PHP Program for Median of two Sorted Arrays of Same Size

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PHP Program for Median of Two Sorted Arrays of Same Size

The median is a value that separates the higher half from the lower half of the data set. To calculate the median of an array, you need to consider the middle element(s) of the sorted array.

Example

<?php
// A Simple Merge based O(n) solution
// to find median of two sorted arrays

// This function returns median of
// ar1[] and ar2[]. Assumptions in
// this function: Both ar1[] and ar2[]
// are sorted arrays Both have n elements
function getMedian($ar1, $ar2, $n)
{
	// Current index of i/p array ar1[]
	$i = 0;

	// Current index of i/p array ar2[]
	$j = 0;
	$count;
	$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
$ar1 = array(1, 3, 5, 7, 9, 11);
$ar2 = array(12, 10 ,8 ,6 ,4, 2);

$n1 = sizeof($ar1);
$n2 = sizeof($ar2);
if ($n1 == $n2)
	echo("Median is " .
		getMedian($ar1, $ar2, $n1));
else
	echo("Doesn't work for arrays".
		"of unequal size");

?>

Output

It will produce the following output:

Median is 11.5

Explanation of code

The provided code implements a simple merge-based solution to find the median of two sorted arrays, $ar1 and $ar2, of the same size. The getMedian function takes the two input arrays and the size n as parameters. It initializes variables to keep track of the current indices, counters, and previous medians. It iterates count from 0 to n, comparing elements from both arrays. It updates the previous and current medians accordingly based on the comparison results.

The function handles cases where one array's elements are smaller than the other array's elements. Finally, it returns the calculated median by averaging the previous and current medians. In the example provided, the driver code creates two arrays, $ar1 and $ar2, and calculates their sizes. It calls the getMedian function to find the median of the arrays and prints the result. If the arrays have unequal sizes, an error message is displayed.

In the example, $ar1 contains [1, 3, 5, 7, 9, 11], and $ar2 contains [12, 10, 8, 6, 4, 2]. Both arrays have the same length, so the algorithm can proceed. The iteration progresses by comparing the elements in the arrays, and the median is updated accordingly. Finally, the median is calculated as (11 + 12) / 2, resulting in a median value of 11.5. Therefore, the output of the code will be "Median is 11.5".

Conclusion

PHP offers a merge-based approach to find the median of two sorted arrays of the same size. By merging the arrays and considering the middle two elements, the program accurately determines the median. It utilizes two indices to traverse the arrays, comparing elements and updating the median variables accordingly.

The resulting median is the average of the middle elements if the array length is even or the middle element if it's odd. This efficient O(n) solution provides a reliable and straightforward method for computing the median of two sorted arrays of the same size in PHP.

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