
#### Problem Statement

Given an array of n elements, write a function to sort the array

#### Approach

- Find a mid point and divide the array into to halves based on the mid point
- Recursively call the merge sort function for both the halves
- Merge the two sorted halves to get the sorted array

#### Time Complexity

`O(n log n)`

#### Space Complexity

`O(n)`

#### Example

```
arr = [1, 3, 9, 5, 0, 2]  

Divide the array in two halves [1, 3, 9] and [5, 0, 2]

Recursively call merge sort function for both these halves which will provide sorted halves
=> [1, 3, 9] & [0, 2, 5]

Now merge both these halves to get the sorted array [0, 1, 2, 3, 5, 9]
```

#### Code Implementation Links

- [Java](https://github.com/TheAlgorithms/Java/blob/master/Sorts/MergeSort.java)
- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/merge_sort.cpp)
- [Python](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_sort.py)
- [C-Sharp](https://github.com/TheAlgorithms/C-Sharp/blob/master/Algorithms/Sorters/Comparison/MergeSorter.cs)
- [C](https://github.com/TheAlgorithms/C/blob/master/sorting/merge_sort.c)
- [Ruby](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/merge_sort.rb)

#### Video Explanation

[A CS50 video explaining the Merge Sort Algorithm](https://www.youtube.com/watch?v=EeQ8pwjQxTM)


Mergesort


#### Problem Statement

Given an unsorted array of n elements, write a function to sort the array

#### Approach

- select the first element of the array
- compare it with its next element
- if it is larger than the next element then swap them
- else do nothing
- keep doing this for every index of the array
- repeat the above process n times.

#### Time Complexity

`O(n^2)` Worst case performance

`O(n)` Best-case performance

`O(n^2)` Average performance

#### Space Complexity

`O(1)` Worst case

#### Founder's Name

- The term âBubble Sortâ was first used by Iverson, K in 1962.

#### Example

```
arr[] = {10, 80, 40, 30}
Indexes: 0   1   2   3    

1. Index = 0, Number = 10
2. 10 < 80, do nothing and continue

3. Index = 1, Number = 80
4. 80 > 40, swap 80 and 40
5. The array now is {10, 40, 80, 30}

6. Index = 2, Number = 80
7. 80 > 30, swap 80 and 30
8. The array now is {10, 40, 30, 80}

Repeat the Above Steps again

arr[] = {10, 40, 30, 80}
Indexes: 0   1   2   3   

1. Index = 0, Number = 10
2. 10 < 40, do nothing and continue

3. Index = 1, Number = 40
4. 40 > 30, swap 40 and 30
5. The array now is {10, 30, 40, 80}

6. Index = 2, Number = 40
7. 40 < 80, do nothing
8. The array now is {10, 30, 40, 80}

Repeat the Above Steps again

arr[] = {10, 30, 40, 80}
Indexes: 0   1   2   3   

1. Index = 0, Number = 10
2. 10 < 30, do nothing and continue

3. Index = 1, Number = 30
4. 30 < 40, do nothing and continue

5. Index = 2, Number = 40
6. 40 < 80, do nothing

Since there are no swaps in above steps, it means the array is sorted and we can stop here.
```

#### Code Implementation Links

- [Java](https://github.com/TheAlgorithms/Java/blob/master/Sorts/BubbleSort.java)
- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bubble_sort.cpp)
- [Python](https://github.com/TheAlgorithms/Python/blob/master/sorts/bubble_sort.py)
- [C-Sharp](https://github.com/TheAlgorithms/C-Sharp/blob/master/Algorithms/Sorters/Comparison/BubbleSorter.cs)
- [Go](https://github.com/TheAlgorithms/Go/blob/master/sorts/bubblesort.go)
- [Ruby](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/bubble_sort.rb)
- [C](https://github.com/TheAlgorithms/C/blob/master/sorting/bubble_sort.c)
- [Scala](https://github.com/TheAlgorithms/Scala/blob/master/src/main/scala/Sort/BubbleSort.scala)
- [Javascript](https://github.com/TheAlgorithms/Javascript/blob/master/Sorts/BubbleSort.js)

#### Video Explanation

[A video explaining the Bubble Sort Algorithm](https://www.youtube.com/watch?v=Jdtq5uKz-w4)

#### Others

Bubble sort is also known as Sinking sort.

#### Animation Explanation

- [Tute Board](https://boardhub.github.io/tute/?wd=bubbleSortAlgo2)


Bubble Sort


#### Problem Statement

Given an array of n elements, write a function to sort the array in increasing order.

#### Approach

- Define a "key" index, the subarray to the left of which is sorted.
- Initiate "key" as 1, ie. the second element of array(as there is only one element to left of the second element, which can be considered as sorted array with one element).
- If value of element at (key - 1) position is less than value of element at (key) position; increment "key".
- Else move elements of sorted subarray that are greater than value of element at "key" to one position ahead of their current position. Put the value of element at "key" in the newly created void.

#### Time Complexity

- `Ð(n^2)` comparisons, `Ð(n^2)` swaps -- Worst Case

- `O(n)` comparisons, `O(1)` swaps -- Best Case

#### Space Complexity

`O(1)` -- (No extra space needed, sorting done in place)

#### Example

```

12, 11, 13, 5, 6

Let us loop for i = 1 (second element of the array) to 4 (Size of input array)

i = 1.
Since 11 is smaller than 12, move 12 and insert 11 before 12
11, 12, 13, 5, 6

i = 2.
13 will remain at its position as all elements in sorted subarray are smaller than 13
11, 12, 13, 5, 6

i = 3.
5 will move to the beginning,
and all other elements from 11 to 13 will move one position ahead of their current position.
5, 11, 12, 13, 6

i = 4.
6 will move to position after 5,
and elements from 11 to 13 will move one position ahead of their current position.
5, 6, 11, 12, 13  -- sorted array
```

#### Code Implementation Links

- [Java](https://github.com/TheAlgorithms/Java/blob/master/Sorts/InsertionSort.java)
- [C](https://github.com/TheAlgorithms/C/blob/master/sorting/insertion_sort.c)
- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/insertion_sort.cpp)
- [C#](https://github.com/TheAlgorithms/C-Sharp/blob/master/Algorithms/Sorters/Comparison/InsertionSorter.cs)
- [Scala](https://github.com/TheAlgorithms/Scala/blob/master/src/main/scala/Sort/InsertionSort.scala)
- [Python](https://github.com/TheAlgorithms/Python/blob/master/sorts/insertion_sort.py)
- [Ruby](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/insertion_sort.rb)

#### Video Explanation

[A CS50 video explaining the Insertion Search Algorithm](https://www.youtube.com/watch?v=DFG-XuyPYUQ)


Insertion Sort


#### Problem Statement

Given an unsorted array of n elements, write a function to sort the array

#### Approach

- select the smallest element from the array
- put it at the beginning of the array
- then select the smallest array from the remaining unsorted list
- append it to the sorted array at the beginning
- keep doing this for every element of the array
- repeat the above process n times

#### Time Complexity

`O(n^2)` Worst case performance

`O(n^2)` Best-case performance

`O(n^2)` Average performance

#### Space Complexity

`O(1)` Worst case

#### Example

```
arr[] = {80, 10, 40, 30}
Indexes: 0   1   2   3    

1. Index = 0
	Select the minimum number from the array (between index 0-3), ie, 10
2. Swap 10  and 80 (arr[0])
3. The array now is {10, 80, 40, 30}

4. Index = 1
	Select the minimum number from the array (between index 1-3), ie, 30
5. Swap 30 and 80 (arr[1])
6. The array now is {10, 30, 40, 80}

7. Index = 2
	Select the minimum number from the array (between index 2-3), ie, 40
8. Swap 40 and 40 (arr[2])
9. The array now is {10, 30, 40, 80}

The array is now sorted.
```

#### Code Implementation Links

- [Java](https://github.com/TheAlgorithms/Java/blob/master/Sorts/SelectionSort.java)
- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/Sorting/Selection%20Sort.cpp)
- [Python](https://github.com/TheAlgorithms/Python/blob/master/sorts/selection_sort.py)
- [Go](https://github.com/TheAlgorithms/Go/blob/master/sorts/selection_sort.go)
- [Ruby](https://github.com/TheAlgorithms/Ruby/blob/master/Sorting/selection_sort.rb)
- [C](https://github.com/TheAlgorithms/C/blob/master/sorting/SelectionSort.c)
- [Scala](https://github.com/TheAlgorithms/Scala/blob/master/src/main/scala/Sort/SelectionSort.scala)
- [Javascript](https://github.com/TheAlgorithms/Javascript/blob/master/Sorts/selectionSort.js)

#### Video Explanation

[A video explaining the Selection Sort Algorithm](https://www.youtube.com/watch?v=f8hXR_Hvybo)

#### Animation Explanation

- [Tute Board](https://boardhub.github.io/tute/?wd=selectSortAlgo2)


TheAlgorithms

Elm

datastructures

Main

divideandconquer

Mergesort

sorts

Bubble Sort

Insertion Sort

Selection Sort

src

Util