Sorting which is one of topic in data sructure is an important thing in real life for facilitate the data management. Data sorting can be implemented by ascending order or descending order. There are some methods for data sorting such as:
 Insertion Sort
 Selection Sort
 Bubble Sort
 Quick Sort
1. Insertion Sort
Straight insertion is a sorting method which takes a parenthesis data on ordered data and shoves data which is bigger than parenthesis data so parenthesis data can be placed on right place. For example, there is an array that contains these number :
If the data above is sorted in ascending by straight insertion, the result is:
Parenthesis Data 
Sorting Result 
12 
In 1st loop, 2nd data of array becomes parenthesis data, then being compared with all previous data (3). If there is no data which is bigger than parenthesis data, there is no data that will be shove backward. 
2 
In 2nd loop, 3rd data of array becomes parenthesis data, then being compared with all previous data (3, 12). There are two data which are bigger than parenthesis data so those data will be shoved one step backward and put parenthesis data at 1st place. 
4 
In 3rd loop, 4th data of array becomes parenthesis data, then being compared with all previous data (2, 3, 12). This data will be placed at 3rd place. 
13 
In 4th loop, 5th data of array becomes parenthesis data, then being compared with all previus data (2, 3, 4, 12). Because there is no data that bigger than the parenthesis data so the parenthesis data still be in the 5th place. 
5 
In 5th loop, 6th data of array becomes parenthesis data, then being compared with all previous data (2, 3, 4, 12, 13). This data will be placed at 4th place. 
Result 

2. Selection Sort
This method is a sorting method that will look for smallest or biggest value depend on ascending or descending order then being placed at the forefront place. After that, it will look for the next smallest or biggest value along all elements of array reduced by 1, and so on. For example, there is an array that contains these number :
If the data above is sorted in ascending by selection method, the result is:
Minimum Value 
Sorting Result 
2 
In 1st loop, it will look for smallest value between 1st and 6th element of array. 2 is the smallest value so its place will be switch with 1st element. 
3 
In 2st loop, it will look for smallest value between 2nd and 6th element of array. 3 is the smallest value so its place will be switch with 2nd element. 
4 
In 3rd loop, it will look for smallest value between 3rd and 6th element of array. 4 is the smallest value so its place will be switch with 3rd element. 
5 
In 4th loop, it will look for smallest value between 4th and 6th element of array. 5 is the smallest value so its place will be switch with 4th element. 
12 
In 5th loop, it will look for smallest value between 5th and 6th element of array. 12 is the smallest value so its place will be switch with 5th element. 
Result 

3. Bubble Sort
This method will switch two element continously until sorting has been finished. This method is not efficient but easy to be realized.
If the data above is sorted in ascending by bubble sort method, the result is:
Note 
Sorting Result 
1st loop, compare 1st and 2nd element. Because 1st is smallest than 2nd so there is no exchange 

2nd loop, compare 2nd and 3rd element. Because 3rd is smallest than 2nd so there is exchange between 2nd and 3rd 

3rd loop, compare 3rd and 4th element. Because 4th is smallest than 3rd so there is exchange between 3rd and 4th 

4th loop, compare 1st and 2nd element. Because 1st is smallest than 2nd so there is no exchange 

And so on until 16th loop. Why it is until 16th loop. It has been sorted at 4th loop. Because there are 5 element so there must be 4 exchange process for each term and also must be done 4 times to ensure that all elements has been sorted. 
Result 

4. QuickSort
This method will make a data table that will be sorted into two parts which are traced from left and from right. For example, there is an array that contains these number :
If the data above is sorted in ascending by selection method, the result is:
Step 
Notes 
1 
 Array will be traced from left and from right.
 Array[1] is the first element from the left, then it will trace from the right to the left to find smaller value than Array[1].
 Array[3] which is smaller than Array[1] will be switched.
 Array[2] is next element from the left. Array[6] which is smaller will be switched.

2 
 We have subarray. There is no switching because Array[1] is smaller than Array[2].
 Array[3] is first element from the left of new array, then it will trace from the right. There is no smaller value than Array[3] so there is no switching.

3 
 When we move Array[3] to left subarray, we know that there is no smaller value than it at right subarray.
 At left subarray, Array[1] as the first element will be compared with another element from the right to the left. But, we don't get any value, so Array[1] must be the smallest value.
 Array[2] and Array[3] are switched.
 First element of right subarray is Array[4]. After tracing from right to left, there is no smaller value than Array[4], so it will be move to left subarray then.
 Second element of right subarray is Array[5]. It will be compared with last element from the right. Because it is bigger, Array[5] is switched by Array[6]

4 
 We have gotten Array[1] and Array[2] sorted.
 Array[3] and Array[4] will be switched after being traced.
 Next, there is no smaller value than Array[5] at right subarray so there is no switching.

5 
 From the third step, we know that there is no smaller value than Array[4] in right subarray, so after it is switched with Array[3] at fourth step, it must be sorted.
 Array[6] is smallest value and there is no smaller value, so it also must be sorted.

Referensi : Belajar Pemrograman dengan Bahasa C++ dan Java  Shalahuddin dan Rosa
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