Sorting an array in Bash using Bubble sort

Prerequisite: Bubble Sort 

Given an array arr sort the array in ascending order using bash scripting.

Examples:  

Input : 9 7 2 5
Output :
Array in sorted order :
2 5 7 9

Approach :

For sorting the array bubble sort is the simplest technique. Bubble sort works by swapping the adjacent elements if they are in the wrong order. 

Example: 

Given array - (9, 7, 2, 5)
After first iteration - (7, 2, 5, 9)
After second iteration - (2, 5, 7, 9)
and so on...

In this way, the array is sorted by placing the greater element at the end of the array.  

# Sorting the array in Bash 
# using Bubble sort

# Static input of Array
arr=(10 8 20 100 12)

echo "Array in original order"
echo ${arr[*]}

# Performing Bubble sort 
for ((i = 0; i<5; i++))
do
    
    for((j = 0; j<5-i-1; j++))
    do
    
        if [ ${arr[j]} -gt ${arr[$((j+1))]} ]
        then
            # swap
            temp=${arr[j]}
            arr[$j]=${arr[$((j+1))]}  
            arr[$((j+1))]=$temp
        fi
    done
done

echo "Array in sorted order :"
echo ${arr[*]}

Output : 

Array in sorted order :
8 10 12 20 100

Optimized Implementation:  The above function always runs O(n^2) time even if the array is sorted. It can be optimized by stopping the algorithm if the inner loop didn’t cause any swap. 

n=5
arr=(10 8 20 100 12) 

echo "Original array is: ${arr[*]}";

flag=1;
for (( i = 0; i < $n-1; i++ ))
do
    flag=0;
    for ((j = 0; j < $n-1-$i; j++ ))
    do
        if [[ ${arr[$j]} -gt ${arr[$j+1]} ]]
        then
            temp=${arr[$j]};
            arr[$j]=${arr[$j+1]};
            arr[$j+1]=$temp;
            flag=1;
        fi
    done

    if [[ $flag -eq 0 ]]; then
          break;
    fi

Output:

Original array is: 10 8 20 100 12
Final sorted Array is 8 10 12 20 100

Worst and Average Case Time Complexity: O(n*n). The worst-case occurs when an array is reverse sorted.

Best Case Time Complexity: O(n). The best-case occurs when the array is already sorted.

Auxiliary Space: O(1)

Boundary Cases: Bubble sort takes minimum time (Order of n) when elements are already sorted.

Sorting In Place: Yes

Stable: Yes