# C++ Program - Bubble Sort

Bubble sort is the simplest sorting algorithm. The Bubble sort is based on the idea that every adjacent elements are compared and swapped if found in wrong order.

### Example:

To understand the bubble sort, lets consider an unsorted array [1, 23, 10, -2] and discuss each step taken to sort the array in ascending order. In every pass, two adjacent elements are checked and swapped if found in wrong order.

First Pass: (1) and (23) are compared and found in correct order(ascending order in this case). After that (23) and (10) are compared, since (23>10), hence these numbers are swapped. Then (23) and (-2) are compared and swapped.

Second Pass: (1) and (10) are compared and found in correct order. Then (10) and (-2) are compared, since (10>-2), hence these numbers are swapped. After that (10) and (23) are compared and found in correct order.

Third Pass: (1) and (-2) are compared, since (1>-2), hence these numbers are swapped. After that (1,10) and (10,23) are checked and found in correct order.

## Implementation of Bubble Sort

```#include <iostream>
using namespace std;

// function for bubble sort
static void bubblesort(int Array[], int n) {
int temp;
for(int i=0; i<n; i++) {
for(int j=0; j<n-i-1; j++) {
if(Array[j]>Array[j+1]) {
temp = Array[j];
Array[j] = Array[j+1];
Array[j+1] = temp;
}
}
}
}

// function to print array
static void PrintArray(int Array[], int n) {
for (int i=0; i<n; i++)
cout<<Array[i]<<" ";
cout<<"\n";
}

// test the code
int main (){
int MyArray[] = {1, 10, 23, 50, 4, 9, -4};
int n = sizeof(MyArray) / sizeof(MyArray[0]);
cout<<"Original Array\n";
PrintArray(MyArray, n);

bubblesort(MyArray, n);
cout<<"\nSorted Array\n";
PrintArray(MyArray, n);
return 0;
}
```

The above code will give the following output:

```Original Array
1 10 23 50 4 9 -4

Sorted Array
-4 1 4 9 10 23 50
```

### Time Complexity:

The time complexity of bubble sort is Θ(N²) in all cases even if the whole array is sorted because the entire array need to be iterated for every element and it contains two nested loops.

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