# Finding median for every window in JavaScript

## Median

Median in mathematics, median is the middle value in an ordered(sorted) integer list.

If the size of the list is even, and there is no middle value. Median is the mean (average) of the two middle values.

## Problem

We are required to write a JavaScript function that takes in an array of Integers, arr, as the first argument and a number num (num <= length of array arr) as the second argument.

Now for each window of size num in the array arr, our function should calculate the median and push that median value into a new array and finally at the end of iteration return that median array.

For example, if the input to the function is −

const arr = [5, 3, 7, 5, 3, 1, 8, 9, 2, 4, 6, 8];
const num = 3;

Then the output should be −

const output = [5, 5, 5, 3, 3, 8, 8, 4, 4, 6];

## Output Explanation:

Starting IndexCurrent WindowCurrent Sorted windowMedian
0[5, 3, 7][3, 5, 7]5
1[3, 7, 5][3, 5, 7]5
2[7, 5, 3][3, 5, 7]5
3[5, 3, 1][1, 3, 5]3
4[3, 1, 8][1, 3, 8]3
5[1, 8, 9][1, 8, 9]8
6[8, 9, 2][2, 8, 9]8
7[9, 2, 4][2, 4, 9]4
8[2, 4, 6][2, 4, 6]4
9[4, 6, 8][4, 6, 8]6

## Example

The code for this will be −

Live Demo

const arr = [5, 3, 7, 5, 3, 1, 8, 9, 2, 4, 6, 8];
const num = 3;
const binarySearch = (arr, target, l, r) => {
while (l < r) {
const mid = Math.floor((l + r) / 2);
if (arr[mid] < target) l = mid + 1;
else if (arr[mid] > target) r = mid;
else return mid;
};
if (l === r) return arr[l] >= target ? l : l + 1;
}
const medianSlidingWindow = (arr = [], num = 1) => {
let l = 0, r = num - 1, res = [];
const window = arr.slice(l, num);
window.sort((a, b) => a - b);
while (r < arr.length) {
const median = num % 2 === 0 ? (window[Math.floor(num / 2) - 1] + window[Math.floor(num / 2)]) / 2 : window[Math.floor(num / 2)];
res.push(median);
let char = arr[l++];
let index = binarySearch(window, char, 0, window.length - 1);
window.splice(index, 1);
char = arr[++r];
index = binarySearch(window, char, 0, window.length - 1);
window.splice(index, 0, char);
}
return res;
};
console.log(medianSlidingWindow(arr, num));

## Code Explanation:

Idea behind this solution is to use binary search to insert right number and remove left number when moving the sliding window to the right.

## Output

And the output in the console will be −

[5, 5, 5, 3, 3, 8, 8, 4, 4, 6 ]