findHappyNumbersRange()

Step 1: Understanding the Problem

We are trying to write a function called findHappyNumbersRange. This function should find all the "happy numbers" within a given range.

A happy number is defined by the following process: starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends are happy numbers.

Let's start by creating a helper function, isHappyNumber, that can determine if a single number is happy.

function isHappyNumber(num) {
  var m, digit ;
  var cycle = [] ;
  
  while(num != 1 && cycle[num] !== true) {
    cycle[num] = true ;
    m = 0 ;
    while (num > 0) {
      digit = num % 10 ;
      m += digit * digit ;
      num = (num  - digit) / 10 ;
    }
    num = m ;
  }
  
  return (num == 1) ;
}

This function keeps replacing the number with the sum of the square of its digits until the number becomes 1 (which means it is a happy number) or it starts to repeat (which means it will never become 1).

Step 2: Extending the Solution

Now we know how to check if a single number is a happy number. We need to extend this approach to a range of numbers. Let's create a function, findHappyNumbersRange, which takes in a start and an end and checks each number to see if it is a happy number.

function findHappyNumbersRange(start, end) {
  var happyNumbers = [];
  
  for (var i = start; i <= end; i++) {
    if (isHappyNumber(i)) {
      happyNumbers.push(i);
    }
  }
  
  return happyNumbers;
}

This function initializes an empty array, happyNumbers. It then loops from the start to the end, checks if each number is a happy number, and if it is, it adds it to the array. Finally, it returns the array of happy numbers.

Step 3: Testing the function

Next, we need to test our function to make sure it works as expected. We can do this by calling the function with a range and logging the result.

console.log(findHappyNumbersRange(1, 100));

This code should output all the happy numbers between 1 and 100.

Step 4: Optimizing the function

Our function works, but it might be a bit slow if we are checking a large range because for every number we are checking if it is a happy number from scratch. We could speed up our function by remembering which numbers are happy numbers. Once we have calculated if a number is a happy number, we can store this information and look it up later if we need to check this number again.

However, for the current basic version of the function, this optimization is not mandatory.

Conclusion

Through steps, we managed to implement the function findHappyNumberRange. The function takes two numbers as arguments representing the start and end of a range and returns an array with all the happy numbers within this range. The helper function isHappyNumber is used to check if a single number is a happy number.

The final implementation is:

function isHappyNumber(num) {
  var m, digit ;
  var cycle = [] ;
  
  while(num != 1 && cycle[num] !== true) {
    cycle[num] = true ;
    m = 0 ;
    while (num > 0) {
      digit = num % 10 ;
      m += digit * digit ;
      num = (num  - digit) / 10 ;
    }
    num = m ;
  }
  
  return (num == 1) ;
}


function findHappyNumbersRange(start, end) {
  var happyNumbers = [];
  
  for (var i = start; i <= end; i++) {
    if (isHappyNumber(i)) {
      happyNumbers.push(i);
    }
  }
  
  return happyNumbers;
}

That's it! You now know how to find a range of happy numbers in JavaScript.