Calculate Median of an Array in JavaScript

In this problem statement, our task is to calculate the median of an array with the help of Javascript functionalities. There are several ways that can be used to solve this task. One simple method to calculate median is using the built-in function of Javascript.

Understanding the problem statement

The problem statement is to write a function in Javascript that will help to calculate the median of a given array. For example, if we have an array of integers [1, 2, 3, 4, 5] so the median of this array is 3. Because 3 is the middle element of the array.

Logic for the given problem

For the code we will create a function to find the median of the array. And inside the function we will calculate the middle index of the array by dividing the length of the array by 2. This index will be the index of the median in the array if the array has an odd number of elements. If the array has an even number of arrays, the index of the median will be the left of the median.

Then we will sort the array in ascending order using the sort() method, which will take a comparison function as a parameter. If the length of the array is even then we will return the average of the two middle values. We will do this by adding the values at the middle index and index to the left of the middle and then dividing the sum by 2. And if the length is odd in the array so we will simply return the middle value.

Algorithm

Step 1 ? Declare a function called median which is using a parameter of array.

Step 2 ? Calculate the mid of the array by dividing the length of the array by 2. It will show the index of the mid element.

Step 3 ? Sort the given array with the help of the sort method.

Step 4 ? And if the array length is even then return the left side mid value.

Step 5 ? Return the result as the mid element of the array.

Code for the algorithm

//function to find the median of the given array
function median(arr) {
   const mid = Math.floor(arr.length / 2);
   const sortedArr = arr.sort((a, b) => a - b);
 
   if (arr.length % 2 === 0) {
      return (sortedArr[mid - 1] + sortedArr[mid]) / 2;
   } else {
      return sortedArr[mid];
   }
}
const arr = [11, 12, 13, 14, 15, 16, 17, 18, 19];
console.log(median(arr));

Complexity

The time taken by the function is O(n log n ), because we have used a sort method which performs quick sort and quicksort takes O(n log n) time to sort the elements. Where n is the size of the given array. And the space used by the code is O(1) as it is storing the result as only the middle element of the array.

Conclusion

The implemented code is providing a simple and efficient solution to find out the median of the given array. The time taken by the created function is O(n log n). There can be a case when the given array is already sorted so in that case the time complexity will be O(n) because it is taking linear time.