C# Program for Median of two sorted arrays of same size

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.

C#

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// A Simple Merge based O(n) solution
// to find median of two sorted arrays
using System;
class GFG {
    // 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 Code
    public static void Main()
    {
        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)
            Console.Write("Median is " + getMedian(ar1, ar2, n1));
        else
            Console.Write("arrays are of unequal size");
    }
}

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Output:

Median is 16


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.

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




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