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https://github.com/elyse502/sorting_algorithms
C - Sorting algorithms & Big O Topics
https://github.com/elyse502/sorting_algorithms
algorithms algorithms-and-data-structures bigo bigocomplexity bigonotation c cprogramming-language sorting-algorithms
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C - Sorting algorithms & Big O Topics
- Host: GitHub
- URL: https://github.com/elyse502/sorting_algorithms
- Owner: elyse502
- Created: 2023-07-20T13:25:34.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-06-25T09:28:58.000Z (5 months ago)
- Last Synced: 2024-06-26T10:25:01.923Z (5 months ago)
- Topics: algorithms, algorithms-and-data-structures, bigo, bigocomplexity, bigonotation, c, cprogramming-language, sorting-algorithms
- Language: C
- Homepage:
- Size: 313 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# 0x1B. C - Sorting algorithms & Big O
In this project, I implemented twelve different sorting algorithms.
# Resourcesđ§”
### Read or watch:
* [Sorting algorithm](https://en.wikipedia.org/wiki/Sorting_algorithm)
* [Big O notation](https://stackoverflow.com/questions/487258/what-is-a-plain-english-explanation-of-big-o-notation)
* [Sorting algorithms animations](https://www.toptal.com/developers/sorting-algorithms)
* [15 sorting algorithms in 6 minutes](https://www.youtube.com/watch?v=kPRA0W1kECg) (_**WARNING**: The following video can trigger seizure/epilepsy. It is not required for the project, as it is only a funny visualization of different sorting algorithms_)
* [CS50 Algorithms explanation in detail by David Malan](https://www.youtube.com/watch?v=yb0PY3LX2x8&t=2s)
* [All about sorting algorithms](https://www.geeksforgeeks.org/sorting-algorithms/)
# More Info
### Data Structure and Functions
* For this project you are given the following **`print_array`**, and **`print_list`** functions:
```groovy
#include
#include
/**
* print_array - Prints an array of integers
*
* @array: The array to be printed
* @size: Number of elements in @array
*/
void print_array(const int *array, size_t size)
{
size_t i;
i = 0;
while (array && i < size)
{
if (i > 0)
printf(", ");
printf("%d", array[i]);
++i;
}
printf("\n");
}
```
```groovy
#include
#include "sort.h"
/**
* print_list - Prints a list of integers
*
* @list: The list to be printed
*/
void print_list(const listint_t *list)
{
int i;
i = 0;
while (list)
{
if (i > 0)
printf(", ");
printf("%d", list->n);
++i;
list = list->next;
}
printf("\n");
}
```
* Our files **`print_array.c`** and **`print_list.c`** (containing the `print_array` and `print_list` functions) will be compiled with your functions during the correction.
* Please declare the prototype of the functions **`print_array`** and **`print_list`** in your **_`sort.h`_** header file
* Please use the following data structure for doubly linked list:
```groovy
/**
* struct listint_s - Doubly linked list node
*
* @n: Integer stored in the node
* @prev: Pointer to the previous element of the list
* @next: Pointer to the next element of the list
*/
typedef struct listint_s
{
const int n;
struct listint_s *prev;
struct listint_s *next;
} listint_t;
```
Please, note this format is used for Quiz and Task questions.
* `O(1)`
* `O(n)`
* `O(n!)`
* n square -> `O(n^2)`
* log(n) -> `O(log(n))`
* n * log(n) -> `O(nlog(n))`
* n + k -> `O(n+k)`
* âŠ
Please use the âshortâ notation (donât use constants). Example: `O(nk)` or `O(wn)` should be written `O(n)`. If an answer is required within a file, all your answers files must have a newline at the end.
## Tests
Here is a quick tip to help you test your sorting algorithms with big sets of random integers: [`Random.org`](https://www.random.org/integer-sets/)
# Background Context
This project is meant to be done by groups of two students. Each group of two should [pair program](https://en.wikipedia.org/wiki/Pair_programming) for at least the mandatory part.
## General
* At least four different sorting algorithms
* What is the Big O notation, and how to evaluate the time complexity of an algorithm
* How to select the best sorting algorithm for a given input
* What is a stable sorting algorithm
# Sorting AlgorithmsđĄđđ
Click to show/hide Content
A `sorting algorithm` is an algorithm that puts elements of a list into an order. The most frequently used orders are `numerical order` and `lexicographical order`, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for `canonicalizing data` and for producing `human-readable` output.
Formally, the output of any sorting algorithm must satisfy two conditions:
1. The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order).
2. The output is a permutation (a reordering, yet retaining all of the original elements) of the input.
# Various Sorting Algorithms are as follows:
## Bubble Sort
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list to be sorted, compares each pair of adjacent items and swaps them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. The algorithm, which is a comparison sort, is named for the way smaller or larger elements "bubble" to the top of the list. Although the algorithm is simple, it is too slow and impractical for most problems even when compared to insertion sort. Bubble sort can be practical if the input is in mostly sorted order with some out-of-order elements nearly in position.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n2)|Ω(n)|
|In-place?|Stable?|
|---|---|
|Yes|Yes|
## Selection Sort
Selection sort is a sorting algorithm, specifically an in-place comparison sort. It has O(n2) time complexity, making it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity, and it has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited.
The algorithm divides the input list into two parts: the sublist of items already sorted, which is built up from left to right at the front (left) of the list, and the sublist of items remaining to be sorted that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n2)|Ω(n2)|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Insertion Sort
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort.
Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. At each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n2)|Ω(n)|
|In-place?|Stable?|
|---|---|
|Yes|Yes|
## Counting Sort
Counting sort is an algorithm for sorting a collection of objects according to keys that are small integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that have each distinct key value, and using arithmetic on those counts to determine the positions of each key value in the output sequence. Its running time is linear in the number of items and the difference between the maximum and minimum key values, so it is only suitable for direct use in situations where the variation in keys is not significantly greater than the number of items. However, it is often used as a subroutine in another sorting algorithm, radix sort, that can handle larger keys more efficiently.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n+k)|Î(n+k>)|Ω(n+k)|
|In-place?|Stable?|
|---|---|
|No|Yes|
## Cycle Sort
Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm. It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n2)|Ω(n2)|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Heap Sort
Heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like that algorithm, it divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element and moving that to the sorted region. The improvement consists of the use of a heap data structure rather than a linear-time search to find the maximum.
The heapsort algorithm involves preparing the list by first turning it into a max heap. The algorithm then repeatedly swaps the first value of the list with the last value, decreasing the range of values considered in the heap operation by one, and sifting the new first value into its position in the heap. This repeats until the range of considered values is one value in length.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n log(n))|Î(n log(n))|Ω(n) (bottom up)|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Merge Sort
Merge sort is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Merge sort is a divide and conquer algorithm.
Conceptually, a merge sort works as follows:
1. Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
2. Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n log(n))|Î(n log(n))|Ω(n log(n))|
|In-place?|Stable?|
|---|---|
|No|Yes|
## Quick Sort
Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.
Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. In efficient implementations it is not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting. It is very similar to selection sort, except that it does not always choose worst-case partition.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n log(n))|Ω(n log(n))|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Radix Sort
Radix sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by the individual digits which share the same significant position and value. A positional notation is required, but because integers can represent strings of characters (e.g., names or dates) and specially formatted floating point numbers, radix sort is not limited to integers.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(nk)|Î(nk)|Ω(nk)|
|In-place?|Stable?|
|---|---|
|Depends on implementation|Depends on implementation|
## Cocktail Sort
Cocktail Sort is a variation of Bubble sort. The Bubble sort algorithm always traverses elements from left and moves the largest element to its correct position in first iteration and second largest in second iteration and so on. Cocktail Sort traverses through a given array in both directions alternatively.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n2)|Ω(n)|
|In-place?|Stable?|
|---|---|
|Yes|Yes|
## Bogo Sort
Also known as Permutation Sort. Stupid Sort, Slowsort, Shotgun Sort, or Monkey Sort, Bogosort randomly generates permutations of the input and checks if it is sorted until it generates one that happens to be sorted by chance. Not meant to be an efficient sort, Bogosort is largely used for educational purposes and for comparison to actual sorting algorithms for contrast. It has a best case of O(n) where the list is already sorted, an average performance of O((n+1)!) and an unbounded worst case performance.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|Unbounded|O((n+1)!)|Ω(n)|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Bozo Sort
Bozosort is somewhat similar to Bogosort in its random behaviour. It works by choosing two random elements of the list and swapping them, until the list is actually sorted.
The running time analysis of a bozosort is difficult, but some estimates are found in H. O(n!) is found to be the expected average case. Considering that every iteration calls a function that checks if the list is ordered or not, that makes the average case actually O((n+1)!)
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|Unbounded|O((n+1)!) (estimated)|Ω(n)|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Shell Sort
Shellsort, also known as Shell sort or Shell's method, is an in-place comparison sort. It can be seen as either a generalization of sorting by exchange (bubble sort) or sorting by insertion (insertion sort).The method starts by sorting pairs of elements far apart from each other, then progressively reducing the gap between elements to be compared. Starting with far apart elements, it can move some out-of-place elements into position faster than a simple nearest neighbor exchange. Donald Shell published the first version of this sort in 1959.The running time of Shellsort is heavily dependent on the gap sequence it uses. For many practical variants, determining their time complexity remains an open problem.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Depends on Implementation|Ω(n log(n))|
|In-place?|Stable?|
|---|---|
|Yes|No|
## IntroSort
Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins with quicksort and switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted. This combines the good parts of both algorithms, with practical performance comparable to quicksort on typical data sets and worst-case O(n log n) runtime due to the heap sort. Since both algorithms it uses are comparison sorts, it too is a comparison sort.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n log(n))|Î(n log(n))|O(n log(n))|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Bucket Sort
Bucket sort is a sorting algorithm that involves first putting elements that need to be sorted into "buckets", sorting these buckets and then merging the results to get the sorted list. It is best used on data that is uniformly distributed over a range and can perform quite well, O(n + m) (where n is the number of elements in the list and m is the number of buckets used). The buckets are typically stored as an array of linked lists so there is an additional space requirement for this sorting algorithm.
For example, if there is a list of numbers in the range 1 to 1000 we can have 10 buckets. All numbers between 1 and 100 get added to the first bucket, between 101 and 200 get added to the second bucket, etc. After all numbers have been added to the appropriate bucket insertion sort is applied to all the buckets. This step is the bottleneck for the algorithm. If the data is not clustered tightly than the sorts can be completed in linear time despite the fact that insertion sort is O(n2). The algorithm degrades as certain buckets get more of the numbers, the worst case being when all the numbers are in a single bucket. The data in the input array must uniformly distributed across the range of bucket values to avoid the polynomial time. The size of each bucket should be equal to the number of buckets. As bucket sort is polynomial in the worse case Quicksort is a more optimal sorting algorithm.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n+k)|Ω(n+k)|
|In-place?|Stable?|
|---|---|
|Yes|Yes|
## Gnome sort
Gnome sort is a sorting algorithm which is similar to insertion sort, except that moving an element to its proper place is accomplished by a series of swaps, similar to a bubble sort. It is conceptually simple, requiring no nested loops. The average, or expected, running time is O(n2) but tends towards O(n) if the list is initially almost sorted.
The algorithm always finds the first place where two adjacent elements are in the wrong order and swaps them. It takes advantage of the fact that performing a swap can introduce a new out-of-order adjacent pair next to the previously swapped elements. It does not assume that elements forward of the current position are sorted, so it only needs to check the position directly previous to the swapped elements.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|O(n2)|Ω(n2)|
|In-place?|Stable?|
|---|---|
|Yes|Yes|
## Comb sort
Comb sort improves on bubble sort. The basic idea is to eliminate turtles, or small values near the end of the list, since in a bubble sort these slow the sorting down tremendously. Rabbits, large values around the beginning of the list, do not pose a problem in bubble sort.
In bubble sort, when any two elements are compared, they always have a gap (distance from each other) of 1. The basic idea of comb sort is that the gap can be much more than 1. The inner loop of bubble sort, which does the actual swap, is modified such that gap between swapped elements goes down (for each iteration of outer loop) in steps of a "shrink factor" k: \[ n/k, n/k2, n/k3, ..., 1 \].
The gap starts out as the length of the list n being sorted divided by the shrink factor k (generally 1.3; see below) and one pass of the aforementioned modified bubble sort is applied with that gap. Then the gap is divided by the shrink factor again, the list is sorted with this new gap, and the process repeats until the gap is 1. At this point, comb sort continues using a gap of 1 until the list is fully sorted. The final stage of the sort is thus equivalent to a bubble sort, but by this time most turtles have been dealt with, so a bubble sort will be efficient.
The shrink factor has a great effect on the efficiency of comb sort. k = 1.3 has been suggested as an ideal shrink factor by the authors of the original article after empirical testing on over 200,000 random lists. A value too small slows the algorithm down by making unnecessarily many comparisons, whereas a value too large fails to effectively deal with turtles, making it require many passes with 1 gap size.
The pattern of repeated sorting passes with decreasing gaps is similar to Shellsort, but in Shellsort the array is sorted completely each pass before going on to the next-smallest gap. Comb sort's passes do not completely sort the elements. This is the reason that Shellsort gap sequences have a larger optimal shrink factor of about 2.2.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n2)|Î(n2/2p),where p is the number of increments|Ω(n log(n))|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Tim sort
Timsort is a hybrid stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data. It uses techniques from Peter McIlroy's "Optimistic Sorting and Information Theoretic Complexity", in Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 467â474, January 1993. It was implemented by Tim Peters in 2002 for use in the Python programming language. The algorithm finds subsequences of the data that are already ordered, and uses that knowledge to sort the remainder more efficiently. This is done by merging an identified subsequence, called a run, with existing runs until certain criteria are fulfilled. Timsort has been Python's standard sorting algorithm since version 2.3. It is also used to sort arrays of non-primitive type in Java SE 7, on the Android platform, and in GNU Octave.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n log(n))|O(n log(n)|O(n)|
|In-place?|Stable?|
|---|---|
|No|Yes|
## Tournament sort
Tournament sort improves upon the naive selection sort by using a priority queue to find the next element in the sort. In the naive selection sort, it takes O(n) operations to select the next element of n elements; in a tournament sort, it takes O(log n) operations (after building the initial tournament in O(n)). Tournament sort is a variation of heapsort.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n log(n))|O(n log(n)|O(n log(n))|
|In-place?|Stable?|
|---|---|
|No|No|
### IN SHORT:
Red and black is used for searching whereas for sorting it is better to use Heapsort(for local projects).The time complexity is for the worst case is "2nlogn" and best case is "n". But it is not stable, if you prefer the stable sort it is better to use the merge sort. O(n) = n log n. If the sorting is for priority of top 10 or least 10, then use priority Queue. (Max-PQ and Min-PQ).
Source : (use this links for the code, it is an industrial code and the code is written in generics(can use any datatypes))
Heap: https://algs4.cs.princeton.edu/code/edu/princeton/cs/algs4/Heap.java.html
Merge: https://algs4.cs.princeton.edu/code/edu/princeton/cs/algs4/Merge.java.html
For other sorting and searching algorithms: https://algs4.cs.princeton.edu/code/
## Bitonic Sort
The Bitonic Sort is a parallel comparison-based sorting algorithm which does O(nlogn) comparisons. It is also called as the Bitonic Merge Sort. The Bitonic Sort is based on the concept of converting the given sequence into a Bitonic Sequence. A Bitonic Sequence is a sequence of numbers which is first strictly increasing then after a point strictly decreasing. Although, the number of comparisons are more than that in any other popular sorting algorithm, It performs better for the parallel implementation because elements are compared in predefined sequence which must not be depended upon the data being sorted. The predefined sequence is called Bitonic sequence. Therefore it is suitable for implementation in hardware and parallel processor array.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(log2n)|O(log2n)|O(log2n)|
|In-place?|Stable?|
|---|---|
|Yes|No|
## Pancake Sort
Pancake sorting is the colloquial term for the mathematical problem of sorting a disordered stack of pancakes in order of size when a spatula can be inserted at any point in the stack and used to flip all pancakes above it. A pancake number is the minimum number of flips required for a given number of pancakes.
Unlike a traditional sorting algorithm, which attempts to sort with the fewest comparisons possible, the goal is to sort the sequence in as few reversals as possible.
Time complexity analysis:
|Worst Case|Average Case|Best Case|
|---|---|---|
|O(n^2)|O(n)|O(n)|
|In-place?|Stable?|
|---|---|
|No|No|
## Stooge Sort
The Stooge sort is a recursive sorting algorithm. It is defined for ascending order sorting.Stooge sort is a recursive sorting algorithm. It is notable for its exceptionally bad time complexity of O(n^(log 3 / log 1.5 ) = O(n2.7095...). The running time of the algorithm is thus slower compared to reasonable sorting algorithms, and is slower than Bubble sort, a canonical example of a fairly inefficient sort. It is however more efficient than Slowsort
## 3 Way Merge Sort
Merge sort involves recursively splitting the array into 2 parts, sorting and finally merging them. A variant of merge sort is called 3-way merge sort where instead of splitting the array into 2 parts we split it into 3 parts.
Merge sort recursively breaks down the arrays to subarrays of size half. Similarly, 3-way Merge sort breaks down the arrays to subarrays of size one third.
# Tasks đ
## 0. Bubble sort: [0-bubble_sort.c](0-bubble_sort.c), [0-O](0-O)
[**`YoutubeVideo`**](https://www.youtube.com/watch?v=lyZQPjUT5B4)
A function that sorts an array of integers in ascending order using the [Bubble sort](https://en.wikipedia.org/wiki/Bubble_sort) algorithm
* Prototype: `void bubble_sort(int *array, size_t size);`
* Youâre expected to print the `array` after each time you swap two elements
Write in the file `0-O`, the big O notations of the time complexity of the Bubble sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 0-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
bubble_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 0-bubble_sort.c 0-main.c print_array.c -o bubble
alex@/tmp/sort$ ./bubble
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
19, 48, 71, 99, 13, 52, 96, 73, 86, 7
19, 48, 71, 13, 99, 52, 96, 73, 86, 7
19, 48, 71, 13, 52, 99, 96, 73, 86, 7
19, 48, 71, 13, 52, 96, 99, 73, 86, 7
19, 48, 71, 13, 52, 96, 73, 99, 86, 7
19, 48, 71, 13, 52, 96, 73, 86, 99, 7
19, 48, 71, 13, 52, 96, 73, 86, 7, 99
19, 48, 13, 71, 52, 96, 73, 86, 7, 99
19, 48, 13, 52, 71, 96, 73, 86, 7, 99
19, 48, 13, 52, 71, 73, 96, 86, 7, 99
19, 48, 13, 52, 71, 73, 86, 96, 7, 99
19, 48, 13, 52, 71, 73, 86, 7, 96, 99
19, 13, 48, 52, 71, 73, 86, 7, 96, 99
19, 13, 48, 52, 71, 73, 7, 86, 96, 99
13, 19, 48, 52, 71, 73, 7, 86, 96, 99
13, 19, 48, 52, 71, 7, 73, 86, 96, 99
13, 19, 48, 52, 7, 71, 73, 86, 96, 99
13, 19, 48, 7, 52, 71, 73, 86, 96, 99
13, 19, 7, 48, 52, 71, 73, 86, 96, 99
13, 7, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 1. Insertion sort: [1-insertion_sort_list.c](1-insertion_sort_list.c), [1-O](1-O)
[**`YoutubeVideo`**](https://www.youtube.com/watch?v=ROalU379l3U)
A function that sorts a doubly linked list of integers in ascending order using the [Insertion sort](https://en.wikipedia.org/wiki/Insertion_sort) algorithm
* Prototype: `void insertion_sort_list(listint_t **list);`
* You are not allowed to modify the integer `n` of a node. You have to swap the nodes themselves.
* Youâre expected to print the `list` after each time you swap two elements
Write in the file `1-O`, the big O notations of the time complexity of the Insertion sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 1-main.c
#include
#include
#include "sort.h"
/**
* create_listint - Creates a doubly linked list from an array of integers
*
* @array: Array to convert to a doubly linked list
* @size: Size of the array
*
* Return: Pointer to the first element of the created list. NULL on failure
*/
listint_t *create_listint(const int *array, size_t size)
{
listint_t *list;
listint_t *node;
int *tmp;
list = NULL;
while (size--)
{
node = malloc(sizeof(*node));
if (!node)
return (NULL);
tmp = (int *)&node->n;
*tmp = array[size];
node->next = list;
node->prev = NULL;
list = node;
if (list->next)
list->next->prev = list;
}
return (list);
}
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
listint_t *list;
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
list = create_listint(array, n);
if (!list)
return (1);
print_list(list);
printf("\n");
insertion_sort_list(&list);
printf("\n");
print_list(list);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 1-main.c 1-insertion_sort_list.c print_list.c -o insertion
alex@/tmp/sort$ ./insertion
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
19, 48, 71, 99, 13, 52, 96, 73, 86, 7
19, 48, 71, 13, 99, 52, 96, 73, 86, 7
19, 48, 13, 71, 99, 52, 96, 73, 86, 7
19, 13, 48, 71, 99, 52, 96, 73, 86, 7
13, 19, 48, 71, 99, 52, 96, 73, 86, 7
13, 19, 48, 71, 52, 99, 96, 73, 86, 7
13, 19, 48, 52, 71, 99, 96, 73, 86, 7
13, 19, 48, 52, 71, 96, 99, 73, 86, 7
13, 19, 48, 52, 71, 96, 73, 99, 86, 7
13, 19, 48, 52, 71, 73, 96, 99, 86, 7
13, 19, 48, 52, 71, 73, 96, 86, 99, 7
13, 19, 48, 52, 71, 73, 86, 96, 99, 7
13, 19, 48, 52, 71, 73, 86, 96, 7, 99
13, 19, 48, 52, 71, 73, 86, 7, 96, 99
13, 19, 48, 52, 71, 73, 7, 86, 96, 99
13, 19, 48, 52, 71, 7, 73, 86, 96, 99
13, 19, 48, 52, 7, 71, 73, 86, 96, 99
13, 19, 48, 7, 52, 71, 73, 86, 96, 99
13, 19, 7, 48, 52, 71, 73, 86, 96, 99
13, 7, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 2. Selection sort: [2-selection_sort.c](2-selection_sort.c), [2-O](2-O)
[**`YoutubeVideo`**](https://www.youtube.com/watch?v=Ns4TPTC8whw)
A function that sorts an array of integers in ascending order using the [Selection sort](https://en.wikipedia.org/wiki/Selection_sort) algorithm
* Prototype: `void selection_sort(int *array, size_t size);`
* Youâre expected to print the `array` after each time you swap two elements
Write in the file `2-O`, the big O notations of the time complexity of the Selection sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 2-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
selection_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89
2-main.c 2-selection_sort.c print_array.c -o select
alex@/tmp/sort$ ./select
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
7, 48, 99, 71, 13, 52, 96, 73, 86, 19
7, 13, 99, 71, 48, 52, 96, 73, 86, 19
7, 13, 19, 71, 48, 52, 96, 73, 86, 99
7, 13, 19, 48, 71, 52, 96, 73, 86, 99
7, 13, 19, 48, 52, 71, 96, 73, 86, 99
7, 13, 19, 48, 52, 71, 73, 96, 86, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 3. Quick sort: [3-quick_sort.c](3-quick_sort.c), [3-O](3-O)
[**`YoutubeVideo`**](https://www.youtube.com/watch?v=ywWBy6J5gz8)
A function that sorts an array of integers in ascending order using the [Quick sort](https://en.wikipedia.org/wiki/Quicksort) algorithm
* Prototype: `void quick_sort(int *array, size_t size);`
* You must implement the `Lomuto` partition scheme.
* The pivot should always be the last element of the partition being sorted.
* Youâre expected to print the `array` after each time you swap two elements
Write in the file `3-O`, the big O notations of the time complexity of the Quick sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 3-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
quick_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 3-main.c 3-quick_sort.c print_array.c -o quick
alex@/tmp/sort$ ./quick
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
7, 48, 99, 71, 13, 52, 96, 73, 86, 19
7, 13, 99, 71, 48, 52, 96, 73, 86, 19
7, 13, 19, 71, 48, 52, 96, 73, 86, 99
7, 13, 19, 71, 48, 52, 73, 96, 86, 99
7, 13, 19, 71, 48, 52, 73, 86, 96, 99
7, 13, 19, 48, 71, 52, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 4. Shell sort - Knuth Sequence: [100-shell_sort.c](100-shell_sort.c)
A function that sorts an array of integers in ascending order using the [Shell sort](https://en.wikipedia.org/wiki/Shellsort) algorithm, using the **`Knuth sequence`**
* Prototype: `void shell_sort(int *array, size_t size);`
* You must use the following sequence of intervals (a.k.a the Knuth sequence):
* `n+1 = n * 3 + 1`
* `1, 4, 13, 40, 121, ...`
* Youâre expected to print the `array` each time you decrease the interval.
**No big O notations of the time complexity of the Shell sort (Knuth sequence) algorithm needed - as the complexity is dependent on the size of array and gap**
```groovy
alex@/tmp/sort$ cat 100-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
shell_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 100-main.c 100-shell_sort.c print_array.c -o shell
alex@/tmp/sort$ ./shell
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
13, 7, 96, 71, 19, 48, 99, 73, 86, 52
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 5. Cocktail shaker sort: [101-cocktail_sort_list.c](101-cocktail_sort_list.c), [101-O](101-O)
A function that sorts a doubly linked list of integers in ascending order using the [Cocktail shaker sort](https://en.wikipedia.org/wiki/Cocktail_shaker_sort) algorithm
* Prototype: `void cocktail_sort_list(listint_t **list);`
* You are not allowed to modify the integer `n` of a node. You have to swap the nodes themselves.
* Youâre expected to print the `list` after each time you swap two elements
Write in the file `101-O`, the big O notations of the time complexity of the Cocktail shaker sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 101-main.c
#include
#include
#include "sort.h"
/**
* create_listint - Creates a doubly linked list from an array of integers
*
* @array: Array to convert to a doubly linked list
* @size: Size of the array
*
* Return: Pointer to the first element of the created list. NULL on failure
*/
listint_t *create_listint(const int *array, size_t size)
{
listint_t *list;
listint_t *node;
int *tmp;
list = NULL;
while (size--)
{
node = malloc(sizeof(*node));
if (!node)
return (NULL);
tmp = (int *)&node->n;
*tmp = array[size];
node->next = list;
node->prev = NULL;
list = node;
if (list->next)
list->next->prev = list;
}
return (list);
}
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
listint_t *list;
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
list = create_listint(array, n);
if (!list)
return (1);
print_list(list);
printf("\n");
cocktail_sort_list(&list);
printf("\n");
print_list(list);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 101-main.c 101-cocktail_sort_list.c print_list.c -o cocktail
alex@/tmp/sort$ ./cocktail
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
19, 48, 71, 99, 13, 52, 96, 73, 86, 7
19, 48, 71, 13, 99, 52, 96, 73, 86, 7
19, 48, 71, 13, 52, 99, 96, 73, 86, 7
19, 48, 71, 13, 52, 96, 99, 73, 86, 7
19, 48, 71, 13, 52, 96, 73, 99, 86, 7
19, 48, 71, 13, 52, 96, 73, 86, 99, 7
19, 48, 71, 13, 52, 96, 73, 86, 7, 99
19, 48, 71, 13, 52, 96, 73, 7, 86, 99
19, 48, 71, 13, 52, 96, 7, 73, 86, 99
19, 48, 71, 13, 52, 7, 96, 73, 86, 99
19, 48, 71, 13, 7, 52, 96, 73, 86, 99
19, 48, 71, 7, 13, 52, 96, 73, 86, 99
19, 48, 7, 71, 13, 52, 96, 73, 86, 99
19, 7, 48, 71, 13, 52, 96, 73, 86, 99
7, 19, 48, 71, 13, 52, 96, 73, 86, 99
7, 19, 48, 13, 71, 52, 96, 73, 86, 99
7, 19, 48, 13, 52, 71, 96, 73, 86, 99
7, 19, 48, 13, 52, 71, 73, 96, 86, 99
7, 19, 48, 13, 52, 71, 73, 86, 96, 99
7, 19, 13, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 6. Counting sort: [102-counting_sort.c](102-counting_sort.c), [102-O](102-O)
A function that sorts an array of integers in ascending order using the [Counting sort](https://en.wikipedia.org/wiki/Counting_sort) algorithm
* Prototype: `void counting_sort(int *array, size_t size);`
* You can assume that `array` will contain only numbers `>= 0`
* You are allowed to use `malloc` and `free` for this task
* Youâre expected to print your counting array once it is set up
* This array is of size **`k + 1`** where k is the largest number in `array`
Write in the file `102-O`, the big O notations of the time complexity of the Counting sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 102-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
counting_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 102-main.c 102-counting_sort.c print_array.c -o counting
alex@/tmp/sort$ ./counting
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 7. Merge sort: [103-merge_sort.c](103-merge_sort.c), [103-O](103-O)
A function that sorts an array of integers in ascending order using the [Merge sort](https://en.wikipedia.org/wiki/Merge_sort) algorithm
* Prototype: `void merge_sort(int *array, size_t size);`
* You must implement the **`top-down`** merge sort algorithm
* When you divide an array into two sub-arrays, the size of the left array should always be <= the size of the right array. i.e. `{1, 2, 3, 4, 5}` -> `{1, 2}, {3, 4, 5}`
* Sort the left array before the right array
* You are allowed to use `printf`
* You are allowed to use `malloc` and `free` only once (only one **call**)
* Output: see example
Write in the file `103-O`, the big O notations of the time complexity of the Merge sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 103-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
merge_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 103-main.c 103-merge_sort.c print_array.c -o merge
alex@/tmp/sort$ ./merge
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
Merging...
[left]: 19
[right]: 48
[Done]: 19, 48
Merging...
[left]: 71
[right]: 13
[Done]: 13, 71
Merging...
[left]: 99
[right]: 13, 71
[Done]: 13, 71, 99
Merging...
[left]: 19, 48
[right]: 13, 71, 99
[Done]: 13, 19, 48, 71, 99
Merging...
[left]: 52
[right]: 96
[Done]: 52, 96
Merging...
[left]: 86
[right]: 7
[Done]: 7, 86
Merging...
[left]: 73
[right]: 7, 86
[Done]: 7, 73, 86
Merging...
[left]: 52, 96
[right]: 7, 73, 86
[Done]: 7, 52, 73, 86, 96
Merging...
[left]: 13, 19, 48, 71, 99
[right]: 7, 52, 73, 86, 96
[Done]: 7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 8. Heap sort: [104-heap_sort.c](104-heap_sort.c), [104-O](104-O)
A function that sorts an array of integers in ascending order using the [Heap sort](https://en.wikipedia.org/wiki/Heapsort) algorithm
* Prototype: `void heap_sort(int *array, size_t size);`
* You must implement the `sift-down` heap sort algorithm
* Youâre expected to print the `array` after each time you swap two elements
Write in the file `104-O`, the big O notations of the time complexity of the Heap sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 104-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
heap_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 104-main.c 104-heap_sort.c print_array.c -o heap
alex@/tmp/sort$ ./heap
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
19, 48, 99, 86, 13, 52, 96, 73, 71, 7
19, 86, 99, 48, 13, 52, 96, 73, 71, 7
19, 86, 99, 73, 13, 52, 96, 48, 71, 7
99, 86, 19, 73, 13, 52, 96, 48, 71, 7
99, 86, 96, 73, 13, 52, 19, 48, 71, 7
7, 86, 96, 73, 13, 52, 19, 48, 71, 99
96, 86, 7, 73, 13, 52, 19, 48, 71, 99
96, 86, 52, 73, 13, 7, 19, 48, 71, 99
71, 86, 52, 73, 13, 7, 19, 48, 96, 99
86, 71, 52, 73, 13, 7, 19, 48, 96, 99
86, 73, 52, 71, 13, 7, 19, 48, 96, 99
48, 73, 52, 71, 13, 7, 19, 86, 96, 99
73, 48, 52, 71, 13, 7, 19, 86, 96, 99
73, 71, 52, 48, 13, 7, 19, 86, 96, 99
19, 71, 52, 48, 13, 7, 73, 86, 96, 99
71, 19, 52, 48, 13, 7, 73, 86, 96, 99
71, 48, 52, 19, 13, 7, 73, 86, 96, 99
7, 48, 52, 19, 13, 71, 73, 86, 96, 99
52, 48, 7, 19, 13, 71, 73, 86, 96, 99
13, 48, 7, 19, 52, 71, 73, 86, 96, 99
48, 13, 7, 19, 52, 71, 73, 86, 96, 99
48, 19, 7, 13, 52, 71, 73, 86, 96, 99
13, 19, 7, 48, 52, 71, 73, 86, 96, 99
19, 13, 7, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
13, 7, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 9. Radix sort: [105-radix_sort.c](105-radix_sort.c)
A function that sorts an array of integers in ascending order using the [Radix sort](https://en.wikipedia.org/wiki/Radix_sort) algorithm
* Prototype: `void radix_sort(int *array, size_t size);`
* You must implement the **`LSD`** radix sort algorithm
* You can assume that `array` will contain only numbers `>= 0`
* You are allowed to use `malloc` and `free` for this task
* Youâre expected to print the `array` each time you increase your **`significant digit`**
```groovy
alex@/tmp/sort$ cat 105-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
radix_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 105-main.c 105-radix_sort.c print_array.c -o radix
alex@/tmp/sort$ ./radix
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
71, 52, 13, 73, 96, 86, 7, 48, 19, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
---
## 10. Bitonic sort: [106-bitonic_sort.c](106-bitonic_sort.c), [106-O](106-O)
A function that sorts an array of integers in ascending order using the [Bitonic sort](https://en.wikipedia.org/wiki/Bitonic_sorter) algorithm
* Prototype: `void bitonic_sort(int *array, size_t size);`
* You can assume that `size` will be equal to `2^k`, where `k >= 0` (when `array` is not `NULL` âŠ)
* You are allowed to use `printf`
* Youâre expected to print the `array` each time you swap two elements
* Output: see example
Write in the file `106-O`, the big O notations of the time complexity of the Bitonic sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 106-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {100, 93, 40, 57, 14, 58, 85, 54, 31, 56, 46, 39, 15, 26, 78, 13};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
bitonic_sort(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 106-main.c 106-bitonic_sort.c print_array.c -o bitonic
alex@/tmp/sort$ ./bitonic
100, 93, 40, 57, 14, 58, 85, 54, 31, 56, 46, 39, 15, 26, 78, 13
Merging [16/16] (UP):
100, 93, 40, 57, 14, 58, 85, 54, 31, 56, 46, 39, 15, 26, 78, 13
Merging [8/16] (UP):
100, 93, 40, 57, 14, 58, 85, 54
Merging [4/16] (UP):
100, 93, 40, 57
Merging [2/16] (UP):
100, 93
Result [2/16] (UP):
93, 100
Merging [2/16] (DOWN):
40, 57
Result [2/16] (DOWN):
57, 40
Result [4/16] (UP):
40, 57, 93, 100
Merging [4/16] (DOWN):
14, 58, 85, 54
Merging [2/16] (UP):
14, 58
Result [2/16] (UP):
14, 58
Merging [2/16] (DOWN):
85, 54
Result [2/16] (DOWN):
85, 54
Result [4/16] (DOWN):
85, 58, 54, 14
Result [8/16] (UP):
14, 40, 54, 57, 58, 85, 93, 100
Merging [8/16] (DOWN):
31, 56, 46, 39, 15, 26, 78, 13
Merging [4/16] (UP):
31, 56, 46, 39
Merging [2/16] (UP):
31, 56
Result [2/16] (UP):
31, 56
Merging [2/16] (DOWN):
46, 39
Result [2/16] (DOWN):
46, 39
Result [4/16] (UP):
31, 39, 46, 56
Merging [4/16] (DOWN):
15, 26, 78, 13
Merging [2/16] (UP):
15, 26
Result [2/16] (UP):
15, 26
Merging [2/16] (DOWN):
78, 13
Result [2/16] (DOWN):
78, 13
Result [4/16] (DOWN):
78, 26, 15, 13
Result [8/16] (DOWN):
78, 56, 46, 39, 31, 26, 15, 13
Result [16/16] (UP):
13, 14, 15, 26, 31, 39, 40, 46, 54, 56, 57, 58, 78, 85, 93, 100
13, 14, 15, 26, 31, 39, 40, 46, 54, 56, 57, 58, 78, 85, 93, 100
alex@/tmp/sort$
```
---
## 11. Quick Sort - Hoare Partition scheme: [107-quick_sort_hoare.c](107-quick_sort_hoare.c), [107-O](107-O)
A function that sorts an array of integers in ascending order using the [Quick sort](https://en.wikipedia.org/wiki/Quicksort) algorithm
* Prototype: `void quick_sort_hoare(int *array, size_t size);`
* You must implement the **`Hoare`** partition scheme.
* The pivot should always be the last element of the partition being sorted.
* Youâre expected to print the `array` after each time you swap two elements
Write in the file `107-O`, the big O notations of the time complexity of the Quick sort algorithm, with 1 notation per line:
* in the best case
* in the average case
* in the worst case
```groovy
alex@/tmp/sort$ cat 107-main.c
#include
#include
#include "sort.h"
/**
* main - Entry point
*
* Return: Always 0
*/
int main(void)
{
int array[] = {19, 48, 99, 71, 13, 52, 96, 73, 86, 7};
size_t n = sizeof(array) / sizeof(array[0]);
print_array(array, n);
printf("\n");
quick_sort_hoare(array, n);
printf("\n");
print_array(array, n);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 107-main.c 107-quick_sort_hoare.c print_array.c -o quick
alex@/tmp/sort$ ./quick
19, 48, 99, 71, 13, 52, 96, 73, 86, 7
7, 48, 99, 71, 13, 52, 96, 73, 86, 19
7, 19, 99, 71, 13, 52, 96, 73, 86, 48
7, 19, 13, 71, 99, 52, 96, 73, 86, 48
7, 13, 19, 71, 99, 52, 96, 73, 86, 48
7, 13, 19, 48, 99, 52, 96, 73, 86, 71
7, 13, 19, 48, 71, 52, 96, 73, 86, 99
7, 13, 19, 48, 52, 71, 96, 73, 86, 99
7, 13, 19, 48, 52, 71, 86, 73, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
7, 13, 19, 48, 52, 71, 73, 86, 96, 99
alex@/tmp/sort$
```
Another example of output:
```groovy
alex@/tmp/sort$ ./quick_2
87, 65, 28, 63, 93, 52, 39, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 11, 16, 21, 75, 36, 71, 8, 45, 38
38, 65, 28, 63, 93, 52, 39, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 11, 16, 21, 75, 36, 71, 8, 45, 87
38, 8, 28, 63, 93, 52, 39, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 11, 16, 21, 75, 36, 71, 65, 45, 87
38, 8, 28, 36, 93, 52, 39, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 11, 16, 21, 75, 63, 71, 65, 45, 87
38, 8, 28, 36, 21, 52, 39, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 11, 16, 93, 75, 63, 71, 65, 45, 87
38, 8, 28, 36, 21, 16, 39, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 11, 52, 93, 75, 63, 71, 65, 45, 87
38, 8, 28, 36, 21, 16, 11, 59, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 26, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
38, 8, 28, 36, 21, 16, 11, 26, 27, 30, 24, 83, 69, 62, 13, 6, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
38, 8, 28, 36, 21, 16, 11, 26, 27, 30, 24, 6, 69, 62, 13, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
38, 8, 28, 36, 21, 16, 11, 26, 27, 30, 24, 6, 13, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
13, 8, 28, 36, 21, 16, 11, 26, 27, 30, 24, 6, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
13, 8, 6, 36, 21, 16, 11, 26, 27, 30, 24, 28, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
13, 8, 6, 11, 21, 16, 36, 26, 27, 30, 24, 28, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
11, 8, 6, 13, 21, 16, 36, 26, 27, 30, 24, 28, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
6, 8, 11, 13, 21, 16, 36, 26, 27, 30, 24, 28, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
6, 8, 11, 13, 21, 16, 28, 26, 27, 30, 24, 36, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
6, 8, 11, 13, 21, 16, 28, 26, 27, 24, 30, 36, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
6, 8, 11, 13, 21, 16, 24, 26, 27, 28, 30, 36, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 69, 83, 88, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 87
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 69, 83, 87, 58, 92, 59, 42, 39, 52, 93, 75, 63, 71, 65, 45, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 69, 83, 87, 58, 45, 59, 42, 39, 52, 93, 75, 63, 71, 65, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 69, 83, 87, 58, 45, 59, 42, 39, 52, 65, 75, 63, 71, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 69, 71, 87, 58, 45, 59, 42, 39, 52, 65, 75, 63, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 69, 71, 63, 58, 45, 59, 42, 39, 52, 65, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 65, 71, 63, 58, 45, 59, 42, 39, 52, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 62, 65, 52, 63, 58, 45, 59, 42, 39, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 65, 52, 63, 58, 45, 59, 42, 62, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 62, 52, 63, 58, 45, 59, 42, 65, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 62, 52, 42, 58, 45, 59, 63, 65, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 59, 52, 42, 58, 45, 62, 63, 65, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 45, 52, 42, 58, 59, 62, 63, 65, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 45, 42, 52, 58, 59, 62, 63, 65, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 42, 45, 52, 58, 59, 62, 63, 65, 71, 69, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 42, 45, 52, 58, 59, 62, 63, 65, 69, 71, 75, 87, 83, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 42, 45, 52, 58, 59, 62, 63, 65, 69, 71, 75, 83, 87, 93, 92, 88
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 42, 45, 52, 58, 59, 62, 63, 65, 69, 71, 75, 83, 87, 88, 92, 93
6, 8, 11, 13, 16, 21, 24, 26, 27, 28, 30, 36, 38, 39, 42, 45, 52, 58, 59, 62, 63, 65, 69, 71, 75, 83, 87, 88, 92, 93
alex@/tmp/sort$
````
## 12. Dealer: [1000-sort_deck.c](1000-sort_deck.c), [deck.h](deck.h)
[**`YoutubeVideo`**](https://www.youtube.com/watch?v=_HJlGWXzlLA)
A function that sorts a deck of cards.
* Prototype: `void sort_deck(deck_node_t **deck);`
* You are allowed to use the C standard library function `qsort`
* Please use the following data structures:
```groovy
typedef enum kind_e
{
SPADE = 0,
HEART,
CLUB,
DIAMOND
} kind_t;
/**
* struct card_s - Playing card
*
* @value: Value of the card
* From "Ace" to "King"
* @kind: Kind of the card
*/
typedef struct card_s
{
const char *value;
const kind_t kind;
} card_t;
/**
* struct deck_node_s - Deck of card
*
* @card: Pointer to the card of the node
* @prev: Pointer to the previous node of the list
* @next: Pointer to the next node of the list
*/
typedef struct deck_node_s
{
const card_t *card;
struct deck_node_s *prev;
struct deck_node_s *next;
} deck_node_t;
```
* You have to push you `deck.h` header file, containing the previous data structures definition
* Each node of the doubly linked list contains a card that you cannot modify. You have to swap the nodes.
* You can assume there is exactly `52` elements in the doubly linked list.
* You are free to use the sorting algorithm of your choice
* The deck must be ordered:
* From `Ace` to `King`
* From Spades to Diamonds
* See example below
```groovy
alex@/tmp/sort$ cat 1000-main.c
#include
#include
#include "deck.h"
void print_deck(const deck_node_t *deck)
{
size_t i;
char kinds[4] = {'S', 'H', 'C', 'D'};
i = 0;
while (deck)
{
if (i)
printf(", ");
printf("{%s, %c}", deck->card->value, kinds[deck->card->kind]);
if (i == 12)
printf("\n");
i = (i + 1) % 13;
deck = deck->next;
}
}
deck_node_t *init_deck(const card_t cards[52])
{
deck_node_t *deck;
deck_node_t *node;
size_t i;
i = 52;
deck = NULL;
while (i--)
{
node = malloc(sizeof(*node));
if (!node)
return (NULL);
node->card = &cards[i];
node->next = deck;
node->prev = NULL;
if (deck)
deck->prev = node;
deck = node;
}
return (deck);
}
int main(void)
{
card_t cards[52] = {
{"Jack", CLUB}, {"4", HEART}, {"3", HEART}, {"3", DIAMOND}, {"Queen", HEART}, {"5", HEART}, {"5", SPADE}, {"10", HEART}, {"6", HEART}, {"5", DIAMOND}, {"6", SPADE}, {"9", HEART}, {"7", DIAMOND}, {"Jack", SPADE}, {"Ace", DIAMOND}, {"9", CLUB}, {"Jack", DIAMOND}, {"7", SPADE}, {"King", DIAMOND}, {"10", CLUB}, {"King", SPADE}, {"8", CLUB}, {"9", SPADE}, {"6", CLUB}, {"Ace", CLUB}, {"3", SPADE}, {"8", SPADE}, {"9", DIAMOND}, {"2", HEART}, {"4", DIAMOND}, {"6", DIAMOND}, {"3", CLUB}, {"Queen", CLUB}, {"10", SPADE}, {"8", DIAMOND}, {"8", HEART}, {"Ace", SPADE}, {"Jack", HEART}, {"2", CLUB}, {"4", SPADE}, {"2", SPADE}, {"2", DIAMOND}, {"King", CLUB}, {"Queen", SPADE}, {"Queen", DIAMOND}, {"7", CLUB}, {"7", HEART}, {"5", CLUB}, {"10", DIAMOND}, {"4", CLUB}, {"King", HEART}, {"Ace", HEART},
};
deck_node_t *deck;
deck = init_deck(cards);
print_deck(deck);
printf("\n");
sort_deck(&deck);
printf("\n");
print_deck(deck);
return (0);
}
alex@/tmp/sort$ gcc -Wall -Wextra -Werror -pedantic -std=gnu89 1000-main.c 1000-sort_deck.c -o deck
alex@/tmp/sort$ ./deck
{Jack, C}, {4, H}, {3, H}, {3, D}, {Queen, H}, {5, H}, {5, S}, {10, H}, {6, H}, {5, D}, {6, S}, {9, H}, {7, D}
{Jack, S}, {Ace, D}, {9, C}, {Jack, D}, {7, S}, {King, D}, {10, C}, {King, S}, {8, C}, {9, S}, {6, C}, {Ace, C}, {3, S}
{8, S}, {9, D}, {2, H}, {4, D}, {6, D}, {3, C}, {Queen, C}, {10, S}, {8, D}, {8, H}, {Ace, S}, {Jack, H}, {2, C}
{4, S}, {2, S}, {2, D}, {King, C}, {Queen, S}, {Queen, D}, {7, C}, {7, H}, {5, C}, {10, D}, {4, C}, {King, H}, {Ace, H}
{Ace, S}, {2, S}, {3, S}, {4, S}, {5, S}, {6, S}, {7, S}, {8, S}, {9, S}, {10, S}, {Jack, S}, {Queen, S}, {King, S}
{Ace, H}, {2, H}, {3, H}, {4, H}, {5, H}, {6, H}, {7, H}, {8, H}, {9, H}, {10, H}, {Jack, H}, {Queen, H}, {King, H}
{Ace, C}, {2, C}, {3, C}, {4, C}, {5, C}, {6, C}, {7, C}, {8, C}, {9, C}, {10, C}, {Jack, C}, {Queen, C}, {King, C}
{Ace, D}, {2, D}, {3, D}, {4, D}, {5, D}, {6, D}, {7, D}, {8, D}, {9, D}, {10, D}, {Jack, D}, {Queen, D}, {King, D}
alex@/tmp/sort$
```
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This repo may contain some errors. If you notice any, please add a pull request._**
## Acknowledgementsđ€đ€
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## đSTAY TUNED!
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