Finding time complexity when while loop included [duplicate]

Question

This question already has an answer here:

• Is there a system behind the magic of algorithm analysis? 3 answers

There are two sorted arrays nums1 and nums2 of size m and n respectively.

Find the median of the two sorted arrays.

Example 1:

nums1 = [1, 3] nums2 = [2]

The median is 2.0

Example 2: nums1 = [1, 2] nums2 = [3, 4]

The median is (2 + 3)/2 = 2.5

Here is my solution:

//Find out the median of two sorted array
public class Median {
public static void main(String args[]){
    int arr1[]={1,2,6};
    int arr2[]={3,5,7};

    int temp[]=new int[(arr1.length)+(arr2.length)];
    int k=0,i=0,j=0,mid=0,k2=0;


    while(i< arr1.length && j<arr2.length) {
        if (arr1[i] < arr2[j]) {
            temp[k] = arr1[i];
            i++;
        } else {
            temp[k] = arr2[j];
            j++;
        }
        k++;
    }
    while (i < arr1.length) {
        temp[k++] = arr1[i++];
    }
    while (j < arr2.length) {
        temp[k++] = arr2[j++];
    }

    int a= temp.length;
    if(a%2==0){
        k2=(temp.length)/2;
        mid = (temp[k2]+temp[k2-1])/2;
    }
    else{
       int k1=(int)(temp.length)/2;
        mid=temp[k1];
    }
    System.out.println("The median of two sorted array is "+mid);
}
}

I want to know that what is the time complexity of my code? Is there any better way to solve this?

I know how to find out the time complexity if there is for loop. But if there is while loop then how could I find out the time complexity?

Answer 1

Let’s say two arrays have a million elements each. A [500,000] = 3,516 and B [500,000] = 12,920. Can you say anything about the median? Is there anything you can do with this information to save a lot of work? What if A[750,000] = 11,416?

Your code takes O(n+m) both in time and space. This can be done in O(ln n + ln m).