SORTING VISUALISATION

Different Sorting Algorithms visualization using pygame!

Available Algorithms:

* BubbleSort
* SelectionSort
* InsertionSort
* QuickSort
* MergeSort

To Run:

	python visualizer.py algo_name

Demo:

Algorithms Implemented:

Bubble Sort

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.

  procedure bubbleSort( list : array of items )
	loop = list.count;
	for i = 0 to loop-1 do:
	swapped = false
	for j = 0 to loop-1 do:
	/* compare the adjacent elements */
	if list[j] > list[j+1] then
	/* swap them */
	swap( list[j], list[j+1] )
	swapped = true
	end if
	end for
	/*if no number was swapped that means array is sorted now, break the loop.*/
	if(not swapped) then
	break
	end if
	end for
	end procedure return list

Time Complexity :

O(n^2)

Space Complexity:

O(2)

Quick Sort (Random Pivot)

QuickSort is a Divide and Conquer algorithm. It picks an element as pivot and partitions the given array around the picked pivot. There are many different versions of quickSort that pick pivot in different ways.

*  Always pick first element as pivot
*  Always pick last element as pivot
*  Pick a random element as pivot (efficeint)

The key process in quickSort is partition(). Target of partitions is, given an array and an element x of array as pivot, put x at its correct position in sorted array and put all smaller elements (smaller than x) before x, and put all greater elements (greater than x) after x. All this should be done in linear time.

  partition(arr[], lo, hi)
	pivot = arr[hi]
	i = lo - 1     // place for swapping
	for j := lo to hi – 1 do
	if arr[j] < pivot then
	i = i + 1
	swap arr[i] with arr[j]
	swap arr[i] with arr[hi]
	return i

   partition_r(arr[], lo, hi)
	r = Random Number from lo to hi
	Swap arr[r] and arr[hi]
	return partition(arr, lo, hi)

   quicksort(arr[], lo, hi)
	if lo < hi
	p = partition_r(arr, lo, hi)
	quicksort(arr, lo , p-1)
	quicksort(arr, p+1, hi)

Time Complexity :

O(n logn)

Space Complexity:

O(n)

Merge Sort

Like QuickSort, Merge Sort is a Divide and Conquer algorithm. It divides the input array into two halves, calls itself for the two halves, and then merges the two sorted halves. The merge() function is used for merging two halves. The merge(arr, l, m, r) is a key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one.

MergeSort(arr[], l,  r)
If r > l
     1. Find the middle point to divide the array into two halves:  
             middle m = l+ (r-l)/2
     2. Call mergeSort for first half:   
             Call mergeSort(arr, l, m)
     3. Call mergeSort for second half:
             Call mergeSort(arr, m+1, r)
     4. Merge the two halves sorted in step 2 and 3:
             Call merge(arr, l, m, r)

Time Complexity :

O(n logn)

Space Complexity:

O(n)

Insertion Sort

Insertion sort is a simple sorting algorithm that works similar to the way you sort playing cards in your hands. The array is virtually split into a sorted and an unsorted part. Values from the unsorted part are picked and placed at the correct position in the sorted part.

 * Iterate from arr[1] to arr[n] over the array.
 * Compare the current element (key) to its predecessor.
 * If the key element is smaller than its predecessor, compare it to the elements before. 
Move the greater elements one position up to make space for the swapped element.

Time Complexity :

 O(n^2)

Space Complexity:

O(1)

Selection Sort

The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from unsorted part and putting it at the beginning.

The algorithm maintains two subarrays in a given array.

* The subarray which is already sorted.
* Remaining subarray which is unsorted.

In every iteration of selection sort, the minimum element (considering ascending order) from the unsorted subarray 
is picked and moved to the sorted subarray.

Time Complexity :

 O(n^2)

Space Complexity:

O(1)