubling the input size makes it eight times slower. Example: matrix multiplication.
O(2^n)	exponential	Very poor performance. You want to avoid these kinds of algorithms, but sometimes you have no choice. Adding just one bit to the input doubles the running time. Example: traveling salesperson problem.
O(n!)	factorial	Intolerably slow. It literally takes a million years to do anything.

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