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package com.thealgorithms.maths;

import java.util.Arrays;

/**

* Utility class for calculating the median of an array of integers.

* The median is the middle value in a sorted list of numbers. If the list has

* an even number

* of elements, the median is the average of the two middle values.

*

* <p>

* Time Complexity: O(n log n) due to sorting

* <p>

* Space Complexity: O(1) if sorting is done in-place

*

* @see <a href="https://en.wikipedia.org/wiki/Median">Median (Wikipedia)</a>

* @see <a href=

* "https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/mean-median-basics/a/mean-median-and-mode-review">Mean,

* Median, and Mode Review</a>

*/

public final class Median {

private Median() {

}

/**

* Calculates the median of an array of integers.

* The array is sorted internally, so the original order is not preserved.

* For arrays with an odd number of elements, returns the middle element.

* For arrays with an even number of elements, returns the average of the two

* middle elements.

*

* @param values the array of integers to find the median of (can be unsorted)

* @return the median value as a double

* @throws IllegalArgumentException if the input array is empty or null

*/

public static double median(int[] values) {

if (values == null || values.length == 0) {

throw new IllegalArgumentException("Values array cannot be empty or null");

}

Arrays.sort(values);

int length = values.length;

if (length % 2 == 0) {

return (values[length / 2] + values[length / 2 - 1]) / 2.0;

} else {

return values[length / 2];

}

}

}