Javascript Coding Test Course, Finding the Sum of the Remainder

Problem Definition

Given an integer array arr and an integer m, write a function to calculate the sum of the remainders when the sum of the array elements is divided by m. However, the sum of the remainders should not be greater than m.

Examples

Input: arr = [1, 2, 3, 4, 5], m = 3
Output: 15 % 3 = 0

Input: arr = [10, 20, 30], m = 5
Output: (10 + 20 + 30) % 5 = 0

Input: arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], m = 7
Output: (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) % 7 = 3

Problem Solving Process

This problem can be solved in the following steps:

Step 1: Understanding the Problem

Calculating the remainder of the sum of all elements in the array divided by m is a basic mathematical problem.
Since it specifies that the sum of the remainders must not be greater than m,
we need to keep this condition in mind while implementing the solution.

Step 2: Designing the Algorithm

A simple algorithm can be used as follows:

  1. Sum all elements of the array arr.
  2. Divide the summed result by m to get the remainder.
  3. Return the result.

Step 3: Coding

Now, let’s implement the algorithm in JavaScript.
First, I will write the basic structure: 

function remainderSum(arr, m) {
    const sum = arr.reduce((accum, value) => accum + value, 0);
    return sum % m;
}

arr.reduce() is used to sum all elements in the array and return the remainder when divided by m.
Next, I will prepare several cases to test this function.

Step 4: Writing Test Cases

console.log(remainderSum([1, 2, 3, 4, 5], 3)); // 0
console.log(remainderSum([10, 20, 30], 5)); // 0
console.log(remainderSum([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 7)); // 3
console.log(remainderSum([15, 25, 35, 45, 55], 10)); // 5
console.log(remainderSum([1, 1, 1, 1, 1], 2)); // 1

Running the above test cases will help verify whether the results for each case are correct. If all results match expectations,
the code is successfully implemented.

Step 5: Optimization and Additional Considerations

The above implementation is simply written to sum all elements of the given array.
However, if the size of the array can be very large, it may be necessary to consider performance factors.
In such cases, optimization can be achieved by calculating the remainders during the summation process itself. 

function optimizedRemainderSum(arr, m) {
    let remainder = 0;
    for (const value of arr) {
        remainder = (remainder + value) % m;
    }
    return remainder;
}

Here, the optimizedRemainderSum function stores intermediate results by calculating the remainder at each step,
thus calculating the final result in a much more efficient manner.

Conclusion

In this lesson, we covered the “Calculating Remainder Sum” problem. It’s a common problem of summing the elements of an array and finding their remainder,
but we also considered ways to optimize the algorithm.
I hope you found useful tips for preparing for coding tests using JavaScript.