# Absolute Values Sum Minimization in JavaScript

In the given problem statement we have to find the absolute value for minimization of the sum in the given array with the help of Javascript functionalities. So we will use basic mathematics for solving the problem.

## Understanding the problem

The problem at hand is to find the absolute values for minimization of the sum. This is the basic problem to solve in mathematics and computer science. This program involves finding a number from the given array which minimizes the sum of the absolute difference between that number and the other item in the array.

## Logic for the given problem

To solve the above problem we will use a simple method to find the absolute values of sum minimization. In this problem first we will create a function to do this task and inside this function we will pass an input array for which we have to find the absolute value. So inside this function we will sort the given array in an order. Then we will check that the length of the array is even or odd. If the length of the array is odd then we will return the middle element as a result. Otherwise we will return the item at the index (length/ 2) - 1.

### Algorithm

Step 1: As we have to find the absolute value of sum minimization for the given array. So the first step is to define the function to do the given task. And name the function as sumMinimization, inside this function we will take an input array as a parameter. And for this array we will find the absolute value.

Step 2: After defining the function we will first sort the items of the given input array in ascending order with the help of sort method and inside the sort method we will use a comparison function to arrange the items in ascending order.

Step 3: So after arranging the items in ascending order we will check the length of the given input array. If the length of the array is odd then the required value will be the middle index. To get the middle index we will use Math.floor function.

Step 4: And if the length of the array is even then we will return the required item at (arr.length/2)-1 index.

Step 5: At the end we will provide the example usage in which an array will be passed to the created function and the result will be printed to the console.

### Example

function sumMinimization(arr) {
// Sort the array in ascending order
arr.sort((a, b) => a - b);

// Check if the array length is odd or even
if (arr.length % 2 === 1) {
// For odd-length array
return arr[Math.floor(arr.length / 2)];
} else {
// For even-length array
return arr[(arr.length / 2) - 1];
}
}
const array = [1, 2, 3, 4, 5];
const result = sumMinimization(array);
console.log(result);


### Output

3

## Complexity

The time complexity of the function for finding the absolute value of sum minimization is O(n log n), in which n is the size of the array. Because we have performed a sort operation on the array. And the space complexity for the function is constant O(1) as we have only used a value of the array to get the result.

## Conclusion

As we explored the problem of finding the absolute value sum minimization in Javascript. We have performed some basic operations on the array like sorting and conditional checking for even and odd lengths. And also used some mathematical formulas to get the required item.

Updated on: 11-Aug-2023

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