What is time complexity for the following code?

Question

It seems the complexity of the following code should be O(n^2) but it\'s O(n), how?

void fun(int n, int arr[])
{
    int i = 0, j = 0;
    for(; i < n; ++         


        

Answer 1

The answer is O(n) because the test condition inside the 'while' loop fails!

while(j < n && arr[i] < arr[j])

In the beginning, i=0 and j=0, which means arr[i] = arr[j], but the while loop test condition says arr[i], and its completely wrong to assume arr[0]

The code only runs the for loop n times.

The final answer is O(n) not O(n^2)

For some clarity, you can go through these two examples

Example 1 :

#include 

int main()
{
    int i = 0, j = 0; 
    int n = 5;
    int arr[] = {6,7,8,9,10,11};
    for(; i < n; ++i) 
    { 
        printf("\nThis is for loop, its running 5 times\n");
         
        while(j < n && arr[i] < arr[j]){ 
            j++;
            printf("\nThis is while loop!\n");
        }
    };
    return 0;
}

The Output is :

This is for loop, its running 5 times

This is for loop, its running 5 times

This is for loop, its running 5 times

This is for loop, its running 5 times

This is for loop, its running 5 times

In the above output, we can't find the print statement present in 'while' loop

Example 2 :

#include 

    int main()
    {
        int i = 0, j = 0; 
        int n = 5;
        int arr[] = {6,7,8,9,10,11};
        for(; i < n; ++i) 
        { 
            printf("\nThis is for loop, its running 5 times\n");
            
            while(j < n && arr[i] <= arr[j]){ 
                j++;
                printf("\nThis is while loop!\n");
            }
        };
        return 0;
    }

Here, a small change is made arr[i] <= arr[j]

'=' is used

Output:

This is for loop, its running 5 times                                                                                                                                          
                                                                                                                                                                               
This is while loop!                                                                                                                                                            
                                                                                                                                                                               
This is while loop!                                                                                                                                                            
                                                                                                                                                                               
This is while loop!                                                                                                                                                            
                                                                                                                                                                               
This is while loop!                                                                                                                                                            
                                                                                                                                                                               
This is while loop!                                                                                                                                                            
                                                                                                                                                                               
This is for loop, its running 5 times                                                                                                                                          
                                                                                                                                                                               
This is for loop, its running 5 times                                                                                                                                          
                                                                                                                                                                               
This is for loop, its running 5 times                                                                                                                                          
                                                                                                                                                                               
This is for loop, its running 5 times

Here, the print statement in while loop is executed, because arr[i]=arr[j], arr[0] = arr[0]

For the 'Example 2' shown above the time complexity is O(n^2)