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Java Program for Median of two sorted arrays of same size

  • Last Updated : 11 Dec, 2021

There are 2 sorted arrays A and B of size n each. Write an algorithm to find the median of the array obtained merging the above 2 arrays(i.e. array of length 2n). The complexity should be O(log(n)).

median-of-two-arrays

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Note : Since size of the set for which we are looking for median is even (2n), we need take average of middle two numbers and return floor of the average.

Method 1 (Simply count while Merging)
Use merge procedure of merge sort. Keep track of count while comparing elements of two arrays. If count becomes n(For 2n elements), we have reached the median. Take the average of the elements at indexes n-1 and n in the merged array. See the below implementation.

Java




// A Simple Merge based O(n) solution
// to find median of two sorted arrays
  
class Main {
    // function to calculate median
    static int getMedian(int ar1[], int ar2[], int n)
    {
        int i = 0;
        int j = 0;
        int count;
        int m1 = -1, m2 = -1;
  
        /* Since there are 2n elements, median will 
           be average of elements at index n-1 and 
           n in the array obtained after merging ar1 
           and ar2 */
        for (count = 0; count <= n; count++) {
            /* Below is to handle case where all 
              elements of ar1[] are smaller than 
              smallest(or first) element of ar2[] */
            if (i == n) {
                m1 = m2;
                m2 = ar2[0];
                break;
            }
  
            /* Below is to handle case where all 
               elements of ar2[] are smaller than 
               smallest(or first) element of ar1[] */
            else if (j == n) {
                m1 = m2;
                m2 = ar1[0];
                break;
            }
  
            if (ar1[i] < ar2[j]) {
                /* Store the prev median */
                m1 = m2;
                m2 = ar1[i];
                i++;
            }
            else {
                /* Store the prev median */
                m1 = m2;
                m2 = ar2[j];
                j++;
            }
        }
  
        return (m1 + m2) / 2;
    }
  
    /* Driver program to test above function */
    public static void main(String[] args)
    {
        int ar1[] = { 1, 12, 15, 26, 38 };
        int ar2[] = { 2, 13, 17, 30, 45 };
  
        int n1 = ar1.length;
        int n2 = ar2.length;
        if (n1 == n2)
            System.out.println("Median is " + getMedian(ar1, ar2, n1));
        else
            System.out.println("arrays are of unequal size");
    }
}




Method 2 (By comparing the medians of two arrays)

This method works by first getting medians of the two sorted arrays and then comparing them.

Java




// A Java program to divide and conquer based
// efficient solution to find
// median of two sorted arrays
// of same size.
import java.util.*;
class GfG {
  
    /* This function returns median 
of ar1[] and ar2[]. 
Assumptions in this function: 
    Both ar1[] and ar2[] are 
    sorted arrays 
    Both have n elements */
    static int getMedian(int ar1[], int ar2[], int n)
    {
        /* return -1 for 
    invalid input */
        if (n <= 0)
            return -1;
        if (n == 1)
            return (ar1[0] + ar2[0]) / 2;
        if (n == 2)
            return (Math.max(ar1[0], ar2[0]) + Math.min(ar1[1], ar2[1])) / 2;
  
        /* get the median of 
    the first array */
        int m1 = median(ar1, n);
  
        /* get the median of 
    the second array */
        int m2 = median(ar2, n);
  
        /* If medians are equal then 
    return either m1 or m2 */
        if (m1 == m2)
            return m1;
  
        /* if m1 < m2 then median must 
    exist in ar1[m1....] and 
                ar2[....m2] */
        if (m1 < m2) {
            if (n % 2 == 0)
                return getMedian(ar1 + n / 2 - 1, ar2, n - n / 2 + 1);
            return getMedian(ar1 + n / 2, ar2, n - n / 2);
        }
  
        /* if m1 > m2 then median must 
    exist in ar1[....m1] and 
                ar2[m2...] */
        if (n % 2 == 0)
            return getMedian(ar2 + n / 2 - 1, ar1, n - n / 2 + 1);
        return getMedian(ar2 + n / 2, ar1, n - n / 2);
    }
  
    /* Function to get median 
of a sorted array */
    static int median(int arr[], int n)
    {
        if (n % 2 == 0)
            return (arr[n / 2] + arr[n / 2 - 1]) / 2;
        else
            return arr[n / 2];
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int ar1[] = { 1, 2, 3, 6 };
        int ar2[] = { 4, 6, 8, 10 };
        int n1 = ar1.length;
        int n2 = ar2.length;
        if (n1 == n2)
            System.out.println("Median is " + getMedian(ar1, ar2, n1));
        else
            System.out.println("Doesn't work for arrays "
                               + "of unequal size");
    }
}


Please refer complete article on Median of two sorted arrays of same size for more details!


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